Magnetic Domain Walls Driven by Interfacial
Phenomena
by
Satoru Emori
Submitted to the Department of Materials Science and Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Materials Science and Engineering MASSAEnIr
at the
MAY 14 2014
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
UBRARIES
October 2013
© Massachusetts Institute of Technolo'y 2013. All rights reserved.
A u th o r ...........
..............................................
Department of Materials Science and Engineering
October 25, 2013
Certified by....
..
.....
Geoffrey S. D. Beach
Associate Professor
Thesis Supervisor
A ccepted by ......................
''
erbrand Ceder
Chairman, Department Committee on Graduate Theses
E
2
Magnetic Domain Walls Driven by Interfacial Phenomena
by
Satoru Emori
Submitted to the Department of Materials Science and Engineering
on October 25, 2013, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Materials Science and Engineering
Abstract
A domain wall in a ferromagnetic material is a boundary between differently magnetized regions, and its motion provides a convenient scheme to control the magnetization state of the material. Domain walls can be confined and moved along nanostrips
of magnetic thin films, which are proposed platforms for next generations of solidstate magnetic memory-storage and logic devices. In these devices, domain walls must
be moved by electric current, rather than by magnetic field, to achieve scalability and
lower-power operation. Recent studies have reported efficient domain-wall motion
driven by current in out-of-plane magnetized multilayer films with strong spin-orbit
coupling. In particular, extraordinary current-driven domain-wall motion has been
observed in atomically-thin ferromagnets sandwiched between a nonmagnetic heavy
metal and an insulator. Through experimental studies on various sputtered magnetic
multilayers, we elucidate the mechanism of such anomalous domain-wall dynamics.
We show that conventional current-induced spin-transfer torques, which drive domain walls in thicker films, are negligible in ultrathin ferromagnets. We also show
that the Rashba field, often reported in materials with strong spin-orbit coupling,
does not contribute to the observed efficient domain-wall motion. The anomalous
dynamics instead emerges from the spin Hall effect: a charge current in the nonmagnetic heavy metal generates a spin current, which exerts a torque on spins in
the adjacent ferromagnet. This spin Hall torque drives domain walls forward if the
domain-wall spins are parallel to the nanostrip axis with a fixed chirality. We reveal that the Dzyaloshinskii-Moriya interaction, arising from spin-orbit coupling and
asymmetric interfaces, stabilizes homochiral domain walls in ultrathin ferromagnets.
Our findings not only provide a route to bolster current-driven domain-wall dynamics,
but also enable new chiral magnetic textures in magnetic heterostructures for device
applications.
Thesis Supervisor: Geoffrey S. D. Beach
Title: Associate Professor
3
4
Acknowledgments
This thesis is a compilation of countless hours of hard work - not just by me, but
also by others who have done a great deal to help me with various parts of the Ph.D.
curriculum and laboratory research.
First, I would like to thank my thesis advisor, Prof. Geoff Beach. I started out with
no background in magnetic materials, and I'm grateful for his patience in mentoring
me step by step for the past five years. I've enjoyed the great opportunity to work
with Geoff from launching the lab (from nearly no infrastructure) to discovering new
phenomena at the forefront of domain-wall spintronics. I'm very thankful for the
amount of time and energy that he has spent in helping me think through problems,
improve my writing and presentations, and even set up and trouble-shoot experiments
in the lab.
Secondly, this thesis work would not have been possible without the help of David
Bono.
He is a fantastic engineer and has helped me tremendously in setting up
electronics for many instruments essential for my thesis work. If it weren't for his
help, my research would have progressed much, much more slowly, and some of the
essential experiments might have been impossible.
I thank Profs. Caroline Ross and Silvija Gradeeak on my thesis committee for
their helpful feedback on the context of my research.
I also thank Prof. Regina
Ragan, my undergraduate research advisor at UC Irvine, for her mentoring.
I have been very lucky to work with skillful and fun people in the Beach lab.
Special thanks to Liz Rapoport for filling our workplace with high-volume joy and
keeping the lab in order, and Uwe Bauer for machining essential experimental setups
and helping me keep things in perspective during crunch times. I thank Tristan
Delaney for helping me get started with micromagnetic simulations; CK Umachi
for conducting temperature-dependent VSM measurements in Chap. 4; Dr. SungMin Ahn for developing and depositing films used in Chaps. 6 and 7; and Parnika
Agrawal for helping set up the large electromagnet system used in Chap. 7. I extend
my thanks to Jonathan Fischer, Dr. Helia Jalili, Helmut Koerner, Dan Montana,
5
Stephen Salinas, and Greg Steinbrecher for their help in setting up our lab in the first
couple of years; and the more recent members, Seong-Hoon Woo and Min-Ae Ouk,
and visitors, Jordan Chesin, Elie Nadal, and Nick Whiteway, Yaxin Wang, Zhiyong
Zhong, and Alex Lellouche for their great camaraderie.
I would like to acknowledge a few researchers from other laboratories for their
help. Special thanks to Prof. Eduardo Martinez from the University of Salamanca for
conducting a great deal of one-dimensional and micromagnetic simulations of domainwall dynamics in Chaps. 6 and 7. My thanks also go to Dr. Chunghee Nam and Mark
Mascaro from Prof. Ross's group for helping me get started in submicron fabrication;
and to Dr. Sam Bowden (NIST), Jean Anne Currivan (MIT, Ross group), Rebecca
Thomas (NCSU), and Kohei Ueda (Univ. of Kyoto) for stimulating discussions and
ideas.
I've relied heavily on shared experimental facilities at MIT for various parts of
sample fabrication and calibration. I owe my thanks to Mark Mondol (Scanning
Electron-Beam Lithography at RLE); Jim Daley (NanoStructures Laboratory); Dr.
Scott Speakman, Libby Shaw, and Shiahn Chen (Center for Materials Science and
Engineering); and Mike Tarkanian (Department of Materials Science and Engineering). My thanks also go to Angelita Mireles and Elissa Haverty for looking after the
financial and social well-being of the entire DMSE grad student community.
Grad school can be grueling sometimes, and I've been very fortunate to have
supportive friends and family. I give special thanks to Ahmed Al-Obeidi and Charles
Sing, my best friends in grad school and apartment-mates, for all the good times and
brotherly support. I also thank my family for helping me grow as a person and a
professional, and supporting my endeavor the last five years from the other side of
the continent and planet. I'm especially grateful to my parents and grandparents for
their love and for showing me the importance of systematic hard work.
Lastly, I'm incredibly lucky to be married to my lovely wife, Meg. Her unwavering
love and care for me have helped me through the toughest stretches of grad school.
I'm looking forward to spending many years growing together with her.
6
I acknowledge the financial support from the Nicholas J Grant Graduate Fellowship,
National Science Foundation Graduate Research Fellowship, and the National Science
Foundation Award number NSF-ECCS -1128439.
7
8
Contents
1
Introduction
19
1.1
Brief Introduction to Ferromagnetism
19
1.2
Domain Walls ................
23
1.3
Domain-Wall Devices . . . . . . . . .
28
1.4
Scope of this Thesis . . . . . . . . . .
31
35
2 Primer to Domain-Wall Dynamics
3
2.1
Field-Driven Domain-Wall Dynamics .............
. . . . .
35
2.2
Spin Polarization of Current . . . . . . . . . . . . . . . . . . . . . . .
41
2.3
Adiabatic Spin-Transfer Torque . . . . . . . . . . . . . . . . . . . . .
43
2.4
Nonadiabatic Spin-Transfer Torque . . . . . . . . . . . . . . . . . . .
47
2.5
Limits of Conventional Magnetic Thin Films . . . . . . . . . . . . . .
50
2.6
Out-of-Plane Magnetized Thin Films . . . . . . . . . . . . . . . . . .
51
2.7
Anomalous Domain-Wall Dynamics and Spin-Orbit Torques
. . . . .
55
2.8
Summary of Current-Induced Spin Torques . . . . . . . . . . . . . . .
62
75
Experimental Methods
3.1
Deposition and Characterization of Thin Films.
. . . . . . . . . . .
75
3.2
Measurements of Magnetic Hysteresis Loops . . . . . . . . . . . . . .
78
3.3
3.2.1
Vibrating Sample Magnetometry
. . . . . . . . . . . . . . . .
80
3.2.2
Magneto-Optical Kerr Effect . . . . . . . . . . . . . . . . . . .
81
3.2.3
Magnetic Properties of Co/Pt Multilayers
. . . . . . . . . . .
83
. . . . . . . . . . . . . . . . . . . . . .
87
Submicron-Scale Lithography
9
4
5
6
3.4
Time-Resolved Scanning Magneto-Optical Kerr Effect Setup.....
89
3.5
Measurements of Domain-Wall Dynamics in Nanostrips . . . . . . . .
93
3.6
Sum m ary
98
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermally Activated Domain-Wall Motion in Co/Pt Multil U'yers
101
4.1
Thermally Activated Domain-Wall Dynamics.
. . .
102
4.2
Experimental Methods . . . . . . . . . . . . .
. . .
104
4.3
Field-Driven Domain-Wall Motion . . . . . . .
. . .
105
4.4
Generalized Arrhenius-Like Relation
. . . . .
..
109
4.5
Current-Induced Effects
. . . . . . . . . . . .
...
111
4.6
Origin of Current-Induced Torques in Co/Pt .
. . .
114
4.7
Nonlinear Current-Induced Effects . . . . . . .
. . .
116
4.8
Sum m ary
..
117
. . . . . . . . . . . . . . . . . . . .
.
.
Current-Driven Domain Wall Dynamics in Pt/Co/GdOx
125
5.1
Expected Strong Rashba Effect in Pt/Co/GdOx . . . . . . . . . . . .
125
5.2
Experimental Details of Pt/Co/GdOx Films and Measurements
. . .
127
5.3
Spin-Torque Efficiency in the Thermally Activated Regime . . . . . .
128
5.4
Assessment of Rashba Field Effects . . . . . . . . . . . . . . . . . . .
132
5.5
High-Speed Domain-Wall Dynamics . . . . . . . . . . . . . . . . . . .
135
5.6
Sum m ary
139
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spin-Orbit Torques from Nonmagnetic Heavy-Metals
145
6.1
Pt- and Ta-Based Ultrathin-Ferromagnet/Oxide Structures . . . .
146
6.2
Heavy-Metal Dependence of Current-Driven Domain Wall Motion
147
6.3
Current-Induced Switching of Uniform Magnetization . . . . . . .
153
6.4
Heavy-Metal Dependence of Current-Induced Torques . . . . . . .
155
6.5
Spin-Hall-Effect-Driven Domain Walls
. . . . . . . . . . . . . . .
157
6.6
Homochiral Domain Walls . . . . . . . . . . . . . . . . . . . . . .
160
6.7
Sum m ary
161
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
7
Statics and Dynamics of Chiral Dzyaloshinskii Domain Walls
7.1
Domain-Wall Motion Assisted by the Spin Hall Effect ............
168
7.2
Quantitative Analysis of Chiral Domain Walls .............
174
7.3
7.4
8
167
174
..........................
7.2.1
Spin Hall Angle ......
7.2.2
Dzyaloshinskii-Moriya Interaction in the Weak Limit
. . . . .
175
7.2.3
Dzyaloshinskii-Moriya Interaction in the Strong Limit . . . . .
178
Dynamics of Chiral Domain Walls under Weak and Strong DzyaloshinskiiM oriya Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183
Sum m ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
186
Conclusions and Outlook
193
8.1
Summary of this Thesis
. . . . . . . . . . . . . . . . . . . . . . . . . 193
8.2
Outlook on Future Developments
. . . . . . . . . . . . . . . . . . . . 196
8.2.1
Towards Viable Domain-Wall Devices . . . . . . . . . . . . . . 196
8.2.2
Implications of the Spin Hall Effect . . . . . . . . . . . . . . . 198
8.2.3
Engineering Chiral Magnetism . . . . . . . . . . . . . . . . . . 200
11
12
List of Figures
. . . . . . . . . . . . . . . . . . .
21
. . . . . . . . . . . . . .
21
1-3
Uniaxial anisotropy in a magnetic material . . . . . . . . . . . . . . .
23
1-4
Formation of a domain wall. . . . . . . . . . . . . . . . . . . . . . . .
24
1-5
Domain-wall motion with and without defects. . . . . . . . . . . . . .
24
1-6
Domain-wall configurations in in-plane magnetized thin films. ....
26
1-7
Domain-wall configurations in out-of-plane magnetized thin films.
1-8
Chiralities of Neel domain walls. . . . . . . . . . . . . . . . . . . . . .
28
1-9
Magnetization switching due to domain-wall motion.
. . . . . . . . .
29
1-10 Illustrations of domain-wall devices. . . . . . . . . . . . . . . . . . . .
30
1-11 Comparison of field- and current-controlled domain-wall devices. . . .
31
2-1
Field-driven domain-wall dynamics. . . . . . . . . . . . . . . . . . . .
37
2-2
Mobility curves of field-driven domain walls in permalloy nanostrips. .
38
2-3
Precessional motion of a domain wall in a permalloy nanostrip. . . . .
39
2-4
Precessional motion of a domain wall in an out-of-plane magnetized
1-1
Exchange interaction among spins.
1-2
Magnetostatics in a ferromagnetic material.
nanostrip.
.
27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
2-5
Conduction electron spins in normal and magnetic metals.
. . . . . .
42
2-6
Schematic of the electronic band structure of a metal ferromagnet. . .
42
2-7
Illustration of domain-wall motion by adiabatic spin-transfer torque.
45
2-8
Domain-wall dynamics driven by adiabatic spin-transfer torque.
. .
46
2-9
Domain-wall dynamics driven by nonadiabatic spin-transfer torque.
13
48
2-10 Mobility curves of domain walls driven by current, with adiabatic and
nonadiabatic spin-transfer torques.
. . . . . . . . . . . . . . . . . . .
49
2-11 Critical domain-wall velocity for precessional dynamics versus perpendicular magnetic anisotropy. . . . . . . . . . . . . . . . . . . . . . . .
53
2-12 Schematic of the Rashba effect in an asymmetric ultrathin magnetic
multilayer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-13 Slonczewski-like torque from the Rashba effect.
56
. . . . . . . . . . . .
59
2-14 Slonczewski-like torque from the spin Hall effect. . . . . . . . . . . . .
59
2-15 Domain-wall motion due to the spin Hall effect in Pt/Co/Pt. . . . . .
61
2-16 Current-driven domain wall mobilities due to conventional spin-transfer
torque and spin-orbit torque . . . . . . . . . . . . . . . . . . . . . . .
63
3-1
Interior of the high-vacuum magnetron sputterer.
76
3-2
X-ray diffraction spectra of Pt/(Co/Pt) 3 multilayers deposited on dif-
. . . . . . . . . . .
ferent buffer layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
3-3
Magnetic hysteresis loops and key parameters. . . . . . . . . . . . . .
80
3-4
Physics of the magneto-optical Kerr effect. . . . . . . . . . . . . . . .
82
3-5
Geometries of magneto-optical Kerr effect measurements. . . . . . . .
83
3-6
Hysteresis loops of Co/Pt multilayers with different Co thicknesses. .
85
3-7
Co-layer thickness dependence of magnetic properties of Co/Pt multilayers.
3-8
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Procedure to fabricate magnetic nanostrip devices using electron-beam
lithography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-9
86
88
Scanning electron micrographs of lithographically patterned nanostrips. 89
3-10 Schematic of the scanning magneto-optical Kerr effect system. ....
91
3-11 Experimental scheme for measuring domain-wall motion. . . . . . . .
94
3-12 Stochastic nature of thermally activated domain-wall motion . . . . .
95
3-13 Averaged reversal transients in the thermally activated and flow regimes. 96
3-14 Field-driven domain-wall mobility in a Co/Pt multilayer nanostrip.
4-1
.
97
Regimes of thermally activated domain-wall motion. . . . . . . . . . .
103
14
4-2
Examples of averaged MOKE transients. . . . . . . . . . . . . . . . . 105
4-3
Field-driven domain-wall velocities in Co/Pt multilayers. . . . . . . .
106
4-4
Activation energy for field-driven domain-wall motion.
107
4-5
Failure of the assumption of a constant pre-exponential v..
. . . . .
109
4-6
Saturation magnetization as a function of temperature. . . . . . . . .
110
4-7
Domain-wall velocity and activation energy versus current density. . .
113
5-1
Experimental scheme for measuring current-assisted domain-wall mo-
. . . . . . . .
tion in Pt/Co/GdOx. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
Thermally activated domain-wall motion in Pt/Co/GdOx driven by
field and current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-3
134
Equivalence of high-speed domain-wall motion driven by field and current. ........
5-6
133
Quantification of current-induced magnetization tilting and reduction
of saturation magnetization. . . . . . . . . . . . . . . . . . . . . . . .
5-5
130
Experimental scheme for measuring current-induced magnetization tilting in Pt/Co/GdOx. . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-4
129
....................................
136
Calculated current-driven domain-wall mobility with and without the
Rashba field in a rough nanostrip. . . . . . . . . . . . . . . . . . . . .
137
6-1
Experimental scheme for measuring domain-wall propagation field. . .
147
6-2
Effect of current on domain-wall motion in Pt- and Ta-based ultrathin
ferromagnets (Pt/CoFe/MgO and Ta/CoFe/MgO).
. . . . . . . . . .
149
6-3
Current-induced domain-wall motion independent of magnetization sense. 150
6-4
Experimental scheme for measuring domain-wall velocity. . . . . . . .
6-5
Domain-wall velocity at higher electron current densities in Pt/CoFe/MgO
and Ta/CoFe/M gO . . . . . . . . . . . . . . . . . . . . . . . . . . . .
151
152
6-6
Current-induced switching under a constant in-plane longitudinal field. 154
6-7
Current-induced effective fields from the Slonczewski-like and field-like
torques. .......
6-8
.......
.............
.. . ......
..
Current-driven dynamics of homochiral Neel domain walls. . . . . . .
15
156
159
7-1
Experimental scheme to measure current-assisted DW motion. .. ..
7-2
In-plane-field dependence of domain-wall motion driven by the spin
169
H all effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170
7-3
Domain-wall orientation under in-plane fields in Ta/CoFe/MgO.
.
172
7-4
Domain-wall orientation under in-plane fields in Pt/CoFe/MgO.
.
173
7-5
Spin structure of left-handed Nel domain walls.
. . . . . . . . . . . .
175
7-6
Rotation of the DW moment parameterized by angle 'b. . . . . . . . .
176
7-7
Rotation of the DW moment under weak DMI and strong DMI. . . . 179
7-8
Definitions of the two angles to parameterize DW moment rotation in
the m acrospin model. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-9
180
Micromagnetically computed rotation of the DW moment under strong
D M I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18 1
7-10 Current-driven dynamics of Dzyaloshinskii domain walls. . . . . . . .
184
7-11 Micromagnetically computed domain-wall line tilting driven by spinH all torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
186
8-1
Current-induced domain-wall motion in Pt/Co/Pt and Pt/Co/GdOx.
194
8-2
Current-induced domain-wall motion in Pt- and Ta-based ultrathin
ferrom agnets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-3
Two key interfacial spin-orbit effects - spin Hall effect and DzyaloshinskiiM oriya interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-4
195
195
Nanostrip device with a magneto-ionic domain-wall trap controlled by
gate voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
197
8-5
Geometries of the conventional spin-transfer torque and spin Hall effect. 199
8-6
Cross section of interfaces. . . . . . . . . . . . . . . . . . . . . . . . . 201
8-7
Skyrmions driven by current . . . . . . . . . . . . . . . . . . . . . . . 202
16
List of Tables
2.1
Comparison of in-plane and out-of-plane magnetized thin-film nanostrips. 52
4.1
Parameters in the generalized Arrhenius-like equation (Eq. 4.4) to
quantify effects of current on DW motion . . . . . . . . . . . . . . . .111
17
18
Chapter 1
Introduction
Domain walls in ferromagnetic materials are boundaries separating regions that are
magnetized differently. Physics of domain walls often governs the operation of magnetic devices, e.g. switching between "0" and "1" digital states, and shifting of information bits. Applying a magnetic field has been the traditionalway to control domain
walls, but manipulating domain walls with electric current has become increasingly
important to improve the performance of magnetic devices. This chapter introduces
the basic physics of domain walls and motivates the study of domain walls for a new
generation of solid-state devices. This chapter also presents a brief outline of this thesis, whose main aim is to understand phenomena leading to efficient current-driven
domain-wall dynamics.
1.1
Brief Introduction to Ferromagnetism
Magnetism of materials arises from the quantized magnetic moments - or "spins"1
-
of electrons. Spins in most materials orient in random directions in the absence
of an external magnetic field. However, spins in some materials align in the same
direction even without an external magnetic field. These materials with magnetic
moments spontaneously ordered in the same direction are called ferromagnetic ma'In this thesis, we use the words "magnetic moments" and "spins" interchangeably. However,
"magnetic moments" are inherent to materials, whereas "spins" may refer to those inherent "magnetic moments" in materials but may also refer to spins in currents flowing through materials.
19
terials. The saturation magnetization M, of a ferromagnetic materials quantifies the
maximum magnetization (per unit volume or mass) that can be attained in the material. In a ferromagnet, increasing temperature decreases Ms, and the ordering of
spins (M, > 0) is retained up to the Curie temperature TC, above which thermal
fluctuations randomize the spin orientation (M, = 0). For practical applications,
we typically want solids with TC > 300 K, which is satisfied by 3d transition metals
(Fe, Co, and Ni) and a wide variety of their alloys.
Although we use ferromagnetic materials in everyday life from refrigerator magnets
to state-of-the-art sensors, ferromagnetism cannot be explained by classical physics.
Instead, ferromagnetism relies on an inherently quantum mechanical phenomenon
called exchange.2 In the presence of ferromagnetic exchange, spins energetically prefer
to align in the same direction (Fig. 1-1). The exchange energy per unit volume is
Eex =
(1.1)
where 0 is the misalignment angle between adjacent spins, x is the separation between
adjacent spins, and A is the exchange stiffness that incorporates the exchange constant
and the structure of the solid.
The exchange interaction does not specify all ordered spins to orient in any particular direction within a material. Instead, the geometric shape and the nano-scale
structure of the material determine the preferred orientation of those magnetic mo2
The net quantum mechanical state of two (or more) electrons must satisfy "exchange symmetry," such that the square modulus of the state remains the same if the electrons are exchanged.
Roughly speaking, ferromagnetic exchange arises from this exchange symmetry and Pauli's exclusion
principle, which requires that no two identical electrons must occupy the same quantum mechanical
state simultaneously. The quantum mechanical state can be specified by the electrons' positions
and spins. Two electrons with the same spin cannot occupy the same position, so they tend to
stay farther away from each other. Having two spins point in the same direction thus reduces the
electrostatic repulsion between the two electrons, and this saving of electrostatic potential energy is
the origin of ferromagnetism. In solids, however, the kinetic energy penalty (described by the band
structure picture) in having a large number of spins aligned in the same direction is greater than the
energy saving from exchange. This trade-off between exchange and kinetic energies is described by
Stoner's criterion. Blundell's Magnetism in Condensed Matter [1] contains an excellent introductory
description of the origin of exchange and Stoner's criterion.
20
x
x
x
x
Figure 1-1: Schematic of the ferromagnetic exchange interaction among spins. A
misalignment of spins 0 leads to an exchange energy penalty, as expressed in Eq. 1.1.
Figure 1-2: Schematic of the magnetostatic interaction. Free magnetic poles form
at the surfaces shaded in red, which generate a demagnetizing field and hence a
magnetostatic energy penalty, as expressed in Eq. 1.2.
ments. In other words, a ferromagnetic material is typically anisotropic, such that it
has an "easy axis" (along which the spins prefer to point) and a "hard axis" (along
which spins do not point, unless a very large external magnetic field is applied).
Depending on which way the magnetic moments (represented by the magnetization vector M) point within a material of a certain shape, different amounts of free
magnetic poles can result at surfaces, as illustrated by the areas shaded in red in
Fig. 1-2. These magnetic poles (or the divergence of the magnetization V -M) generate a stray field, 3 or demagnetizing field Hd, that raises the net energy of the material.
In other words, the demagnetizing field resists the orientation of the moments along
that particular direction. The energy per unit volume due to the demagnetizing
field,
also called the shape anisotropy energy or magnetostatic energy is
3
This stray field (demagnetizing field) must arise because there
can be no free magnetic
"monopoles," as indicated by Gauss's law for magnetism, V - B =
V - (H + 47rM) = 0 in CGS
units or V -B = V - po(H + M) = 0 in SI units. If there exists V - M 4 0, then there also must be
some resulting V -H = 0 to ensure that Gauss's law holds. See Blundell's Magnetism in Condensed
Matter [1].
21
1
2
Ems = -M
Hd.
(1.2)
Here, Hd is related to the magnetization M through
Hd = -NM,
where N is the demagnetizing tensor, i.e. (Hd)
(1.3)
-
N M. Calculating N for an
arbitrary sample shape is not trivial, but N for some common geometries can be found
in literature, e.g. [2] for rectangular prisms that well represent patterned strips of thin
films. Qualitatively, the magnetostatic interaction can be understood from Fig. 1-2:
it is energetically favorable for magnetic moments to point along the longest axis of a
sample, so that the samples has minimal free poles and demagnetizing field. Because
of magnetostatics, magnetic moments tend to lie within the plane of a magnetic thin
film.
The atomic-scale structure of a sample - e.g. crystal structure, bonding of dissimilar atoms - is often a dominant source of magnetic anisotropy. The relationship
between structure and magnetization fundamentally arises from spin-orbit coupling,
which can be considered as a built-in effective field in a material depending on the
profiles of orbitals constituting the solid. Phenomenologically, magnetic moments in
a crystal solid may preferentially orient along a particular crystallographic axis, e.g.
(111) in FCC Co, in which case the anisotropy is referred to as "magnetocrystalline."
It is also possible to engineer "interfacial" anisotropy by interfacing ultrathin-film
layers of different materials, e.g. multilayers of Co/Pt. The energy per unit volume
in the simplest case with one easy axis (uniaxial anisotropy) is
Ean = K sin 2 0,
22
(1.4)
I
,
Figure 1-3: Schematic of uniaxial aniosotropy. The blue disks schematically represent
atomic orbitals constituting a crystallographic plane. The magnetization prefers to
align along the axis (dotted line) set by the crystallographic structure in the material.
A misalignment 0 from the easy-axis results in an anisotropy energy penalty (Eq. 1.4).
where 0 is the deviation of the magnetization from the easy axis (Fig. 1-3, and K is
the uniaxial anisotropy constant. Generally, the anisotropy energy is larger in crystals
of lower symmetry.
Strains in a material alter its structure and hence the atomic orbitals, so magnetization may also couple strongly to strains through spin-orbit coupling. This
"'magneto-elastic" interaction is often significant in thin films deposited on substrates
with different lattice parameters, and is well documented e.g. in ferromagnetic semiconductors on GaAs substrates [3]. Although the magneto-elastic interaction is also
likely significant in multilayers of ultrathin films investigated in this thesis, it is outside the scope of most studies presented here.
1.2
Domain Walls
Ferromagnetic materials contain groups of magnetic moments aligned in the same direction even in the absence of an external magnetic field. However, not all magnetic
moments necessarily align in the same direction in a macroscopic piece of ferromagnet. For instance, a ferromagnetic material may be demagnetized such that its net
magnetization is small or zero. In a demagnetized material, there are regions, called
magnetic domains, within which all magnetic moments are aligned, but these domains
23
(a)
(b)
I)
Bloch domain wall
Neel domain wall
Figure 1-4: (a) Schematic of a uniformly magnetized piece of material, exhibiting
a large stray field. (b) Schematic of a demagnetized (two-domain) material with a
domain wall in the middle, exhibiting a smaller stray field than (a) due to magnetic
flux closure. Two possible internal configurations of the domain wall are also shown.
(a)
(H off)
(b)
(H off)
Figure 1-5: (a) Domain-wall motion in a perfect magnetic material. (b) Domain-wall
motion and pinning in a magnetic material with defects (black notches).
combined lead to a net zero magnetization for the entire material (Fig. 1-4(b)). A
boundary separating adjacent domains are called a domain wall.
Domain walls (DWs) have a finite width, with the magnetic moments rotating
gradually to bridge between the moments in the two domains. Forming a DW costs
a finite amount of energy, because the moments within the DW do not align perfectly parallel with respect to each other (costing exchange energy) and deviate from
24
the preferred axis of magnetization orientation of the material (costing anisotropy
energy).
For example, the energy per unit area
c-BDW
of a simple Bloch DW is a
function of the exchange stiffness A and the uniaxial anisotropy constant K:
'BDW =r
AK.
(1.5)
Nevertheless, DWs often form spontaneously in ferromagnetic materials, because completely magnetizing the material in one direction can cost magnetostatic energy, which
arises from the large stray magnetic field from the material's free surfaces (Fig. 14(a)).
In other words, to reduce the stray field, ferromagnets may develop many
domains separated by DWs (e.g. Fig. 1-4(b)). This is why specially engineered materials 4 are required to make permanent magnets, which remain uniformly magnetized
without developing many domains oriented in different directions. The spontaneous
formation of DWs is also why a piece of ferromagnetic material (e.g. a paper clip) is
not necessarily a permanent magnet.
However, it is possible to magnetize the ferromagnet by applying a magnetic
field, which causes domains magnetized parallel to the field to grow and domains
magnetized opposite to the field to shrink 5 . This evolution of domains occurs through
motion of DWs (Fig. 1-5). When the external field is removed, DWs may move back to
their original positions and the ferromagnet is back to having domains of equal size, i.e.
the magnetostatic equilibrium, if the material is free of defects (Fig. 1-5(a)). In real
materials, DWs may be pinned (trapped) even after the field is removed ((Fig. 1-5(b)).
Such DW pinning occurs at defects, which act as local potential energy minima for the
DW. Common DW pinning sites can arise from intrinsic material defects (e.g. grain
boundaries, voids, roughness) or be engineered through sample shape (e.g. notches,
kinks) or local modification of material properties (e.g. ion irradiation). DWs are
4
for example, by attaining strong uniaxial anisotropy
5The tendency for magnetic moments tend to align with magnetic field is explained by the
reduction in the "Zeeman energy." Note that the equilibrium orientation of magnetic moments is
attained by minimizing the net energy, which may include the Zeeman energy, magnetostatic energy,
exchange energy, and anisotropy energy, to name a few.
25
transverse wall
vortex wall
~1'
10
5.
0I.
0
50
100
150 20
250 30
350 400 450 500
strip width w(nm)
Figure 1-6: Domain-wall configurations in in-plane magnetized thin-films strips of
permalloy (NisoFe 2O). The spin configurations were calculated using the OOMMF
micromagnetic simulation package. The phase diagram shows the range of strip
thickness and width within which the two wall configurations are stable, calculated
by micromagnetic simulations in [4].
therefore objects that can be controlled: they can be moved by magnetic field and
trapped by defects.
The configuration of a DW is determined by the combined effects of exchange,
magnetostatics, and anisotropy (from the material's atomic-scale structure). We show
possible DW configurations in magnetic thin films patterned into nanostrips in Figs. 16 and 1-7. Permalloy (NisoFe 2 0) is an extensively studied material, in which the DW
configuration is governed almost entirely by exchange and magnetostatics (shape
anisotropy).6
As such, magnetic moments in domains in permalloy nanostrips lie
within the film plane and orient along the long axis (Fig. 1-6). Thin, narrow permalloy
strips at equilibrium, i.e. under no external fields, exhibit simple Noel DWs that are
commonly called "transverse" DWs. Thicker and wider strips exhibit more complex
"vortex" DWs, in which magnetic moments curl around a nm-scale core with outof-plane magnetization.'
In both cases, the DW width in permalloy (and in-plane
6
1n other words, permalloy exhibits very little inherent magnetic anisotropy.
Although the out-of-plane magnetized core incurs a large magnetostatic energy penalty, the
curling of magnetic moments in the vortex DW saves magnetostatic energy by minimizing free poles
7
26
Bloch wall
N6el wall
Figure 1-7: Domain-wall configurations in out-of-plane magnetized thin-films strips.
The spin configurations were calculated using the OOMMF micromagnetic simulation
package. The illustrations below show the free magnetic poles formed in each type of
domain wall.
magnetized thin films in general) is on the order of the strip width ~100 nm.
In the presence of strong out-of-plane uniaxial anisotropy (perpendicular magnetic anisotropy) [5], a thin film is out-of-plane magnetized.
DWs in out-of-plane
magnetized thin films are narrow (< 10 nm wide) and take on simple Bloch or Neel
configurations (Figs. 1-4 and 1-7). These DWs can be approximately thought of as
rectangular prisms, as illustrated by the dotted lines in Fig. 1-7. Bloch DWs are magnetostatically preferred in most out-of-plane magnetized nanostrips of width ;> 100
nm, so that free magnetic poles ("+" and "-" illustrated in Fig. 1-7) form only at the
ends of long axis of the "rectangular prism," i.e. the edges of the strip. According to
magnetostatics, N~el DWs form spontaneously only in narrow (< 100 nm) strips [6].
An experimental study by Koyama et al. [7] shows a transition between Bloch and
N6el DWs in nanostrips of Co/Ni multilayer thin films at width ~60 nm.
A special type of DWs can form in out-of-plane magnetized ultrathin multilayer
films with structural asymmetry. Specifically, an additional energy term (DzyaloshinskiiMoriya interaction) dominates over magnetostatics and stabilizes N~el DWs even in
wide nanostrips. Furthermore, these N~el DWs have a fixed handedness, or chirality
(Fig. 1-8), which does not emerge from the commonplace exchange, magnetostatic,
and anisotropy energy terms. The details of such homochiral Neel DWs stabilized by
at the strip's edges. The width of the strip has to be wide enough for this vortex to form, so that
there is enough space for moments to curl without large exchange energy penalty.
27
left-handed Nel wall
right-handed Neel wall
Figure 1-8: Chiralities of Neel domain walls.
the Dzyaloshinskii-Moriya interaction are in Chaps. 6 and 7.
1.3
Domain-Wall Devices
Ferromagnetic materials are used in many digital memory devices, such as hard drives
and, more recently, magnetic random access memory (MRAM). Most of such modern
memory devices consist of magnetic thin films, which are straightforward to deposit
on a variety of substrates. The digital information, bits of "0" and "1," are expressed
by the two distinct states of magnetization in the ferromagnet, "left" and "right" (or
"up" and "down"). Switching between these two states can be attained by moving a
DW as illustrated in Fig. 1-9. DW motion can be triggered by an external magnetic
field or electric current.
Typical commercial standards require that stored data remain stable for at least
-10 years against thermal fluctuations and stray magnetic fields, and a sufficiently
large energy barrier AE should prevent spontaneous switching. This stability requirement can be roughly modeled using an Arrhenius expression
I
= Fo exp
(kBT
)
(1.6)
where T = 10 years, To ~ 10-' s is the inverse of attempt frequency for DW dis-
placement, kB is the Boltzmann constant, and T is the temperature. The depth of
the potential energy well for DW pinning based on Eq. 1.6 is AE ~ 40kBT. The
requirement for commercial devices is more stringent at AE ~ 60kBT to minimize
bit error rate to <10-9. The information storage scheme based on DW motion can
28
V
domain
Figure 1-9: Magnetization switching due to domain-wall motion.
readily fulfill this requirement, because strong pinning sites can be engineered to trap
DWs, e.g. [8] and [9] showing AE > 60kBT. 8
DW motion therefore is a convenient way of manipulating the magnetization state
of a memory device.'
For instance, a thin-film heterostructure device with three
regions can be designed such that the magnetizations of the two end regions are
fixed1 0 and the middle region can be magnetized in either direction (Figs. 1-9 and
1-10(a)).
One DW always exists in such a structure, and the bit can be toggled
between "0" and "1" by simply moving the DW across the middle region (Fig. 19). NEC in Japan has proposed a DW-motion MRAM [8] based on this three-region
structure combined with a sensing element such as a magneto-tunnel junction (MTJ)
as illustrated in Fig. 1-10(a).
A large number of these MRAM structures can be
connected together to build a logic device [13].
Furthermore, multiple bits can be
accommodated in a narrow (~100 nm or less) and long (>pm) track of magnetic thin
film (Fig. 1-10(b)).
This "racetrack memory" device [14], proposed by IBM, may
attain an information storage density and manufacturing cost comparable to those
8AE is related to the "effective" magnetic field necessary to displace a DW out of the
pinning
site; this "effective" field includes an external magnetic field, thermal fluctuations, and some currentinduced effects that scale in the same way as external magnetic field. Of course, we still need to be
able to move DWs to rewrite stored data, and large AE ordinarily means that DW motion is more
difficult. Fortunately, it is possible to move DWs using a driving force that is insensitive to AE, e.g.
current-induced adiabatic spin-transfer torque [7, 8, 9, 10]. It is also possible to toggle the strength
of pinning, i.e. reduce AE only when stored information needs to be modified, through gate voltage
as shown in [11].
9
DWs, confined in patterned magnetic thin-film tracks, can also be used as carriers of biological
agents tagged to superparamagnetic microparticles [12]. In this case, DW motion is an essential part
of a "lab-on-a-chip" scheme, allowing for reliable high-speed sorting of biological agents.
' 0The magnetization in a ferromagnetic thin film can be effectively "fixed" by interfacing it with a
layer of "hard" ferromagnet with a significantly larger switching field, as done in [8]. Alternatively,
by interfacing a ferromagnetic thin film with an antiferromagnetic thin film, the magnetization in
the ferromagnet can be fixed in one one direction through a phenomenon called "exchange bias."
29
(a)
(b)
domain walls
Figure 1-10: Illustrations of domain-wall devices: (a) domain-wall motion magnetic
random access memory and (b) racetrack memory.
of conventional magnetic hard drives, while achieving speed, mechanical robustness,
and low power consumption similar to charge-based solid-state memory devices. The
operation of this device requires simultaneous, uniform shifting of multiple bits in the
same direction, so that magnetic bits can be read and written by the stationary read
and write elements. Physically, to shift all these bits uniformly, multiple DWs must
be moved at the same time.
The conventional way to move DWs is to apply an external magnetic field. Indeed,
a complete set of logic devices based on DWs driven by rotating magnetic field have
been demonstrated [15]. However, there are a few problems with using the fielddriven scheme for advanced devices. First of all, localizing a strong magnetic field
to a small confined area is difficult (Fig. 1-11(a)). As the devices are scaled down
and the density of devices per area increases, it becomes challenging to manipulate a
DW in one device while keeping DWs in the neighboring devices intact. Furthermore,
two adjacent DWs move in opposite directions under a uniform magnetic field (Fig.
1-11(c)), so devices requiring unidirectional motion of DWs, such as the racetrack
memory, are very difficult to implement with the field-driven scheme."
Fortunately, there exists an alternative means to drive DWs, if the magnetic
medium is a metal: an electric current can move DWs through spin-torque effects,
e.g. those described in Chap. 2. Spin torques are current-induced torques on magnetization from angular momentum transfer between quantum-mechanical spins, and
are fundamentally different from current-induced Amerpian (Oersted) fields based on
magnetic
"Multiple DWs in a curved track can be moved in the same direction using a rotating
uniform
a
using
field [12, 15]. DWs in any arbitrary shape can also be moved in the same direction
[16].
magnetic field if the track has a specially engineered anisotropy profile ("DW ratchet")
30
(a)
(c)
(b)
(d)
Figure 1-11: Comparison of field- and current-controlled domain-wall devices. Scalability of domain-wall devices controlled by (a) magnetic field and (b) electric current.
Motion of two adjacent domain walls driven by (c) magnetic field and (d) electric
current.
classical physics. By patterning electrical contacts to each device, DWs in select devices can be manipulated by current while other devices are left intact (Fig. 1-11(b)).
The driving force on DWs also scales with current density, rather than current itself.
These features make current-driven DW motion attractive for scaling down and increasing the areal density of devices. Moreover, multiple DWs driven by current can
move in the same direction in a uniform fashion, permitting shifting of bits without
destroying stored information (Fig. 1-11(d)).
1.4
Scope of this Thesis
The main aim of this thesis is to pinpoint a strong current-induced effect that enables highly efficient DW motion. In particular, we experimentally investigate DW
dynamics in nanostrips of out-of-plane magnetized multilayers, driven by both magnetic field and electric current, to reveal the magnitude, symmetry, and origin of
current-induced torques. This thesis is then organized as follows:
* Chapter 2 reviews different types of current-induced torques that have been
shown or theorized to drive DWs in thin-film nanostrips.
31
"
Chapter 3 describes key experimental techniques to fabricate and characterize
magnetic thin films and nanostrips.
" Chapter 4 reveals the lack of conventional spin-transfer torque effects in Co/Pt
multilayers through careful studies of thermally activated DW motion.
* Chapter 5 confirms a high spin-torque efficiency in an asymmetric multilayer of
Pt/Co/GdOx but that the Rashba field is likely absent.
" Chapter 6 reveals that spin-orbit torques in Pt- and Ta-based ultrathin ferromagnets are opposite in polarity and arise from the spin Hall effect, and that
DWs in these multilayers have a fixed chiral texture.
* Chapter 7 quantifies the interfacial Dzyaloshinskii-Moriya interaction stabilizing the homochiral DWs in the Pt- and Ta-based ultrathin ferromagnets, and
elucidates the unique dynamics of homochiral DWs.
* Chapter 8 summarizes the findings of this thesis and discusses possible directions
for future applications.
32
Bibliography
[1] Blundell, S. Magnetism in Condensed Matter (Oxford University Press, USA,
2001), 1 edn.
[2] Aharoni, A. Demagnetizing factors for rectangular ferromagnetic prisms. Journal
of Applied Physics 83, 3432 (1998).
[3] De Ranieri, E. et al. Piezoelectric control of the mobility of a domain wall driven
by adiabatic and non-adiabatic torques. Nature Materials 12, 808-814 (2013).
[4] Nakatani, Y., Thiaville, A. & Miltat, J. Head-to-head domain walls in soft nanostrips: a refined phase diagram. Journal of Magnetism and Magnetic Materials
290-291, 750-753 (2005).
[5] Johnson, M. T., Bloemen, P. J. H., Broeder, F. J. A. d. & Vries, J. J. d. Magnetic
anisotropy in metallic multilayers. Reports on Progress in Physics 59, 1409-1458
(1996).
[6] Jung, S.-W., Kim, W., Lee, T.-D., Lee, K.-J. & Lee, H.-W. Current-induced domain wall motion in a nanowire with perpendicular magnetic anisotropy. Applied
Physics Letters 92, 202508 (2008).
[7] Koyama, T. et al. Observation of the intrinsic pinning of a magnetic domain
wall in a ferromagnetic nanowire. Nature Materials 10, 194-197 (2011).
[8] Fukami, S. et al. Low-current perpendicular domain wall motion cell for scalable
high-speed MRAM. In VLSI Technology, 2009 Symposium on, 230 -231 (2009).
33
[9] Fukami, S., Suzuki, T., Nagahara, K., Ohshima, N. & Ishiwata, N. Large thermal stability independent of critical current of domain wall motion in Co/Ni
nanowires with step pinning sites.
Journal of Applied Physics 108, 113914
(2010).
[10] Kim, K.-J. et al. Two-barrier stability that allows low-power operation in currentinduced domain-wall motion. Nature Communications 4 (2013).
[11] Bauer, U., Emori, S. & Beach, G. S. D. Voltage-controlled domain wall traps in
ferromagnetic nanowires. Nature Nanotechnology 8, 411-416 (2013).
[12] Rapoport, E., Montana, D. & Beach, G. S. D. Integrated capture, transport, and
magneto-mechanical resonant sensing of superparamagnetic microbeads using
magnetic domain walls. Lab on a Chip 12, 4433-4440 (2012).
[13] Currivan, J., Jang, Y., Mascaro, M. D., Baldo, M. A. & Ross, C. A. Low Energy
Magnetic Domain Wall Logic in Short, Narrow, Ferromagnetic Wires. Magnetics
Letters, IEEE 3, 3000104 (2012).
[14] Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic Domain-Wall Racetrack
Memory. Science 320, 190 -194 (2008).
[15] Allwood, D. A. et al. Magnetic Domain-Wall Logic. Science 309, 1688 -1692
(2005).
[16] Franken, J. H., Swagten, H. J. M. & Koopmans, B. Shift registers based on
magnetic domain wall ratchets with perpendicular anisotropy. Nature Nanotechnology 7, 499-503 (2012).
34
Chapter 2
Primer to Domain-Wall Dynamics
Scalable, low-power solid-state magnetic devices rely on robust domain-wall motion
driven by electric current. Here, we review mechanisms of domain-wall motion. We
first introduce field-driven domain-dynamics and then devote most of this chapter to
current-drivendynamics. Each of the current-drivenmechanisms drives domain walls
through a transfer of angular momentum between electron spins from the current and
magnetic moments in the domain walls. Conventional "spin-transfertorques" arise
from a spin-polarized current within the bulk of the ferromagnet. By contrast, "spinorbit torques" emerge from spin-orbit coupling effects with a heavy element interfaced
with the
ferromagnet. Multilayered films
consisting of a ultrathin ferromagnet and a
heavy metal have been reported to exhibit especially efficient current-induced torques,
but the physics for these observationhas remained elusive. This review emphasizes the
need for investigating spin-orbit torques in interface-dominated materials, so that it
will be possible to engineer high-performance magnetic devices in a coherent manner.1
2.1
Field-Driven Domain-Wall Dynamics
One might expect domain-wall (DW) dynamics driven by magnetic field to be straightforward. A magnetic domain grows if it is magnetized in the same direction as an
'Chappert et al. provide an overview of "spintronic" devices in [1]. Articles by Ralph and
Stiles [2] and Brataas et al. [3] are general reviews of current-induced spin torques on magnetization.
35
external field, and an oppositely magnetized domain shrinks; the DW separating those
two domains then moves (as illustrated earlier in Fig. 1-5). One would also expect
the speed of the DW to scale monotonically with the field magnitude.
Although
we can trivially determine the net direction of DW motion from the field direction,
the actual field-driven dynamics of a DW turns out to be much more complex, because a magnetic field exerts a torque orthogonal to both the field and magnetization.
This torque then distorts the internal magnetic moment of the DW, which can then
generate other torques.
Magnetization dynamics is often modeled using the Landau-Lifshitz-Gilbert (LLG)
equation, which shows the time rate of change of the normalized magnetization vector 2 m = M/M, driven by different torque contributions:
am
at
=
-xylm
x Heff + am x am
at
(2.1)
where -y is the gyromagnetic ratio and a is the Gilbert damping parameter. The
first term on the right-hand side represents the net torque exerted by the "effective"
magnetic field Heff, which incorporates the influences of ferromagnetic exchange,
anisotropy, magnetostatics, etc. in the material, as well as externally applied magnetic
field. This field torque causes the magnetization to precess (rotate) about Heff. The
second term represents damping which brings the magnetization towards the direction
of Heff. The strength of damping is quantified by a.
Fig. 2-1 illustrates field-driven DW dynamics in in-plane and out-of-plane magnetized thin-film nanostrips, according to a simplified one-dimensional representation
of the LLG equation (Eq. 2.1). Here, we discuss DW dynamics in the in-plane magnetized case, such that the equilibrium DW configuration is transverse (Fig. 2-1(a)).
The torque from the applied field -1-ym x H lifts ("cants") the DW moment out
of the film plane. The out-of-plane component of the DW moment builds new free
2
The amplitude of each magnetic moment is assumed to be equal to the saturation magnetization
per unit volume, i.e. JM = M,. The LLG equation is valid for temperatures sufficiently below the
Curie temperature, such that the amplitude of IM = Mj is conserved. The normalized vector m
then represents the direction of the magnetization. Calculating magnetization dynamics near the
Curie temperature requires a different model, e.g. Landau-Lifshitz-Bloch equation.
36
H > HW
H < H.
(a)
-|yjm x H
H
amax
..
yIm x Hd
am X
-
Z
y
x
H > Hx
HH
(b)
-yim x H
am x a
tli~m
Hd
Figure 2-1: Field-driven domain-wall dynamics in an (a) in-plane magnetized thin
film and (b) out-of-plane magnetized thin film. The driving torque for below and
above the Walker-breakdown threshold Hw are shown.
magnetic poles at the film surfaces, generating a demagnetizing field Hd. Under a
sufficiently small applied field such that the DW moment does not cant beyond ' with
respect to the film plane, the demagnetizing field drives the DW forward through the
torque -17ym x Hd. If the applied field exceeds the threshold Hw (the "Walker field"
named after [4]), the DW moment no longer maintains a constant canting angle and
instead rotates (precesses) about the x-axis, as illustrated in the "H > Hw" case
of Fig. 2-1(a). In this high-field case, the damping torque am x a! drives the DW
forward.
Using the above simple one-dimensional description, the DW speed as a function
of field amplitude [5, 6] is characterized by the "mobility" parameter /t = 17|A/a,
where A is the DW width. The DW speed v scales linearly with the magnitude of
the applied field H for the sub-Walker threshold case (H < Hw),
v = pH.
37
(2.2)
(c)
(b)
(a)
250
150
2500
1500
200
Hw
4Hw
2000
15
E100
EE
5
S1000
A
A
100
50
500
0
0
0
0
100
200
H (Oe)
300
400
0
20
60
40
H (Oe)
80
100
0
20
40
H (Oe)
60
80
Figure 2-2: (a) Mobility curve for a 500 nm by 20 nm Permalloy wire, calculated
using the 1D model. (b) Mobility curve computed using LLG numerical simulations
for a 200 nmx20 nm Permalloy wire (line is a visual guide). (c) Measured mobility
curve for a 490 nmx20 nm Permalloy nanowire. Note different axis scales for each
figure. Adapted from [5].
Above the Walker threshold (H > Hw), the DW speed approaches
v -+ a2/pH.
(2.3)
3
Note that with o < 1, as is the case for most magnetic materials , the effective
field-driven DW mobility above the Walker threshold (Eq. 2.3) is smaller than that
for the sub-threshold regime (Eq. 2.4). Hw is therefore the threshold field beyond
which the DW mobility drops substantially [4], and this mobility decrease is commonly called "Walker breakdown." Such non-monotonic relationships between DW
speed and applied field are seen in the simple one-dimensional model (Fig. 2-2(a)), as
well as in two- (or three-) dimensional micromagnetic calculations (Fig. 2-2(b)) and
experimental results (Fig. 2-2(c) and [6]).
Because the Walker threshold marks the onset of the precession of the DW moment, Hw should be proportional to the energy barrier KDW to trigger DW precession, i.e. the energy barrier between the two extreme DW configurations. For
an in-plane magnetized nanostrip described by the one-dimensional model, the two
For in-plane magnetized thin films of permalloy, a ~ 0.02. Even in out-of-plane magnetized
Co/Pt-based multilayers whose damping is considered to be "strong," a is only ~ 0.3.
3
38
100 nm
antivortex core
Figure 2-3: Precessional motion of a domain wall in a permalloy nanostrip, simulated
using the OOMMF micromagnetic simulation package. The time interval between
adjacent snapshots is 2 ns.
configurations are (1) the DW moment lying within the film plane (m ~
the DW moment canted all the way to lie out of the film plane (m
-
y)
and (2)
i). The Walker
field derived from the one-dimensional model [5] is then
Hw =
a
KDW-
MS
(2.4)
The Walker fields obtained from experiments (Fig. 2-2(c)) and realistic micromagnetic
calculations (Fig. 2-2(b)) are about an order of magnitude smaller than the value predicted by the one-dimensional model (Fig. 2-2(a)). This large deviation indicates that
the energy barrier for triggering DW precession is considerably lower in real samples.
DW "precession" in an in-plane magnetized nanostrip actually occurs through the
periodic transition between transverse and "antivortex" configurations, as shown by
micromagnetic snapshots in Fig. 2-3. In other words, the energy barrier KDW arises
from the nucleation of an antivortex DW, which is energetically less costly than cant39
120 nm
Figure 2-4: Precessional motion of a domain wall in an out-of-plane magnetized
nanostrip, simulated using the OOMMF micromagnetic simulation package. The
time interval between adjacent snapshots is 2 ns.
ing all magnetic moments within a transverse DW. 4 These observations suggest that
one must be careful in using the one-dimensional model to analyze DW dynamics in
in-plane magnetized systems.
Field-driven DW dynamics in an out-of-plane magnetized nanostrip can be understood, similarly to the in-plane magnetized case, by referring to the one-dimensional
model as illustrated in Fig. 2-1(b). In this case, the DW moment cants and precesses
within the film plane, and full precession in the "H > Hw" regime occurs through
a periodic transformation between Bloch and Neel configurations.
Micromagnetic
calculations in Fig. 2-4 show qualitatively similar behavior. Although the DW moments do not rotate together to form a coherent Neel configuration in this case, DW
dynamics in out-of-plane magnetized nanostrips computed from the one-dimensional
model and micromagnetic simulations typically are in good quantitative agreement
with each other (see [8, 9] for example), in contrast with the enormous deviation for
4
1n wider in-plane magnetized nanostrips in which vortex DWs are stable at equilibrium, the
"'precession" process occurs through periodic annihilation and nucleation of vortex cores at the
nanostrip edges. See [7] for example.
40
in-plane magnetized nanostrips (Fig. 2-2).
In out-of-plane magnetized thin films, the energy barrier KDW for inducing full
precession is significantly less than the in-plane magnetized case. This is because
the magnetostatic energy penalty in canting the DW moment to a N6el configuration is less than the penalty for canting the moment perpendicularly an in-plane
magnetized film. Thus, assuming similar Gilbert damping parameters a, an out-ofplane magnetized film exhibits a smaller Hw and lower maximum DW speed than
its in-plane magnetized counterpart. 5 Although this may appear to be a disadvantage, the reduced energy barrier for precession actually becomes advantageous for
current-induced DW motion by adiabatic spin-transfer torque (see Secs. 2.3 and 2.6).
2.2
Spin Polarization of Current
As explained in Sec. 1.3, injecting current is a preferred method of manipulating
DWs in ferromagnetic material structures. It is well known from classical physics that
electric current generates magnetic field through Ampere's law. This classical currentinduced field, known as Amperian field or Oerted field, scales with the magnitude of
current and is typically weak in submicron-scale magnetic thin-film devices. The
Oersted field also does not have the proper symmetry to drive DWs forward in many
cases.
We are instead interested in fundamentally different phenomenona, arising from
quantum mechanics, in which the driving force (torque) scales with current per unit
cross-sectional area of a sample (current density). In particular, we take advantage of
spins flowing with current and magnetic moments in materials. The spins of conduction electrons flowing through a normal metal, in which magnetic moments are not
aligned, do not orient in any particular direction. By contrast, conduction electrons
in a magnetic metal exhibiting uniform magnetization become "spin-polarized" - that
is, a majority of the spins of these electrons become aligned with the direction of the
'At low driving fields, narrow DWs in out-of-plane magnetized thin films become pinned by
nano-scale defects and move very slowly by thermal activation, and Walker breakdown is typically
obscured by the mobility of thermally activated motion. See [10] for example.
41
(a)
(b)
magne ization
electron flow
Figure 2-5: Conduction electron spins in (a) normal and (b) magnetic metals. In the
magnetic metal, the current is spin-polarized.
g(EF)
E
g(E
EF
3d (localized)
*
(free)
g4 (E)
gt(E)
Figure 2-6: Simplified schematic of the electronic band structure of a metal ferromagnet, plotted as energy E versus density of states g(E). The material is magnetized in
the "t" direction, because there are more "t" electron than "4" electrons as a result
of the split 3d band. Therefore, "T" is the majority spin, and "4" is the minority spin.
The resistivity is larger for minority-spin electrons ({), because there are more localized 3d states to scatter into at the Fermi level EF, whereas majority-spin eletrons
(T) conduct more like free electrons.
magnetization in the material (Fig. 2-5).
Electrons injected into a ferromagnet spontaneously become spin-polarized to
some extent (i.e. one can think of a ferromagnet as a natural "spin filter"), because
electrons with different spins flow through the ferromagnet with different resistivities.
The magnitude of spin-polarization P is quantified as
P =
-
PT
P + PT,
42
(2.5)
where pt is the resistivity for electrons with spins aligned parallel to the magnetization in the material (conventionally termed "spin-up" or "majority spins") and p
is the resistivity for those aligned antiparallel to the magnetization ("spin-down" or
"minority spins"). Typically, 3d transition metal ferromagnets (Fe, Co and Ni) and
their alloys, often used in magnetic devices, exhibit positive spin polarization P > 0,
because their electronic band structure is such that majority spins experience less
scattering than minority spins. This spin-dependent scattering arises from different
densities of states at the Fermi level for those two types of electrons.
This spin-
dependent resistivity, which is the source of spin polarization of conduction electrons,
is illustrated in Fig. 2-6.
The spin polarization of current is experimentally measurable. One approach is
to probe the difference in the Fermi-level densities of states for spin-up and -down
electrons, e.g. through spin-dependent reflection at the surface of a ferromagnet interfaced with a superconductor ("Andreev reflection") [11]. Another method is to
measure the current-induced phase shift in spin waves propagating through a ferromagnet ("spin-wave Doppler effect") [12, 13]. It is also possible to extract the spin
polarization of current from the change in the DW velocity driven by adiabatic spintransfer torque, as done in [14, 15, 16]. Some of these measurements have estimated
the spin polarization of current in Ni80 Fe 20 to be ~~0.4-0.7. However, the actual magnitudes in many ferromagnetic structures are not well known. For instance, current
in ultrathin ferromagnets, especially those interfaced with nonmagnetic heavy metals,
may experience considerable interfacial scattering that reduces the spin polarization
compared to the bulk value. A recent study by Tanigawa et al. [15] shows the spin
polarization to be ~0.7 in Co/Ni multilayers with ferromagnetic thicknesses >4 nm,
but no spin polarization is evidenced at thicknesses <1 nm.
2.3
Adiabatic Spin-Transfer Torque
Assuming that the spin polarization is substantial, current can exert a torque on DWs
in ferromagnets through a mechanism known as spin-transfer torque (STT). Berger
43
proposed in 1978 [17] that current could drive DWs through STT, and he and his
coworkers followed up with a series of experiments in the 1980s [18, 19] demonstrating
DW motion in macroscopic magnetic films using large currents. In the 2000s, STTdriven DW motion became an active area of research, motivated by the possibility
to realize scalable, high-performance magnetic devices. Advances in submicron-scale
lithography also allowed DWs to be confined in magnetic nanostrips and investigated
more readily in conjunction with analytical and micromagnetic models. Moreover,
because the STT on DWs scales with current density, rather than current itself, DWs
could be driven with lower magnitudes of current in nanostrips than in macroscopic
samples in experiments by Berger et al. Studies by Grollier et al. [20], Tsoi et al. [21],
and Yamaguchi et al. [22] were some of the first studies demosntrating that current
alone could displace DWs in nanostrips of permalloy (NisoFe 2o).
The originally proposed mechanism of STT arises from a transfer of angular momentum between the spins of conduction electrons and magnetization in the material,
as illustrated in Fig. 2-7. As described previously (Sec. 2.2), conduction electrons in
a ferromagnetic material naturally become spin-polarized. When these spin-polarized
electrons cross a DW, their spins are flipped as they track the locally varying magnetization in the DW, resulting in a change in the spin angular momentum of the
electrons. Because the combined angular momentum of the conduction electron spins
and the magnetic moments within the material must be conserved, there also must
be a change in the angular momentum of the magnetic moments, i.e. the magnetic
moments in the DW must be flipped. Consequently, the DW moves in the direction
of the electron flow. This mechanism of current-induced DW motion by exchange
of spin angular momentum is called adiabatic STT, because the torque arises from
perfect adiabatic tracking of the DW magnetization profile by conduction electron
spins.
To put a DW in continuous motion through adiabatic STT, there exists a finite
energy barrier (hence a finite threshold current density) that must be overcome. This
barrier is "intrinsic," meaning the threshold current density exists even in a perfectly
44
spin-polarized
electron flow
DW
electron spins track local magnetization
and rotate when crossing DW
magnetization must rotate (DW must move)
to conserve net angular momentum
Figure 2-7: Illustration of domain wall motion by adiabatic spin-transfer torque..
defect-free material6 . The finite energy barrier exists because adiabatic STT does not
propel a DW directly. Instead, adiabatic STT under a sub-critical threshold current
density distorts a DW, and above the threshold causes a DW to move by "precesssion"
(i.e. periodic change in its configuration) rather than by rigid translation (Fig. 28). The origin of such DW dynamics can be understood through the LLG equation
incorporating an adiabatic STT term:
8m
at
8
-ym x Heff + am x
m -(u
- V)m.
(2.6)
The third term on the right-hand side represents adiabatic STT. This torque scales
with the spin drift velocity u, which is
U =
BPJe
2|elMs'
(2.7)
where g is the g-factor, P is the spin polarization of current, e is the electron charge,
and M, is the saturation magnetization; Je is the current density vector, with its
direction along electron flow. According to Eq. 2.6, if spin-polarized electrons flow
in the x-direction, adiabatic STT scales with the x gradient of the magnetization
am/ax.
Although the LLG equation may be used in a micromagnetic model that fully
takes into account the two- or three-dimensional magnetization configuration of a
DW, it is often applied to a greatly simplified one-dimensional model. The threshold
6
This is in contrast to field-driven DW motion, for which no threshold field exists in a defectfree material. The energy barrier for field-driven DW is therefore "extrinsic" that arises from DW
pinning due to defects.
45
(a)(b
(precession)
Figure 2-8: Domain-wall dynamics driven by adiabatic spin-transfer torque. in an (a)
in-plane magnetized thin film and (b) out-of-plane magnetized thin film.
current density can indeed be understood qualitatively in an in-plane (x) magnetized
nanostrip with the DW mangetic moment oriented transverse (y) to the strip axis,
as illustrated in Fig. 2-8(a). One might expect the DW to simply move along the
x-axis, because the adiabatic STT term in Eq. 2.6 rotates the DW moment towards
x parallel to the electron flow.
However, this magnetization rotation in the DW
leads to Om/&t having an x-component while m having a y-component, so that
the damping torque am x H now points along the z-axis. The adiabatic STT, in
concert with the damping torque, therefore cants the DW moment and generates a
demagnetizing field Hd (Fig. 2-8(a)), similar to the field-induced DW canting in Fig. 21. If the adiabatic STT (i.e. spin-polarized current density) is not large enough, the
canted DW moment comes to a standstill, because demagnetizing torque -
yIm x Hd
and adiabatic STT balance at at an equilibrium DW canting angle. Thus, there is
effectivelya magnetostatic (demagnetizing) energy penalty for having an out-of-plane
component in m. The DW can move forward only when the adiabatic STT is strong
enough to overcome the demagnetizing torque.
Under sufficiently large adiabatic
STT, the DW moves by precession, or by rotating its magnetic moment about the
x-axis (Fig. 2-8(a)), in a corkscrew-like manner.
Based on the one-dimensional description of a DW, Tatara and Kohno [23] derived
the threshold current density to be proportional to the hard-axis anisotropy of the
DW, or the energy penalty KDw associated with canting the DW moment. In inplane magnetized nanostrips, this threshold current density can be reduced by making
46
the cross section closer to a square [24], so that the magnetostatic energies for y- and
z-oriented DWs are similar. This idea can be extrapolated to a cylindrical nanowire,
in which the magnetostatic energy barrier is exactly zero [25], although it is more
difficult to integrate cylindrical wires in substrate-based devices. One approach that
has gained considerable interest in the last few years is to use out-of-plane magnetized
thin films, which will be discussed in Sec. 2.6.
2.4
Nonadiabatic Spin-Transfer Torque
According to the one-dimensional description of adiabatic STT [23], the threshold
current density to move DWs in permalloy nanostrips should be extremely high at
Jth
~ 1013 A/M 2 . Many experiments, however, demonstrated current-driven DW
motion in permalloy at J ~ 1012 A/M 2 . Moreover,
Jth
was reported to vary with the
strength of DW pinning due to defects [26]. The one-order-of-magnitude deviation
and the extrinsic variation in
Jth
led to the proposal of another kind of current-
induced spin torque [27, 28], often called nonadiabaticSTT. The LLG equation that
incorporates nonadiabatic STT is
am
m
_
at = -7m x Heff +Cm x aat
(U - V)m - Om x [-(u - V)m].
(2.8)
As can be seen in the last term of the right-hand side, nonadiabatic STT is parameterized by
#
and is orthogonal to adiabatic STT. The symmetry of nonadiabatic STT
acting a DW is identical to that of a torque from applied magnetic field that drives a
DW [28], which can be seen by comparing the field torque -I yIm x H in Fig. 2-1 and
nonadiabatic STT -0m x [- (u -V)m] in Fig. 2-9. Nonadiabatic STT then makes
extrinsic (i.e.
Jth
Jth
is no longer governed by the intrinsic threshold for adiabatic STT),
so that DWs in perfectly defect-free materials can be driven with small current densities (Fig. 2-10). Furthermore, DWs can conceivably be driven by nonadiabatic STT
at high speeds through rigid translation, rather than lossy precession that inevitably
accompanies adiabatic-STT-driven DW motion. For these reasons, nonadiabatic STT
47
(a)
()DW
-#lM X [-U - v~]transla-
-Jim x [-(u V)m]
ta
ion
Uioe
_'4V~ra
U~Je
U~1,
Figure 2-9: Domain-wall dynamics driven by nonadiabatic spin-transfer torque. in
an (a) in-plane magnetized thin film and (b) out-of-plane magnetized thin film.
has been actively investigated both theoretically and experimentally.
Analogous to field-driven DW motion below and above the Walker-field threshold
(Fig. 2-1), nonadiabatic STT drives a DW through rigid translation at a small current,
whereas it drives a DW through precession at a large current. Therefore, in the ideal
case of a defect-free nanostrip, Walker breakdown should be evident in current-driven
DW mobility curves with sufficiently large / (Fig. 2-10). According to the onedimensional model [28], analogous to Eq. 2.4, the expected speed of a DW driven by
Je below the precessional threshold Jth is
I-.
/
(2.9)
For the precessional regime of DW motion (Je > Jth), analogous to Eq. 2.3, the DW
speed approaches
v -4 u.
(2.10)
Eq. 2.10 indicates that adiabatic STT, proportional to the amplitude of the spin
drift velocity u and independent of /, is the dominant factor in driving motion of a
precessing DW [29].
The microscopic origin of nonadiabatic STT is not entirely clear. However, roughly
speaking, nonadiabatic STT may be regarded as any spin-torque that is not adiabatic
STT but arises from conduction electron spins in a ferromagnet crossing a DW (or
48
1200
1000
800 -
0.10
0.04
600
400
0.02
0.01
200
0
0
0
200
400
600
800
1000
u (rrVs)
Figure 2-10: Computed mobility curves (velocity versus spin drift velocity) of domain
walls driven by current, with adiabatic and nonadiabatic spin-transfer torques at
different values of nonadiabatic parameter /, adapted from [28].
any spatially varying magnetization texture). For example, conduction electrons may
be reflected from a very narrow DW, instead of crossing and tracking the local magnetization, and directly transfer linear momentum to the DW magnetization [23]. The
DW width would have to be close to or smaller than the Fermi wavelength (~nm in
3d transition metals) for this linear momentum transfer to be significant. Another
possible origin of nonadiabatic STT is the scattering (also called "relaxation" or "mistracking") of spins as they cross a DW [27, 28]. Such spin scattering is often thought
of as the major source of nonadiabatic STT in technologically relevant materials, and
attempts have been made to enhance nonadiabatic STT by doping permalloy with
heavy 4f metals that may serve as spin scatterers [30, 31].7
There is an even greater controversy regarding the true magnitude of nonadiabatic
STT, even in the most widely studied material of permalloy (as summarized in [32]).
The magnitude of nonadiabatic STT is often discussed in terms of the ratio of / with
respect to the Gilbert damping parameter a, because both nonadiabatic STT and
magnetization damping may involve scattering or relaxation of spins through their
7
The utility and validity of such attempts are controversial. Our recent
study [16] shows that
increasing the concentration of a 4f dopant, Gd, decreases the spin polarization of current. Nonadiabatic STT, like adiabatic STT, also scales with the spin polarization; so even if the nonadiabatic
parameter 3 is increased nontrivially, nonadiabatic STT itself may not be enhanced by incorporating
spin scatterers.
49
interactions with lattice vibrations, impurities, and orbital moments. A number of
studies suggest that O/a ~ 1 [33, 34, 35],8 whereas some report 3/a ~ 10 [38, 39].
Such a large discrepancy in estimates makes it difficult to specify the exact magnitudes
and engineer nonadiabatic STT. 9
2.5
Limits of Conventional Magnetic Thin Films
Regardless of the true mechanism and magnitude of nonadiabatic STT, currentinduced DW motion in conventional in-plane magnetized thin films - mostly of
permalloy - faces severe obstacles for viable applications.
First, the typical cur-
rent density to trigger DW motion and attain high velocities of ~10-100 m/s is ~1012
A/M 2 . This high current can lead to large dissipation, accompanied by excessive
Joule heating of ~100 K, which is detrimental for the power-efficiency of devices as
well as reliable retention of stored information if the heating approaches or exceeds
the Curie temperature. Repeated injection of such high current pulses may also lead
to substantial damage in devices through electromigration.
Furthermore, the widths of DWs in in-plane magnetized thin-film nanostrips are
large, on the order of the nanostrip width (-100 nm). Vortex DWs in particular can
extend over several 100 nm or even close to pm. With DWs occupying large space,
the maximum information storage density would thus be limited. Even if transverse
DWs appear as equilibrium configurations, these DWs transform into vortex DWs
when driven at high current densities [36, 37], similar to the periodic transformation ("precession") between transverse and antivortex configurations computed by
8
0/a exactly equaling 1 constitutes a special situation, in which a DW can be translated rigidly
without precession at any magnitude of driving current. This type of rigid translation is, however,
unlikely because current pulses have been shown to distort the configuration of DWs [36, 37]. This
observation suggests that /a - 1 is possible but not /a = 1.
9
It is also possible that nonadiabatic STT does not play a significant role in observed DW
dynamics in permalloy, and that the apparent shortcomings of adiabatic STT (which led to the
proposal of nonadiabatic STT) may be due to the inability of the one-dimensional model to capture
the full dynamics of complex DW configurations [5]. Indeed, a micromagnetic study of vortex DWs
driven only by adiabatic STT (i.e. 3 = 0) taking into account thermal effects and edge defects shows
continuous motion at J ~ 1012 A/M 2 [7], comparable to experiments. Recent micromagnetic results
also indicate that the threshold current density for DW motion is insensitive to //a in realistic
permalloy strips with defects distributed within the strips [40, 41].
50
micromagnetic (Fig. 2-3). In a real nanostrip, this transformation (governed by the
nucleation of vortex or antivortex cores) is influenced heavily by random edge defects and introduces stochasticity in DW motion [33, 36]. The dynamics of DWs in
permalloy is therefore problematic for reliable device operation.
2.6
Out-of-Plane Magnetized Thin Films
For the reasons described above, studies of current-driven DW dynamics in the last
several years have shifted toward a different class of materials: thin films with outof-plane magnetization. Table 2.1 summarizes the key differences between in-plane
and out-of-plane magnetized thin films. Most thin films are naturally in-plane magnetized because of the large magnetostatic energy penalty associated with orienting
magnetization out-of-plane, which results in free magnetic poles (stray fields) on the
top and bottom surfaces of the film. Since the shape of the film determines the energetically favorable magnetization orientation, this kind of magnetostatic anisotropy
is also called "shape anisotropy."
To bring the magnetization out of the film plane, another type of anisotropy generally called perpendicular magnetic anisotropy - is needed to overcome shape
anisotropy.
A common way is to take advantage of composite multilayered thin
films, in which interfaces contribute to strong perpendicular magnetic anisotropy
through spin-orbit coupling.' 0 Examples include multilayers of Co/Pt, Co/Ni, and
Co/oxide
[42]."
Co/Pt in particular has been studied and used extensively as
magneto-optical recording media since the 1980s, and is often regarded as the prototypical thin-film system exhibiting out-of-plane magnetization. In all such multi1'0 From the point of view of an electron spin in an atomic orbital, the nucleus appears to be
orbiting around the electron spin, i.e. the electron spin may feel coupling depends on the profile of
the orbital, which then is affected by bonding of atoms constituting the solid. An effective built-in
field (e.g. perpendicular magnetic anisotropy) may arise from spin-orbit coupling at an interface of
two different elements.
"Crystalline alloys of CoPt and FePt exhibit strong perpendicular magnetic anisotropy as well.
In this case, the origin of perpendicular anisotropy is "magnetocrystalline," the crystallographic
orientation in the bulk of the alloy. Strong perpendicular magnetic anisotropy can also be attained
in amorphous alloys of 4-f rare-earth metals and 3-d transition metals, e.g. TbCoFe, in which the
spin-orbit coupling effect arises from the bonding between 3-d and 4-f metal atoms.
51
in-plane magnetized
out-of-plane magnetized
wide (>100 nm),
complex vortex, transverse DWs
high energy barrier for
spin-transfer torque
homogenous materials,
anisotropy from film shape
magnetostatic
energy penalty
narrow (<10 nm),
simple Bloch, Neel DWs
low energy barrier for
spin-transfer torque
composite materials,
anisotropy from structure
interfaces (spin-orbit coupling)
to overcome magnetostatics
Table 2.1: Comparison of in-plane and out-of-plane magnetized thin-film nanostrips.
layers, the thickness of each ferromagnetic layer needs to be small, typically <1 nm,
to ensure that the interfacial perpendicular anisotropy (which scales inversely with
magnetic layer thickness) dominates over shape anisotropy.
The DW width in an out-of-plane magnetized film is <10 nm, about an order
of magnitude narrower than DWs in permalloy. The DW configuration is a simple
Bloch type in most experimentally studied nanostrips, according to magnetostatics.1 2
Such a Bloch DW may also precess by periodically transforming to a Noel DW,
but the DW remains compact during the precession, as shown in micromagnetic
simulation snapshots in Fig. 2-4. The energy barrier KDW required to drive DWs
in precessional motion is lower by an order of magnitude in out-of-plane magnetized
thin films than in in-plane magnetized counterparts. The intrinsic threshold current
density Jth for DW motion through adiabatic STT is then substantially smaller in
out-of-plane magnetized nanostrips. The reduced precessional threshold in out-ofplane magnetized films has been shown numerically by [8, 43, 44] and summarized
' 2 Bloch DWs are magnetostatically favorable in out-of-plane magnetized nanostrips with widths
>100 nm. Neel DWs become magnetostatically favorable over Bloch DWs only for nanostrip widths
substantially smaller than 100 nm. However, as we show later in this thesis, N6el DWs are stabilized
in wide nanostrips if a sufficiently strong interfacial Dzyaloshinskii-Moriya interaction is present in
an ultrathin ferromagnet sandwiched between dissimilar materials.
52
in-plane magnetized
800
(D
600 -
-
400 -
out-of-plane magnetized
-+-field-driven (v~ Hw)
---- current-driven (Uth Jth)
200 -
0.0
0.5
1.0
1.5
2.0
Normalized PMA
2.5
Figure 2-11: Critical domain-wall velocity for the onset of precessional dynamics versus the magnitude of perpendicular magnetic anisotropy (PMA). The normalized is
the ratio of the uniaxial anisotropy constant K, to the out-of-plane demagnetizing
energy constant poMs 2/2; "normalized PMA > 1" denotes out-of-plane magnetization. In the field-driven case, a domain wall moves by precession when driving field H
exceeds Hw; the maximum speed Vw is attained at H just below Hw. In the current
driven case, a domain wall moves by precession when spin drift velocity u exceeds
Uth, which is proportional to the intrinsic threshold current density Jth for motion
by
adiabatic spin-transfer torque. Adapted from [44].
in Fig. 2-11.
Koyama et al. have experimentally attained Jth ~ 2 x 1011 A/M 2 in Co/Ni multilayer nanostrips with optimized widths of 50-80 nm [45], at which the magnetostatic
energy for Bloch and Neel DWs are approximately equivalent and DW precession is
facilitated." The minimization of Jth with the reduction of Bloch-Neel magnetostatic
energy barrier is consistent with DW motion by adiabatic STT predicted by numerical modeling [8]. Koyama et al. also demonstrate that Jth [45] and the current-driven
DW velocity [47] are independent of DW pinning strength variation of ±50 Oe. This
insensitivity to 'field indicates that adiabatic STT - rather than nonadiabatic STT 3
1
Another method to lower the precessional energy barrier, and
hence Jth is to use a material
with a small saturation magnetization M,. This approach has been demonstrated experimentally
in TbCoFe [46] with M, ~ 100 emu/cm 2 , several times smaller than Co/Ni. The reported
Jth for
TbCoFe is ~5 x 1010 A/m 2 .
53
is responsible for the observed DW motion in Co/Ni. Moreover, according to Kim et
al. from the same group, the energy barrier to displace a DW from a pinning site by
adiabatic STT is distinct from that by external magnetic field [48]. These findings indicate that a material system with strong pinning can be used for current-driven DW
devices, so that the stability of stored information is robust against stray magnetic
fields and thermal fluctuations, while the current density required to move DWs may
remain low. For adiabatic STT to be strong, the total ferromagnetic thickness needs
to be sufficiently large,
>1
nm, because conduction electron spins tend to de-polarize
from interfacial scattering in ultrathin ferromagnets [15].
While a coherent set of results have been obtained for current-driven DW motion
in Co/Ni, experimental results have been much more controversial for multilayers of
Co/Pt. The first reported experiment of current-induced effects on DW motion in
an out-of-plane magnetized metallic thin film was on a Co/Pt multilayer [49], predating Co/Ni experiments by a few years. In this pioneering study, Ravelosona et
al. show a significant reduction in the required field to de-pin a DW from a defect in a Co/Pt multilayer with increasing current density [49]. The observed linear
change in the depinning field AHdep with current density Je suggests a spin-torque,
e.g. nonadiabatic STT (Sec. 2.4), whose effect on a DW is similar to that of an
applied magnetic field. Boulle et al. have reported a similar trend with a high "efficiency" of e = AHdep/AJe ~ 10 Oe/(10" A/M 2 ) presumed be a consequence of strong
nonadiabatic STT [50]. Other studies indicate similar efficiencies" and nonadiabatic
parameters derived from current-induced modifications in DW velocity [51, 52]. These
reported nonadiabatic STT may be attributed to narrow DWs leading to electronDW momentum transfer. Another possible source of such large nonadiabaticity is
spin-orbit coupling, which is also essential for perpendicular magnetic anisotropy
at Co/Pt interfaces, leading to spin mistracking across DWs. In contrast to these
reports, a few other studies report no effects from current, other than Joule heating [53, 54, 55, 56, 57]. Furthermore, in some cases with evidently strong spin-torque
"In general, the spin-torque "efficiency" refers to a linear scaling factor that relates the effects of
applied field and current in driving a DW.
54
effects, current-induced DW motion in Co/Pt occurs in the direction against electron
flow [52, 57, 58], opposite to what is expected from conventional STTs (Secs. 2.3, 2.4).
This wide disparity of experimental results in similar all-metallic Co/Pt multilayers
suggests that an alternative current-induced mechanism is required.
2.7
Anomalous Domain-Wall Dynamics and SpinOrbit Torques
In addition to the anomalies observed in all-metallic Co/Pt multilayers, even more
remarkable experimental observations have been reported for DW motion - and other
current-induced magnetization dynamics - in ultrathin Co sandwiched between a
nonmagnetic heavy metal and insulator. Moore and Miron et al. show fast currentdriven DW motion at ~100 m/s in nanostrips of Pt(3nm)/Co(0.6nm)/AlOx(2nm)
in the direction against electron flow [54]. A follow-up study indicates a large spintorque efficiency of 161 = 80 Oe/(10") A/m 2 , from which an enormous nonadiabatic
coefficient of 10
1 is deduced [55]. Such extraordinarily efficient current-driven DW
motion (against electron flow) has also been reported in similar ultrathin asymmetric
structures, including Pt/Co/Ni/Co/TaN [59] and Pt/Co/MgO [60]
Moore and Miron et al. also report in Pt/Co/AlOx a strong current-induced
Rashba field, an effective in-plane field transverse to the nanostrip (current) axis [61].
The estimated magnitude of this reported Rashba field is 10 kOe per 1012 A/M
2
of cur-
rent and apparently assists switching in uniformly magnetized Pt/Co/AlOx [61]. An
independent study by Pi et al. reports a similar Rashba field with a smaller estimate
of 3 kOe per 1012 A/rM2 [62]. In all of these studies [54, 55, 61, 62], the control samples
of symmetric Pt(3nm)/Co(0.6nm)/Pt(3nm) do not exhibit any current-induced DW
motion or Rashba field.
The Rashba effect in general is the spin-polarization of electrons (spin-dependent
splitting of electronic bands) that scales with the momentum (wavevector k) of the
electrons. In particular, the Rashba effect has been reported to arise in a mate55
Figure 2-12: Schematic of the Rashba effect in an asymmetric ultrathin magnetic
multilayer with out-of-plane magnetization. (a) The asymmetric multilayer has an
inherent electric field from built-in potential gradient VU. Electrons flowing at velocity v feels a relativistic effective Rashba field HR. The R~ashba field polarizes (tilts)
the spins of conduction electrons. The tilted conduction electron spins and the local
magnetization m interact through "s-d" exchange coupling, causing the magnetization to tilt away from the out-of-plane axis. (b) The Rashba field acts as an in-plane
transverse field. It locks the Bloch configuration of a domain wall, but does not drive
the wall forward.
rial with structural inversion symmetry, e.g. the asymmetric ferromagnetic thin-film
sandwich of Pt/Co/AlOx [61], in which there exists an asymmetric electric potential
in the out-of-plane direction (Fig. 2-12), denoted by unit vector z. When electrons
flow through the ferromagnetic Co layer, they experience an electric field from the
asymmetric potential. From the rest frame of the conduction electrons, the electric
field is effectively a magnetic field, 15 and the electron spins become polarized (tilted)
due to this effective magnetic field. The tilted electron spins can then exert a torque
on the magnetization, 16 thereby tilting the magnetization away from the out-of-plane
axis (Fig. 2-12).
The torque from the Rashba effect is often referred to as a spin-orbit torque [64],
5 This effective
w (relativistic) field is of the form
v x E, where v is the electron's velocity and
E is the electric field from the lab frame. Therefore, the effective magnetic field must be orthogonal
to both the electron flow direction (nanostrip axis) and the electric field (out-of-plane axis).
' 6 The tilted electrons exert this torque on the magnetization through the so-called s-d exchange
interaction, in which the moments of the magnetization (localized d-band electrons) and conduction
electron spins (free s-band electrons) prefer to align in the same direction. The strength of this s-d
exchange interaction Jsd is related to the spin polarization of the current P and the Fermi energy
EF, as Jsd ~PEF [63].
56
because it arises from the interaction between spins (of both conduction electrons
and magnetization) and orbitals (constituting the electric potential VU across the
ferromagnet (Fig. 2-12)). The Rashba spin-orbit torque is also an interfacial phenomenon, because it relies on spin-orbit coupling at dissimilar interfaces sandwiching
the ultrathin ferromagnet, e.g. Pt/Co and Co/oxide.
The Rashba spin-orbit torque exerted on the magnetization m arises from the
effective Rashba field [63]
HR -
-2
pPame
Jel
h~e|Ms
X
(2.11)
Je),
where aR is the Rashba parameter, me is the electron mass, h is the reduced Planck
constant, and je is the unit vector in the direction of electron flow."
The Rashba
field indeed is related the average electron wavevector (k), which scales with JeJe.
The direction of
HR
is orthogonal to the out-of-plane (z) axis and current direction,
so HR is oriented in-plane and transverse to the nanostrip (current) axis.
Because the Rashba field is effectively an in-plane transverse magnetic field, it
alone cannot drive a DW forward in an out-of-plane magnetized nanostrip. Miron et
al. have attributed the extraordinarily rapid current-driven DW motion to a combina-
tion of the Rashba field and large negative nonadiabatic STT [65]1: the Rashba field
locks the Bloch configuration of DWs (Fig. 2-12(b)), allowing the strong nonadiabatic
STT (Sec. 2.4) to propel DWs rapidly through smooth, rigid translation, rather than
through lossy, turbulent precession. Miron et al. attributed the extraordinarily large
DW speeds (>100 m/s) at high current densities to this combination of the Rashba
field and strong nonadiabatic STT [65].
The torque arising directly from the Rashba field is often called a "field-like
"The negative sign in front of 2.11 comes from the definition of current polarity, which we define
in terms of electron flow whereas the original work [63] and others define it in terms of conventional
current (flow of positive charges).
18
The "negative" nonadiabatic STT is necessary to account for the DW motion against electron
flow, and may theoretically arise from either P < 0 or 0 < 0. There is, however, no conclusive
evidence that one of these conditions holds in Pt/Co/AlOx.
57
torque," and is expressed as
T1R,FL =
-Nylm
x HR.
(2.12)
In addition to this field-like torque, it has been proposed that the Rashba effect can
also generate a "Slonczewski-like" torque 19
'rR,SL
=
-Nylm x (m x
3HR).
(2.13)
This indirect Rashba torque results from spin relaxation, analogous to the theorized
origin of nonadiabatic STT (Sec. 2.4) [67, 68], and hence incorporates the nonadiabatic parameter 3. Also analogous to the relative directionality of adiabatic and nonadiabatic STTs, the direction of TR,SL is orthogonal to rR,FL. A theoretical work [68
has suggested that, with specific magnitudes of parameters, this indirect Rashba
torque combined with a Rashba field and nonadiabatic STT can cause DW motion
against electron flow, even if P > 0 and / > 0. Furthermore, the indirect Rashba
torque has been attributed to current-induced switching in out-of-plane magnetized
submicron Pt/Co/AlOx squares (Fig. 2-13(a)) [69]. As illustrated in Fig. 2-13(b),
if the magnetization is tilted slightly along the current axis (i.e. under a small applied in-plane bias field), the indirect Rashba torque leads to an effective field with
an out-of-plane component Hs,. Depending on the direction of current and in-plane
bias field, this effective field HS, may either switch ("j > 0, H > 0" in Fig. 2-13(b))
or stabilize ("j < 0, H > 0" and "j > 0, H < 0") the out-of-plane magnetization.
Because the Rashba effect appeared to be common in ultrathin ferromagnetic metals
and to offer a robust route to manipulate magnetization, a large number of theoretical studies on the origins and possible enhancement of the Rashba torques have been
published in the past few years.
However, few experimental studies have been conducted to confirm the Rashba
9
The name "Slonczewski-like" comes from a study by Slonczewski [66], in which a spin torque
in magnetic multilayers (spin valves) is formulated. The "Slonczewski-like" torque (Eqs. 2.13 and
2.14) is also called the "anti-damping torque" or simply the "Slonczewski torque."
58
(a)
(b)
H,
M
~KHR
HRI
H
i
1>0, H >0
i< 0,H>0
>0. H <0
Figure 2-13: Slonczewski-like torque from the Rashba effect. Adapted from [69]. (a)
Schematic of the Pt/Co/AlOx square with out-of-plane magnetization. (b) Schematics of switching and stabilization of magnetization M due to the indirect (Slonczewskilike) Rashba torque. The Rashba effect generates two effective fields: the direct
Rashba field HR, and the indirect Rashba field HS = m x LHR (Eq. 2.13). An
in-plane bias field H along the current (x) axis tilts M slightly and builds a finite
x-component M,. The z-component of the indirect Rashba field Hsz acts on the
tilted M as an out-of-plane field. For the "j > 0, H > 0" case, Hs, switches the
tilted M to "down" (-z); for the other two cases, Hs, stabilizes M at "up"
(+z).
(a)
z
H
H
(b)
1-.&
6
'
nn-4
3
0-
_ f0ran
-3-
-20
-10
0
10
20
I~c (mA)
Figure 2-14: Slonczewski-like torque from the spin Hall effect. Adapted from [70]. (a)
Schematic of magnetization switching in Pt/Co/AlOx due to the spin Hall effect. Hext
is the external bias field to tilt the magnetization M, and Han is the perpendicular
anisotropy field resisting M-tilting; Text and Han are the corresponding torques. The
spin current from Pt impinging on the Co layer (red spins) generate the spin Hall
torque TST = -SH (Eq. 2.14). The effective field from the spin Hall torque (not shown)
acts as an out-of-plane field to switch or stabilize the magnetization M, similar to
Hs, in Fig. 2-13. (b) Switching of out-of-plane magnetization (proportional to RH)
by current, due to the spin Hall effect.
59
torques in similar material systems. Instead, a series of experiments by Liu et al. [70,
71, 72] have proposed an alternative spin-orbit mechanism based on the spin Hall
effect. The spin Hall effect is the generation of a spin current orthogonal to a charge
current flowing through a paramagnetic (not ferromagnetic) material, e.g. heavy
metal with strong spin-orbit coupling (e.g.
Pt, Ta, W). This spin current arises
from spin-dependent scattering of conduction electrons in the heavy metal, such that
spins of one orientation scatter in a particular direction whereas spins of the other
orientation scatter in the opposite direction. Because the diffusion length of spins
in a heavy metal is ~nm, polarized spins from the spin Hall effect can accumulate
on the top and bottom sides of the Pt underlayer in Pt/Co/AlOx. The accumulated
spins at the top Pt surface then exert a torque on the magnetization in the adjacent
Co layer.
This spin Hall torque can be written as
TSH = -1y7m
HSH
x
m x H(
x
(2.14)
Je)).
parameterizes the spin Hall effect through the spin Hall angle
0
SH
~ Is/e, where
I is the resulting spin current and I the injected charge current. The expression for
HSH is
HSH
where
tF
ShOSH
= 2
e
Je
(2.15)
is the thickness of the ferromagnetic layer adjacent to the heavy metal.
The symmetry of the spin-Hall-effect torque is Slonczewski-like, which may also
arise from the Rashba effect. The similarity can be seen by comparing Eqs. 2.13
and 2.14. Determining whether the Rashba or spin Hall effect is responsible for the
anomalous current-induced switching (and DW motion) in Pt/Co/AlOx has thus been
controversial.
Liu et al. [70] show current-induced switching in Pt/Co/AlOx, similar to the study
by Miron et al. [69], and conclude that the strong spin Hall effect in Pt is responsible
for the switching, whereas the Rashba field is vanishingly small. Moreover, they also
report current-induced magnetization switching by taking advantage of strong spin
60
M,
H-1
y
Figure 2-15: Domain-wall motion due to the spin Hall effect in Pt/Co/Pt. The
influence of the spin Hall effect is color-coded in purple, whereas the influence of the
conventional spin-transfer torques is color-coded in yellow. Here, a Pt/Co/Pt sample
with a thicker Pt at the bottom is illustrated; only the dominating spin current from
the thicker bottom Pt layer is shown. Under the application of an applied magnetic
field in the x direction (Hx), the Nel wall can be stabilized, with its internal magnetic
moment oriented along the field. The two domain walls move in opposite directions
when driven by the spin Hall effect (purple arrows). Adapted from [73].
Hall effects in Ta [71] and W [72].
These studies highlight the possibility to use
spin currents from nonmagnetic metals to control moments in adjacent ferromagnets.
Their results and analysis also suggest that the spin Hall torque should be strong
enough to influence current-driven DW dynamics.
However, the spin Hall effect torque (or the Rashba Slonczewski-like torque) cannot drive a DW of Bloch configuration, expected in most out-of-plane magnetized thin
films. By substituting the internal moment of a Bloch DW, i.e. m orthogonal to both
i and j., into Eq. 2.14, the resulting torque rSH (or TR,SL) is zero. For the spin Hall
(or Rashba) effect alone to move DWs, they must be Neel, as pointed out by [74].
Haazen et al. experimentally demonstrated spin-Hall-induced DW motion in outof-plane magnetized Pt/Co/Pt by forcing DWs to take Neel configurations with an
in-plane bias field [73]. In this case, the internal moments of two adjacent Neel DWs
("up-down" and "down-up" DWs) are in the same direction, so the effective spin-Hall
field on both of these DWs are in the same direction. Therefore, the spin Hall effect
leads to an expansion of the domain (red region in Fig. 2-15) and the two DWs move
61
in opposite directions (purple arrows in Fig. 2-15). However, in Pt-based asymmetric
magnetic multilayers [54, 59, 60, 65], both "up-down" and "down-up" DWs always
move in the same direction (against electron flow) when driven by current. This unidirectionality of DW motion indicates that another physical phenomenon, inherent
to these asymmetric multilayers, must stabilize Neel DWs in alternating directions,
i.e. with a uniform chirality [74].
2.8
Summary of Current-Induced Spin Torques
We now have a number of current-induced spin torques that can potentially exist in
out-of-plane magnetized multilayers (heavy-metal/ultrathin-ferromagnet/insulator)
exhibiting anomalous DW dynamics:
" adiabatic STT, which drives DWs into precessional motion if the driving current
density exceeds the intrinsic threshold;
" nonadiabatic STT, which pushes DWs (similar to a driving magnetic field) if
the driving current density exceeds DW pinning strength (extrinsic threshold);
" Rashba field-like torque, which acts as an effective magnetic field transverse
to the nanostrip, reportedly enabling rapid, rigid translation of Bloch DWs in
concert with nonadiabatic STT;
" Rashba Slonczewski-like torque, which can drive magnetization switching and
possibly DW motion;
" spin Hall torque, which may (similar to the Rashba Slonczewski-like torque)
drive magnetization switching and possibly DW motion.
The adiabatic and nonadiabatic STTs act on a magnetization gradient, i.e. a DW,
and are "bulk" effects that depend on spin angular momentum transfer within the
ferromagnetic layer. Adiabatic STT is a well established mechanism that has been
shown to drive DWs in magnetic films of thickness > 1 nm, e.g. Co/Ni multilayers
62
(b)
(a)
,__400
120-m
.?
100-
g0
Ty.SOO
-
A T.-200K
300
T.- 50KE
200
6
4)
40O
20-
8.0
I
A
100
1.5
1.0
0.5
2
Current density, Je (1012 A/m )
2.0
0
0
12
Current density, -Je (10
12
2
A/M )
3
Figure 2-16: Current-driven domain wall mobilities due to (a) conventional spintransfer torque in a "thick" Co/Ni multilayer (from [14]) and (b) spin-orbit torques
in ultrathin Pt/Co/AlOx (from [65]). (a) was measured at a few different surrounding
temperatures, whereas (b) was measured at room temperature -300 K.
and TbFeCo alloys, whereas the magnitude of nonadiabatic STT remains controversial. These STTs cannot fully account for anomalously high efficiencies and DW
motion opposing electron flow in the ultrathin ferromagnetic multilayers. Therefore,
"spin-orbit torques" from the Rashba and spin Hall effects have been proposed as
alternative sources of torques in addition to - or in lieu of - the conventional STTs.
The Rashba and spin Hall torques are "interfacial" effects that arise from structural
asymmetry in the multilayer. The Rashba and spin Hall torques are finite even in the
absence of magnetization gradient, such that they may assist switching of a uniform
magnetization. Although the Rashba and spin Hall torques do not have the proper
symmetry to drive Bloch DWs, the Rashba or spin Hall effect can lead to a finite
Slonczewski-like torque on Neel DWs.
Fig. 2-16 shows mobility curves of DWs driven by current in two distinct multilayered structures: a symmetric Co/Ni multilayer with a total ferromagnetic thickness
of 5.1 nm [14] and an asymmetric Pt/Co/AlOx with an ultrathin ferromagnet 0.6
nm thick [65].
The observed DW dynamics in Co/Ni is governed by conventional
adiabatic STT, and the velocity saturates at <100 m/s at high current densities (Fig.
2-16(a)), exhibiting v ~
J1e
as predicted theoretically [23]. Indeed, a series of ex-
periments have confirmed that adiabatic STT can account for current-induced DW
dynamics in "thick" Co/Ni multilayers.
63
By contrast, the DW velocity in "ultrathin" Pt/Co/AlOx increases linearly beyond
Here, the high-current mobility
100 m/s at large current densities (Fig. 2-16(b)).
exceeds the velocity limit of conventional STTs, set by the spin-drift velocity u (Eq.
2.7), indicated by the shaded area in Fig. 2-16(b). Furthermore, current-driven DW
motion in Pt/Co/AlOx occurs against electron flow (Je < 0). The anomalous effects
in Pt/Co/AlOx, also observed in similar ultrathin asymmetric structures including
Pt/Co/Ni/Co/TaN [59] and Pt/Co/MgO [60], suggest the presence of significant
spin-orbit torques that are dominant over conventional STTs.
By incorporating all of these listed spin torques, we would have an LLG equation
with many terms,
am
at
-
8m1-ym
x Hff
+am
x
am
at
-(u - V)m - #m x [-(u - V)m]
LYm x (m x
-iylm
x HR
-iylm
x [m x HH
-
x Je)],
LHR)
(2.16)
which contain many material-dependent parameters such as a, Ms, P, 3, aR, and
0
SH.
Adjusting these parameters within a one-dimensional or micromagnetic numer-
ical model would likely reproduce the experimentally observed DW dynamics, although - with this many parameters - attaining good agreement between the model
and experimental results does not necessarily guarantee that the correct physics is
reproduced. Furthermore, determining all of these parameters from experiments is
extremely challenging, and deliberately engineering these parameters to enhance DW
dynamics is even more so. To resolve the confusion of having all these torques, it
is desirable to identify one dominant current-induced torque. With the predominant torque identified, coherent tuning of material parameters for enhanced device
performance may become feasible.
We note that the spin Hall torque (Eqs. 2.14 and 2.15) is physically distinct
from the other spin torques in that it does not rely on the in-plane spin-polarized
current within the ferromagnet. In other words, the spin Hall torque is independent
64
of P, because the torque arises from the spin current generated in the nonmagnetic
heavy metal, rather than the spin polarization of charge current in the ferromagnet.
By contrast, the conventional STTs and Rashba torques require that the spins of
conduction electrons in the ferromagnet to be aligned with the local magnetization,
i.e. that P to be finite. We show through a series of experiments that the magnitude
of P in ultrathin ferromagnets is a key in resolving the origin of the anomalous DW
dynamics.
65
66
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[53] Suzuki, T., Fukami, S., Nagahara, K., Ohshima, N. & Ishiwata, N. CurrentDriven Domain Wall Motion, Nucleation, and Propagation in a Co/Pt MultiLayer Strip with a Stepped Structure. IEEE Transactions on Magnetics 44,
2535-2538 (2008).
[54] Moore, T. A. et al. High domain wall velocities induced by current in ultrathin
Pt/Co/AlOx wires with perpendicular magnetic anisotropy. Applied Physics
Letters 93, 262504 (2008).
[55] Miron, I. M. et al. Domain Wall Spin Torquemeter.
Physical Review Letters
102, 137202 (2009).
[56] Cormier, M. et al. Effect of electrical current pulses on domain walls in Pt/Co/Pt
nanotracks with out-of-plane anisotropy: Spin transfer torque versus Joule heating. Physical Review B 81, 024407 (2010).
[57] Lavrijsen, R. et al. Asymmetric Pt/Co/Pt-stack induced sign-control of currentinduced magnetic domain-wall creep.
Applied Physics Letters 100, 262408-
262408-5 (2012).
[58] Kim, K.-J. et al. Electric Control of Multiple Domain Walls in Pt/Co/Pt Nanotracks with Perpendicular Magnetic Anisotropy. Applied Physics Express 3,
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72
[59] Ryu, K.-S., Thomas, L., Yang, S.-H. & Parkin, S. S. P. Current Induced Tilting
of Domain Walls in High Velocity Motion along Perpendicularly Magnetized
Micron-Sized Co/Ni/Co Racetracks. Applied Physics Express 5, 093006 (2012).
[60] Koyama, T. et al. Current-Induced Magnetic Domain Wall Motion in a Co/Ni
Nanowire with Structural Inversion Asymmetry.
Applied Physics Express 6,
033001 (2013).
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ferromagnetic metal layer. Nature Materials 9, 230-234 (2010).
[62] Pi, U. H. et al. Tilting of the spin orientation induced by Rashba effect in
ferromagnetic metal layer. Applied Physics Letters 97, 162507-162507-3 (2010).
[63] Manchon, A. & Zhang, S. Theory of nonequilibrium intrinsic spin torque in a
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[64] Gambardella, P. & Miron, I. M. Current-induced spin-orbit torques. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering
Sciences 369, 3175-3197 (2011), PMID: 21727120.
[65] Miron, I. M. et al. Fast current-induced domain-wall motion controlled by the
Rashba effect. Nature Materials 10, 419-423 (2011).
[66] Slonczewski, J. Current-driven excitation of magnetic multilayers. Journal of
Magnetism and Magnetic Materials 159, L1-L7 (1996).
[67] Wang, X. & Manchon, A. Diffusive Spin Dynamics in Ferromagnetic Thin Films
with a Rashba Interaction. Physical Review Letters 108, 117201 (2012).
[68] Kim, K.-W., Seo, S.-M., Ryu, J., Lee, K.-J. & Lee, H.-W. Magnetization dynamics induced by in-plane currents in ultrathin magnetic nanostructures with
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73
[70] Liu, L., Lee, 0. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. CurrentInduced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin
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torques for efficient domain-wall motion. Physical Review B 87, 020402 (2013).
74
Chapter 3
Experimental Methods
3.1
Deposition and Characterization of Thin Films
All thin films studied in this thesis were deposited using a high-vacuum magnetron
sputtering setup, a modified Sputtered Films Incorporated (SFI) system [1, 2], whose
schematic is shown in Fig. 3-1. A turbomolecular pump attains a background pressure
of ~10-
Torr. An improved background pressure of -8-20x 10-
Torr is achieved
by using two liquid nitrogen cold traps. The sputtering gas is ultrahigh purity Ar
(99.999%), and a sputtering pressure of 2.0 mTorr or 3.0 mTorr is maintained by
balancing the pumping speed through a mechanical baffle and the flow rate of Ar
fixed at 30.0 sccm (standard cubic cm/min).
This sputtering system is equipped with four sputtering guns (Fig. 3-1(j)). All
metals are sputtered using DC power supplies.
Ferromagnetic metals (and some
nonmagnetic metals) are sputtered from two-piece donut-shaped targets in SFI guns
with especially strong built-in magnetic fields. Metals such as Ta and Cu are sputtered
from a 2" planar U.S. sputtering gun, whereas precious metals such as Pt and Au
are sputtered from a 1" planar U.S. sputtering gun. Oxides of Ta and Gd are DCsputtered under a partial pressure of ultrahigh purity 02 <0.1 mTorr introduced into
the chamber through a flow meter. Insulating materials such as MgO are sputtered
using an RF power supply.
Each sputtering gun is directed upwards and covered with a cylindrical chimney
75
ad
Ci
h
Figure 3-1: Interior of the high-vacuum magnetron sputterer: (a) substrate table, (b)
hole for mounting a substrate holder, (c) liquid nitrogen reservoir, (d) table rotation
assembly, (e) mask table, (f) hole for mounting a mask, (g) pins to align the mask and
substrate table, (h) chamber floor, (i) cutaway showing the jack and bellows below
the chamber floor, (j) chimney and a sputtering gun assembly. Adapted from [1, 2].
to limit the angular dispersion of the sputtered material. A pneumatically actuated
shutter at the top of each chimney is opened and closed for deposition with controlled
timing. Substrates' are mounted on the substrate table (Fig. 3-1(a)), face down towards the sputtering guns. Deposition can be done with the substrate table either
stationary above a particular gun or rotating with a period of 1.7 s. The deposition
rate with the rotating mode is lower by a factor of ~7 compared to the stationary
mode. The rotating mode therefore allows for more precise control of thickness of
ultrathin films studied in this thesis. 2 The sputtering system is also equipped with a
'Typical substrates used in this thesis are m3 80-ym thick Si(100) with a 50-nm thick overlayer
of thermally grown oxide.
2
Though not used in this thesis, the rotating mode also allows for co-sputtering
from multiple
guns to attain flexibility in sample composition.
76
second disk called the "mask changer" (Fig. 3-1(e)), originally designed to accommodate shadow masks for depositing spin-valve devices in [1, 2]. Here, we use the mask
changer to block off select substrates during rotating depositions, so that thin films
of different thicknesses or compositions can be deposited in one pump-down.
The sputtering rate typically scales with the sputtering current (or sputtering
power in the case of RF sputtering). The deposition rate of a material is calibrated by
measuring the thickness of a "calibration film" and dividing by the sputtering time for
this film. Film thickness is measured with X-ray reflectometry (XRR) using a Bruker
D8 HRXRD system. The reflected intensity of the X-ray from the film is recorded as
a function of incident angle 0 (or more conventionally 20) between the film plane and
the beam, which is kept between -0.2' and , 10'. This reflectivity spectrum exhibits
periodic fringes (peaks and troughs) arising from the interference of reflected beams
from the substrate/film interface and the film/air interface. 3 The thickness of the
film is inversely proportional to the spacing of the fringes. The density 4 of the film
is related to the critical angle at which the reflectivity spectrum exhibits the initial
drop. The thickness of the film can be extracted by fitting the reflectivity spectrum
to a simulated one with both the thickness and density as adjustable parameters.
Magnetic properties of thin films are often influenced by crystallographic texture.
For example, a (111) crystallographic texture is essential for perpendicular magnetic
anisotropy in Co/Pt-based multilayer films. Such textures can be characterized with
X-ray diffraction (XRD), which is similar to XRR except the incident angle is larger
100 and peaks of detected X-ray intensity result from interference of beams from
parallel atomic planes. Fig. 3-2 shows XRD spectra of Pt/(Co/Pt) 3 multilayers with
different underlayers. The multilayer whose Pt underlayer is directly on the Si/SiO 2
substrate does not develop significant (111) texture.
3
By contrast, Ta and TaOx 5
1f the film has two layers (e.g. by design or due to native oxide), the reflectivity spectrum
exhibits two distinct wavelengths of fringes. A heavy-metal under may be needed to measure the
thickness of a material whose effective density is similar to that of the Si substrate, so that sufficient
contrast is obtained in the resulting fringes.
4
effective density of electrons that the X-ray interacts with
5
TaOx was used in addition to Ta metal in to investigate the efficacy of an insulating buffer layer
and minimize current shunting. However, the resistivity of sputtered Ta (3 phase) is sufficiently
higher than Co and Pt, such that the use of Ta metal as a buffer layer is also appropriate for
77
8000
TaOx (30 A)
--
CoIt111)
Ta (30 A)
Pt (120 A)
6000
~
8
A
4000
Pt(1 11)
CO(1 11) -
-
-
2000
-
36
38
42
40
20 (degrees)
44
Figure 3-2: X-ray diffraction spectra of Pt/(Co/Pt) 3 multilayers with to0 = 7
deposited on different buffer layers.
A
buffer layers promote (111) texture in the Pt/(Co/Pt) 3 multilayer. Ta (or TaOx) is
6
therefore used as buffer layers in all Co/Pt-based films in this thesis.
3.2
Measurements of Magnetic Hysteresis Loops
The plot of the magnetization M versus external magnetic field H - the magnetic
hysteresis loop - reveals essential properties of a magnetic material. Hysteresis loops
are often measured with magnetic field swept along two distinct axis orthogonal to
each other: easy axis and hard axis. Simplified examples of hysteresis loops are shown
in Figs. 3-3(a),(b).
The magnetization prefers to orient along the easy axis, determined by the net
uniaxial magnetic anisotropy from the shape or nanoscale structure of the material
(Sec. 1.1). A material magnetized by a field along the easy axis may remain magnetized in the same direction even after the field is turned off. Because the direction
of the remanent magnetization depends on the direction of the previously applied
field, the material may exhibit two distinct magnetization states at zero field (which
can constitute the digital bits stored in nonvolatile magnetic memory devices). The
minimizing shunting.
6Ta also serves as a good adhesion layer between the SiO substrate surface and the first Pt layer,
2
due to the high oxidation potential of Ta.
78
critical field required to switch the magnetization, or to attain M = 0, is called the
coercive field (or coercivity) H, (Fig. 3-3(a)). By contrast, an external magnetic field
needs to stay on to keep the material magnetized along the hard axis, and the magnetization exhibits a one-to-one, reversible relationship with respect to the applied
field (Fig. 3-3(b)).
For an ideal hard-axis loop, H, = 0 and the more meaningful
critical field is the saturation field (or anisotropy field) Hk required to magnetize the
material fully (Fig. 3-3(b)), i.e. M = M, where M, is the saturation magnetization.
Hk
is related to the strength of uniaxial magnetic anisotropy in the material, and the
effective uniaxial anisotropy energy density may be written as Keff
HkM,/2 (in
CGS units).
The loops in Figs. 3-3(a),(b) are derived from the Stoner-Wohlfarth model [3, 4],
which models the magnetization in a material as a single domain, i.e. one macroscopic magnetic moment is rotated to magnetize or switch the material.
In this
single-domain case, H, along the easy axis is determined by the strength of uniaxial
anisotropy, such that H, = Hk. However, the single-domain behavior is rare because
real materials can have magnetic domains and domain walls (DWs), as discussed in
Secs. 1.2 and 1.3. In the realistic multi-domain case, magnetization switching occurs
through the nucleation of a reverse magnetized domain, followed by the expansion
of this domain (DW mQtion), and H, along the easy axis is typically much smaller
than Hk. For a macrospic sample (-mmxmm continuous thin film), the measured
easy-axis coercivity H, ~ 100 Oe in Fig. 3-3(c) is significantly less than the hard-axis
saturation field Hk ~ 8000 Oe in Fig. 3-3(d). Furthermore, the shape of the measured
hard-axis M-vs-H relation (Fig. 3-3(d)) deviates from Fig. 3-3(b), possibly because
of a distribution in anisotropy strength throughout the film (different regions of the
film saturating at different fields) or a small misalignment in the applied field with
respect to the hard axis.
The following subsections describe experimental techniques to obtain magnetic
hysteresis loops of thin films in this thesis - vibrating sample magnetometry (Sec.
3.2.1), magneto-optical Kerr effect polarimetry (Sec. 3.2.2) - as well as a case study
of magnetic properties of Co/Pt multilayer films with different thicknesses.
79
()M
(a)
M
M(b)M
M
H
M
-
H
H
Hh
H__S2
H(
(d)
() 2000
1000
1000
E
v'E
U.
n
-1000
-1000
-05
-2000 --10
200
-5
_ 1
0
H (kOe)
0.5
0.0
*
5
)
-2000
-10
10
-5
0
5
10
Hh (kOe)
Figure 3-3: Magnetic hysteresis loops and key parameters. (a) Expected hysteresis loop with external field He along the easy axis. M, is the saturation magnetization, and H, is the coercive field. (b) Expected hysteresis loop with external
field Hh along the hard axis. Hk is the hard axis saturation field (anisotropy field).
magnetized
(c, d) Easy-axis (c) and hard-axis (d) hysteresis loop of out-of-plane
Ta(4nm)/Pt(3nm)/Co(0.9nm)/GdOx(3nm) measured with a vibrating sample magnetometer (Sec. 3.2.1). The inset of (c) reveals H, ~ 100 Oe. The easy-axis is out of
the film plane, and the hard axis is within the film plane.
3.2.1
Vibrating Sample Magnetometry
Vibrating sample magnetometry (VSM) is a widely used technique to measure magThe magnetic sample hanging on a glass rod is vibrated,
producing a periodic change in magnetic flux <D through pickup coils and hence an
induced voltage V ~ dJD/dt (Faraday's law) in the pickup circuit. The magnetization
netic hysteresis loops.
of the sample is directly proportional to V4, and the linear scaling factor between the
detected signal and the magnetization is calibrated using a nickel standard of known
magnetization.
Thin-film samples deposited on wafers are cut into squares of a few mm x mm, and
attached to the rod with vacuum grease. For magnetic films <1 nm thick, a few pieces
80
can be attached on top of each other to increase the signal. The noise level of the VSM
system is ~10-6-10-5 emu. The net ferromagnetic volume of the measured film must
be known to obtain the normalized magnetization, typically expressed in the unit
emu/cm 3 . This volume can be found from simply areaxthickness for precision-diced
samples, or by weighing the wafer pieces to extract the total area.
By measuring the magnetization while stepping through a range of external magnetic field, a hysteresis loop is obtained. The direction of the field may be in-plane
or out-of-plane with respect to the measured film, and the typical time required to
obtain a complete loop is ~10 minutes or longer. Although most loops are acquired at
room temperature, a furnace tube combined with a liquid-nitrogen cryogenic system
can be used to conduct measurements from -100 to ~500 K.
3.2.2
Magneto-Optical Kerr Effect
Magneto-optical Kerr effect (MOKE) polarimetry is an alternative technique to obtain
magnetic hysteresis loops. Although MOKE cannot provide an absolute quantitative
measure of magnetization, it can measure the magnetization (on a relative scale) of
a very small and thin film very quickly (e.g. less than 1 s). In a MOKE setup, a
linearly polarized laser beam illuminates the thin-film sample. 7 Due to an interaction
between polarized light and the magnetization in the film, the polarization in the
reflected light is rotated with respect to the incident light. The polarization shift,
detected by passing the reflected beam through an analyzer (polarizer in front of
the detector) nearly cross-polarized with the incident polarizer, is proportional to
the magnetization in the material. The detected intensity of the beam through the
polarizer measured under a sweeping external magnetic field thus produces hysteresis
loop. 8
The "interaction" between linearly polarized light and magnetization fundamentally responsible for MOKE is the photon-induced electronic excitation between en7
The light may penetrate up to ~10 nm deep into a metal film to produce MOKE signal. MOKE
is therefore suited to characterize magnetic thin films but not bulk materials.
8
A MOKE "microscope" also takes advantage of the magnetization-dependent polarization shift,
as illustrated in Fig. 3-4(a), to image differently magnetized domains in thin films.
81
()
10
Light
source
Detector
Analyzer
Polarizer
Sample
(b)
(c)
+1/2
-1/2
A
\/+\P*
B
<
+1/2
-1/2
Figure 3-4: Physics of the magneto-optical Kerr effect. Adapted from [5]. (a) Illustration of polarization rotation for linearly polarized light reflected from a magnetic film.
Note that differently magnetized domains (gray and white) rotate the polarization
differently. In MOKE microscopy, this contrast in polarization rotation can be used
to form an image of magnetic domains. In MOKE polarimetry, the polarization rotation (MOKE signal) is recorded as a function of applied magnetic field (or injected
current) to obtain hysteresis loops. MOKE signal can also be recorded as a function
of time for temporal characterization of magnetization dynamics. (b) Decomposition
of linearly polarized light into two circularly polarized components. (c) Absorption
of circularly polarized light between spin-split electronic states.
ergy levels split due to the magnetization. Linearly polarized light can be separated
into two components with opposite circular polarizations (Fig. 3-4(b)). Each photon
constituting a particular circularly polarized component has angular momentum of
the same magnitude, L
ponent has L = -1.
=
+1.'
Each photon in the other circularly polarized com-
These photons can excite electrons in the magnetic material, in
which electronic energy levels are split into S = -1/2
(majority spin state, aligned
with the magnetization) and S = +1/2 (minority spin state) as illustrated in Fig.
3-4(c). An L = +1 photon can be absorbed as it excites an electron from the groundstate S = -1/2 level to the excited S
from the ground-state S
written in the unit of
+1/2 level, due to conservation of angular
photon can be absorbed absorbed when exciting an electron
momentum; an L = -1
9
=
=
+1/2 to the excited S = -1/2. In this illustrated case
h.
82
longitudinal MOKE
transverse MOKE
polar MOKE
magnetization
Figure 3-5: Geometries of magneto-optical Kerr effect (MOKE) measurements. The
longitudinal and polar configurations result in polarization rotation of the reflected
light, whereas the transverse configuration modifies the amplitude of the reflected
light.
(Fig. 3-4(c)), there are more S = -1/2 electrons at the ground state, so more L = +1
photons are absorbed. The reflected light has a different makeup of the two circularly
polarized components, compared to the incident light, and therefore has a rotated
polarization.1 0 The magnitude and direction of polarization rotation depends on the
magnitude and direction of the magnetization, which modifies the spin-dependent
occupation of the ground-state levels and hence photonic absorption.
There are three different major optical configurations of MOKE (Fig 3-5). Longitudinal MOKE and transverse MOKE are used to measure in-plane magnetized films.
In most experiments in this thesis, we use polar MOKE that detects the out-of-plane
component of the magnetization. Polar MOKE signal from out-of-plane magnetized
thin films are typically very large, allowing for sensitive measurement of magnetization even in an atomic monolayer of ferromagnet.
3.2.3
Magnetic Properties of Co/Pt Multilayers
Here, we present a case study of Co/Pt multilayers measured primarily with MOKE.
These Co/Pt multilayers were deposited on three different types of buffer layers between the substrate and Co/Pt. The influence of these buffer layers on the strength
of perpendicular magnetic anisotropy (promoting magnetic easy axis out of the film
10The reflected light also develops an ellipticity, which may be compensated by having a tuned
quarter-wave plate before the detector - or may be used instead of (or together with) polarization
shift to measure the magnetization.
83
place) is investigated. The MOKE setup in this study was designed for measuring
continuous films 1 and used a HeNe continuous wave laser with 633-nm wavelength.
The laser beam is reflected at normal incidence for polar-MOKE measurements, while
it is reflected at an angle of ~45' for longitudinal-MOKE measurements. The sweep
rate of the magnetic field was 0.2 Hz. 1 2
To compare the influence of these buffer layers in detail, we have measured inplane and out-of-plane hysteresis loops over a range of to0 spanning the transition
from perpendicular to in-plane anisotropy. A subset of these loops is shown in Fig. 36. The multilayers grown on a Pt buffer layer maintain full out-of-plane remanent
magnetization up to t00 = 6 A, but at to0 = 7
and for to0 > 7
A,
A, the
out-of-plane loop is sheared,
the multilayers exhibit clear in-plane anisotropy. By contrast,
multilayers with Ta metal or TaOx buffer layers remain completely out-of-plane magnetized at remanence up to to0 = 10
A. Compared
to Pt underlayers, both metallic
Ta and resistive TaOx buffer layers increase by more than 50% the upper limit of to0
for these Co/Pt multilayers to exhibit out-of-plane magnetization.
The perpendicular anisotropy field Hk, estimated from the hard-axis saturation
field (in-plane loop for Hk > 0 and out-of-plane loop for Hk < 0," is plotted versus
to0 in Fig. 3-7(a). These data indicate that Ta metal and TaOx buffer layers produce
multilayers with nearly identical PMA, which is uniformly stronger than for multilayers grown on Pt alone over this range of to0 . The effective PMA energy density
is defined as Keff = HkM,/2, where M, is the saturation magnetization normalized
by the Co volume. As shown in Fig. 3-7(b), M, of our Co/Pt multilayers measured
by vibrating sample magnetometry (VSM) is significantly greater than that of -40nm thick Co films at 1360±30 emu/cm 3 . This enhancement of magnetization in the
Co/Pt multilayers, also observed by [6] and [7], is likely due to the polarization of
Pt at the Co/Pt interface, and a weak dependence of M, on 1/tc, is thus observed
"1 In Sec. 3.4, we use another MOKE setup designed for lithographically patterned nanostrips.
"For films with strong PMA whose coercivities can vary significantly with the field sweep rate,
the out-of-plane field was swept at a fixed rate of ~800 Oe/s.
13
1n cases where remanent magnetization in either direction was small (i.e.
the magnetic
anisotropy was close to the transition between in-plane and out-of-plane), HK was estimated from
the difference between the saturation fields in the in-plane and out-of-plane directions.
84
in-plane
out-of-plane
(a) 1
tOo
(b)
=7 A
0
-1
(c)
1 t :7 A
0
4
-&-TaOx (30 A)
--- Ta (30 A)
-1
Pt (12o A)
(d) 1
1
- Nor
0
I
-A-TaOx (30 A)
-+Ta (30 A)
-u-Pt (120 A)
I
-.
omens
SO"ON
tc.
9~
0
=9A
Co
-1
-1
(e)
I
1
Em-
(f)
I
a-TaOx
.. *-
0
Ta
0
-
1
Taox
0
-2in
-1
-1000
-1
-500
0
H. (0e)
500
1000
-500-250
0
250 50o
-6000-4000-2000 0 2000 4000 6000
H, (0e)
Figure 3-6: MOKE hysteresis loops of Co/Pt multilayers with to0 = 7, 9, 11 A, obtained with magnetic fields in the (a, c, e) out-of-plane direction H2 and (b, d, e)
in-plane direction Hi..
(Fig. 3-7(b)). In Fig. 3-7(c), we plot the product of tc, and Keff, using the mean
saturation magnetization M,=1670t70 emu/cm 3 from our VSM data. This quantity may be interpreted in terms of phenomenological surface (Ks) and volume (Ky)
contributions to the total PMA energy density,
Keff tCo = 2Ks + Kvtco.
For the multilayers on Pt, and for those on Ta and TaOx with tc o > 10
(3.1)
A, the
data
follow a straight line with a slope consistent with a volume contribution dominated
85
(a)
6000
4000
11
-
1
1
A
TaOx (30A)
Ta (3oA)
Pt (120A)
-
2000
0
0
-2000 -
(b)
1800
-
51600
E
A
1400
(C)
N
M. of Co film
TaOx
Pt
0.3A
TaOx
0
0.2
0
t
-
Ta
Pt
0.1
A'
-0.1
-0.2
I
I
I
6
7
8
9
tCO
I
I
I
10
11
12
(A)
Figure 3-7: Co-layer thickness dependence of magnetic properties of Co/Pt multilayers.
= -1.75x 107 erg/cm 3 .
by the out-of-plane shape anisotropy energy, Ky ~ -27rM
By contrast, the data for the TaOx and Ta buffer samples at tco < 10
A show
a much
weaker slope with to0 , suggesting an additional positive volume-like contribution to
Keff that acts counter to the shape anisotropy. This additional Ky contribution is
responsible for extending the range of to0 over which net PMA is observed.
Fig. 3-2 shows XRD spectra that give insight into the structural role of the buffer
layers in enhancing PMA. Co/Pt multilayers with tc, = 7
A
grown on both Ta and
TaOx buffer layers show coherent Co/Pt (111) texture, with a single (111) peak
located between the bulk Co and Pt (111) peak positions, along with a weak super-
86
lattice side peak structure. The Ta-based buffer layers allow for smooth layer-by-layer
(Frank-van der Merwe) growth of Pt and Co layers, which predominantly develop the
thermodynamically favorable (111) orientation [8].
The same multilayer grown on
the thick Pt buffer layer, however, shows only a single broad peak near the Pt(111)
bulk peak position, with smaller peak area despite the much greater total Pt thickness in this film. Coherent (111) texture in Co/Pt multilayers is well known to be
associated with strong PMA [6, 9], through an increase in the magnetocrystalline
anisotropy KMc that may be oriented along the film normal and a magnetoelastic
strain contribution KME due to coherent growth of the lattice-mismatched Co and
Pt layers [10, 11]. The combination of enhanced magnetocrystalline (KMc > 0) and
magnetoelastic (KME > 0) contributions thus offsets the shape anisotropy:
(3.2)
Kv = -2-rMS 2 + KMc - KME
From Fig. 3-2, both Ta metal and TaOx are equally effective in promoting (111)
texture in a Pt overlayer. The additional magnetocrystalline and strain contributions
to PMA permit Co/Pt multilayers on TaOx and Ta buffer layers to maintain out-ofplane remanent magnetization up to a larger to0 of 10 A. Beyond this layer thickness,
the coherent layer growth and strain can no longer be accommodated, and strain
relaxation is expected [10, 11].
We speculate that for to0 > 10
A,
the strain is
relieved and the KME contribution to PMA is diminished, so Kv reflects only the
shape anisotropy and remaining small KMC component.
3.3
Submicron-Scale Lithography
All magnetic nanostrips measured in this thesis are fabricated using electron-beam
lithography, magnetron sputtering (see Sec. 3.1), and liftoff. The first step is to spincoat 100-200 nm of poly(methyl methacrylate) (PMMA) on a substrate of Si(100)
with 50 nm of SiO 2 overlayer, 1 4 and to bake at >100 'C (above the glass transition
14The oxide overlayer prevents shunting of current in the substrate, for current-driven DW measurements. A high-resistivity undoped Si wafer was found to shunt current due to photo-generated
87
(1) spin coat
(3) develop pattern
(2) e-beam write
PMMA
SiO 2/Si
(5) liftoff
(4) deposit material
Figure 3-8: Procedure to fabricate magnetic nanostrip devices using electron-beam
lithography.
temperature of PMMA) to relax the PMMA chains. The nanostrips and alignment
marks are written using the Raith 150 scanning electron-beam writer equipped with
a laser-interferometer. The acceleration voltage used is 10 kV, and the aperture size
is 30 or 60 pm.
Because PMMA is a positive resist, exposed PMMA is removed
by immersing ("developing") the sample in a solution of methyl isobutyl ketone and
isopropanol with a 1:3 volume ratio, forming "trenches" (see Fig. 3-8). The sample
is then etched lightly in a plasma asher at 50 W for about 2 seconds for additional
cleaning of the bottom of the trenches.
The magnetic film is deposited using the magnetron sputterer described in Sec.
3.1. The substrate is loaded such that the nanostrips align along the circumferential
direction of the rotating substrate table. This ensures that the deposited material
comes into the trenches parallel to the nanostrips, thereby reducing deposition of
sputtered material on the side walls of the long direction of the strips. The excess
sputtered material and PMMA are removed in the "liftoff" process by immersing the
substrate in n-methyl-2-pyrrolidone or acetone.
The resulting nanostrips are imaged with a scanning electron microscope(Zeiss/Leo
Gemini 982 SEM) at 5 kV of beam voltage. This SEM is equipped with a conventional secondary electron (SE) detector located to the side of the imaging chamber, as
well as an in-lens SE detector located at the bottom of the electron-beam objective,
directly above the imaged substrate. The conventional SE detector, generally sensicarriers during magneto-optical Kerr effect measurements
88
(b)
(a)
(c)
Figure 3-9: Scanning electron micrographs of a lithographically patterned nanostrip
with electrodes, imaged using (a) the conventional secondary electron detector and
(b) the in-lens secondary electron detector. (c) Zoomed-in micrograph of a 500-nm
wide strip obtained with the in-lens secondary electron detector.
tive to topographical profiles, tends to provide better contrast between the deposited
(mostly) metal patterns and the Si0 2 substrate at low magnification, as seen in Fig.
3-9(a) compared to a micrograph of the same pattern obtained with the in-lens detector (Fig. 3-9(b)). The in-lens SE detector generates high-contrast images at high
magnifications and can reveal nanoscale roughness at the edges of nanostrips arising
from the liftoff process (Fig. 3-9(c)).
A second layer of lithography similar to the above is conducted to place contacts on
the magnetic nanostrips. To minimize damage on the ultrathin magnetic structures,
the baking temperature is limited to 90 'C and less than 1 minute. The contacts
are patterned with electron-beam lithography by using coordinates defined during
the first layer of lithography, resulting in a typical placement error of <1 [um. The
sputtered contacts are 100-nm thick Cu with 2-nm thick Ta underneath that improves
adhesion of Cu with Si0 2.
3.4
Time-Resolved Scanning Magneto-Optical Kerr
Effect Setup
The dynamics of propagating DWs in nanostrips can be characterized using magnetooptical Kerr effect (MOKE) polarimetry (Sec. 3.2.2) with a focused probing laser
89
spot and a high-resolution scanning sample stage. This technique was pioneered
by Allwood et al [12]. The MOKE setup in this thesis, which incorporates a highbandwidth detector for time-resolved measurements of fast domain walls, is based
on a similar design by Beach and Nistor et al.[13] in their previous studies of DW
dynamics in permalloy nanostrips, such as in
[14].
The "time-resolved" part of this MOKE technique signifies that we can characterize the dynamics of a DWs while a magnetic field or electric current drives it. This is
in contrast with MOKE microscopy (or magnetic force microscopy) [15] often used to
image static configurations of a DW, but only after the DW has been driven by pulses
of field or current (e.g. [16, 17]). The "scanning" component of MOKE polarimetry
allows for great flexibility in measurement, because DW motion (or magnetization
switching) can be detected anywhere along the magnetic nanostrip of almost any
shape and structure, as opposed to electrical detection techniques that allow detection only within limited spacial windows (e.g. "Hall crosses" using the anomalous
Hall effect) or require special device structures that may produce artifacts in DW
dynamics (e.g.
"spin valves" using the giant magnetoresistance).
In this section,
we describe key components of our scanning MOKE polarimeter and measurement
procedures used in the studies of DW dynamics in out-of-plane magnetized strips
described in the ensuing chapters.
The optical configuration of our MOKE setup is "polar," where the signal is
related to the out-of-plane component of the magnetization, and the incident beam
is normal to the sample plane.15 A schematic of this MOKE setup is illustrated in
Fig. 3-10.
The light source a continuous-wave diode laser (CrystalLaser) with a
wavelength of 532 nm, collimated with a 10 x beam expander and linearly polarized
with a polarizer. The beam is focused to a ~ 2 - 3-nm spot 16 with a 10x objective,
mounted on a piezoelectric stepper (Newport). The objective lens is shielded from
5
1
The beam path is slightly offset from normal to avoid interference between the incident and
reflected beams, which would couple very strongly to small mechanical vibrations and render the
MOKE signal too noisy.
16
The spot size is estimated from the "knife-edge" technique[13]: The focused spot is scanned over
the sharp edge of a lithographically defined pad, producing a reflectivity profile that can be fitted
with an error function. The 1/e width of the derivative of the error function, a Gaussian profile, is
the estimated spot size.
90
CCD
damera
polarizer
beam
xpander
beam
splitters
beam
expander
diode
laser
I
anal zer
quar~ter
waveplate
ob jective lens
phot(omulti
tube
electrical probe
needles
sa mple substrate
ele tromagnet
scanning stage
Figure 3-10: Schematic of the scanning magneto-optical Kerr effect system.
magnetic field with a high-permeability Mu metal cylinder to minimize background
signal from Faraday rotation inside the objective. To minimize laser-induced heating
to <1 K, the incident power is attenuated to 1 mW. 7 The focused spot is placed on
a desired location of the sample, which is mounted on a high-resolution motion stage
(Aerotech A3200) with a minimum step size of 10 nm.
The reflected light passes through a quarter-wave plate to eliminate ellipticity
and then enters the detector setup, consisting of a polarizer and a photomultiplier
tube (Hamamatsu) with a risetime of ~10 ns.
Slower DW motion (<1 m/s) is
detected using a DC-coupled channel of the photomultiplier tube, connected to a lownoise voltage preamplifier (Stanford SR560) with a 10-30 kHz bandpass filter setting,
allowing for a signal-to-noise ratio of >10 in single-shot measurements for Co/Pt
multilayers (see for example Fig. 3-12). Such low-bandwidth data are digitized with
a Measurement Computing USB-1208HS-4AO digitizer. The MOKE signal for faster
"Laser-induced heating was estimated by measuring the coercive field of a Am-scale Co/Pt multilayer structure as a function of laser power and of substrate temperature. The estimated heating
was ~2 K for 5 mW of incident power, and -16 K for 10 mW.
91
DW motion is measured through an AC-coupled channel and a digital scope (Gage)
with a 1-GHz sample acquisition rate. LabVIEW programs are used to control the
measurement sequence and record the MOKE signal. The combination of the highresolution scanning stage and the high-bandwidth detector and scope allows for the
detection of fast DWs propagating at up to -100 m/s.
Electrical contact must be made between a lithographically patterned sample and
voltage (or current) sources to generate a localized Oersted field for DW initialization,
as well as to drive DWs through spin-torque effects. Tungsten probe needles with a
-25-tm tip diameter are landed on the Cu contact pads (Sec. 3.3) using Signatone
probe positioners and imaging through a CCD camera (Fig. 3-10). Current pulses
are output from HP 3314A and/or 8116A function generators, which are connected
to the probes through coaxial cables. Copper foil connects the ground shields of the
coaxial cables close to the sample to minimize the pulse risetime to <8 ns.
The DW-velocity measurement procedure begins by saturating the magnetic nanostrip with an out-of-plane field. A reverse domain is nucleated in the nanostrip using
an Oersted field from a 25-ns long (FWHM) current pulse through the orthogonal
Cu line (Fig. 3-11). The amplitude of this nucleation pulse is 50-200 mA, depending
on the Oersted field required to locally reverse the magnetization. A DW is subsequently driven away from the Cu nucleation line by an out-of-plane field and/or a
current. For most measurements presented in this thesis, the field is output by an
electromagnet with a ~1-cm diameter iron core.18 The current through the magnetic
nanostrip to drive DWs is injected by a true DC-current source 19 or a second voltage
pulse generator (Fig. 3-11).
In addition to measuring DW motion under a constant driving field, a local hysteresis loop can be obtained from a nanostrip by acquiring MOKE signal under sweeping out-of-plane magnetic field. From this hysteresis loop measurement, it is possible
1 The risetime for this magnet is estimated to be -500
ps from the Faraday rotation signal
reflecting from a silver-coated glass slide. Because of this slow risetime, to measure the DW velocity
driven by the out-of-plane field from this magnet, the field is ramped up to the setpoint before the
DW is nucleated.
19
This current source (courtesy of David Bono) has a response time of <5 ns and therefore has
a fast enough compliance to voltage shift presented to the output terminal by the nucleation pulse
generator.
92
to distinguish two types of coercive fields in the nanostrip: the field Hp,,op required to
propagate a DW and the field H,,e required to nucleate a reverse domain. Provided
that Hprop < Hnue, Hprop is equivalent to the coercive field observed when a DW is
initialized with the nucleation pulse, whereas Hnuc is the coercive field with no initial-
ized DW. The sweeping frequency (-10 Hz) and amplitude (-100 Oe) of the driving
field in this thesis are low enough that Hprop is typically governed by thermally activated motion in a nonuniform pinning potential landscape. The change in Hprop as a
function of injected current density establishes an equivalence between driving field
and current, which therefore is a measure of the efficiency of current-induced effects
on DW motion.
As described in Sec. 3.5 and subsequent chapters, DW dynamics in the thermally
activated regime can be heavily affected by the sample temperature, even if its fluctuation is -1
K. Therefore, a thermoelectric module with a feedback mechanism is used
to maintain the sample substrate temperature to within ±0.2 K or less. This thermoelectric module is installed directly on top of the electromagnet described above. The
sample substrate and the K-type thermocouple that measured the sample substrate
are both fixed on the module with thermal paste. All measurements described in Sec.
3.5 were conducted at a setpoint temperature of 300 K.
3.5
Measurements of Domain-Wall Dynamics in
Nanostrips
Here, we show that the MOKE technique reveals two distinct regimes of DW dynamics
in a 500-nm wide Co/Pt multilayer 20 nanostrip, patterned using the lithographic
procedure described in Sec. 3.3. The strong perpendicular anisotropy in Co/Pt leads
to a narrow DW, only a few nm wide, that can interact strongly with nanoscale
defects constituting a nonuniform potential energy landscape within the nanostrip
(e.g. edge/topographical roughness, grain boundaries, voids). Under a small driving
20
Si / SiO 2 (500) / TaOx(40) / Pt(16) / [Co(tCo)/Pt(10)]2 / Co(tc,)/ Pt(16), where numbers in
parentheses indicate thicknesses in A
93
10pm
-- PG1
(
il
DC-1/ PG2
Osc
Figure 3-11: Experimental scheme for measuring domain-wall motion, superposed
on a scanning electron micrograph of a nanostrip device. The pulse generator (PG1)
outputs the nucleation pulse and is monitored by the oscilloscope (OSC). A nucleated
DW is driven along the magnetic nanostrip by the out-of-plane field and detected as
it passes through the focused laser spot (MOKE). A driving current may also be
injected through the magnetic nanostrip with a DC current source (DC-I) or another
pulse generator (PG2).
force, a DW is subject to pinning by the pinning landscape and moves by the thermally
activated process of creep or depinning. In this regime, DW motion is expected to be
slow (v < 10 m/s) and stochastic. Under a sufficiently large driving force, a DW is
affected minimally by the pinning landscape and thus flows with a constant mobility
g = v/H, where v is the DW velocity and H is the driving field.
The stochasticity of thermally activated DW motion in the low drive-field regime
is illustrated in Fig. 3-12. Single-shot MOKE signal transients measured at the
same position and driving field (Fig. 3-12(a)) show magnetization switching due
to DW motion at different times, some with intermediate steps corresponding to
pinning within the probed region. This stochastic DW motion is manifested in a
distribution of switching times t,,, defined as the time at which the normalized MOKE
signal switches sign. The histograms at two different probed positions on the strip
(Fig. 3-12(b)) show that the distribution of to, is broader and skewed toward longer
times farther away from the point of DW nucleation. Averaged curves of 100 MOKE
transients (Fig. 3-12(c)) become exponential-decay curves, again showing greater
94
(a) 1.
t$ 101
s
00 5 1
15 20
101
2
1
t(mr)
(msE)
Sm)t
(c)
(b)
__
..
t (ms)
_
_
_
_
_
_
601
lb112-1m
6U 0 4' x =2.8
020
0
4 580
120 6m
x =8.8jpm
0.
.-.
--
1.02
te (ms)
te (ms)
20
-15
t (ins)
Figure 3-12: Stochastic nature of thermally activated DW motion, measured at driving field H=152 Oe. (a) Single-shot MOKE signal transients measured at x = 8.8
ptm. (b) Distribution of switching times tp due to DW motion 2.8 and 8.8 um away
from the point of DW nucleation. (c) Averaged DW transients at different points on
the strip (each an average of 100 transients). The inset shows a plot of average DW
arrival time ti/2 against probed position, with the linear fit used to estimate the DW
velocity v =4.9 x 0- in/s.
breadth with increasing distance from the point of DW nucleation. The average DW
arrival time ti/ 2 is defined as the time at which the probability of switching due to
DW motion is 50%, i.e. half life of the exponential decay. Unless otherwise indicated,
averaged MOKE transients were measured x
=
8.8pm away from the point of DW
nucleation, so that the average DW velocity was calculated as v
x/ti/2 .
For faster DW motion, with arrival times approaching the time scale of the ~ 25
ns nucleation pulse, the MOKE signal was measured at six different positions along
the strip. To gain a sufficient signal-to-noise ratio on the high bandwidth channel,
the MOKE signal was averaged over 500 cycles. Averaged transients at driving fields
H < 220 Qe as illustrated in Fig. 3-13(a) are fitted well with exponential decay
curves, with greater temporal spread in transient signals farther away from the point
of DW nucleation. As shown previously by the low-bandwidth measurements, the
exponential decay profiles exhibiting greater breadth with increasing distance from the
95
(a)
(b)
1.0
0.5
W 0.0-2.m
wO.
0-0.5
A
-1.0
*
2.8 gm
2.8 pm
10.8 m
4.8 pm
6.8 pm
-8.8 pm
0 1 2 3 4 5 6 7 8
0.00.20.40.60.8 1.0
t (gs)
4.0
t (ps)
(C)
0 195 Oe
* 200 Oe
A 203 Oe
y 209 Oe
* 215 Oe
221 Oe
P 227 Oe
3.0
'
2.0
1.0 0.0
233
.
0
2
4
6 8
x (pm)
Oe
10 12
5.6
Figure 3-13: Averaged reversal transients at driving fields (a) H = 200 Oe (v
m/s) and (b) H = 233 Oe (v = 21.6 m/s), measured at different positions away from
the point of DW nucleation. The continuous curves show (a) exponential decay and
(b) error function fits to the data. (c) Plot of average DW arrival time ti/ 2 as a
function of probed position. DW velocities are extracted from linear fits.
nucleation point emerge from a statistical distribution in DW arrival times, indicating
that DW motion is stochastic and thermally activated in this field regime. The DW
arrival time t 1 / 2 is plotted against probed position, and the DW velocity was extracted
by linear regression, as shown in Fig. 3-13(c).
At higher driving fields H > 220 Oe, the averaged MOKE transients (Fig. 313(b)) are better fitted with error function curves. The temporal width of the averaged reversal transients, on the order of 100 ns, is independent of the probed position,
indicating that DWs passed through the probed regions deterministically. The velocity is again extracted by linearly fitting the DW arrival time ti/ 2 (half way time of the
error function curve) versus probed position (Fig. 3-13(c)). At the highest driving
field shown 2 1 , the DW velocity exceeds 20 m/s. The ratio of the laser spot size to
21
At even higher fields H > 235 Oe, spontaneous nucleation of DWs became prevalent, and it was
not possible to correlate DW transit time with respect to probed position.
96
(a)
(b)
2
,
,
10
,25
20-
100
102
E'O10~-
CO15
E'1
>
I
10010
100
140 180
H (0e)
0
220
50
100 150 200 250
H (0e)
Figure 3-14: Field-driven domain-wall mobility in a Co/Pt multilayer nanostrip. (a)
DW velocity v plotted on a logarithmic scale against driving field H. (b) v plotted
on a linear scale against H, with the line serving as a guide for the eye to estimate
the DW mobility p ~ 0.09 m/(s Oe).
the temporal width of the reversal transients (Fig. 3-13(b)) roughly corresponds to
this extracted velocity, implying that the width of the reversal transients resulted
from DW transit time through the Gaussian spot profile, rather than the statistical
distribution in arrival times due to stochastic motion. As DWs move rapidly and
deterministically, these data indicate that DW dynamics in this driving field range
are in the viscous flow regime.
In Fig. 3-14, we lastly present the measured velocity-field characteristic for DW
motion in this Co/Pt strip for a field range spanning 104-233 Oe, corresponding to
nearly eight decades in DW velocity. Up to H ~ 220 Oe, the DW velocity increases
exponentially with the driving field. Since thermally activated dynamics follow an
Arrhenius-type relation v ~ exp(-E(H)/kBT), where E(H) is the activation energy
barrier determined by the driving field, the exponential increase in velocity is another
indication that DW motion is thermally activated at H < 220 Oe. Above H > 220
Oe, the DW velocity scales much more weakly with field, approaching a linear v-vs-H
characteristic. DW motion above this critical field is therefore governed by viscous
flow dynamics, consistent with the MOKE transient measurements. From these data,
we estimate a DW mobility (pu = v/H) of 0.09 m/(s Oe), comparable to the mobility
extracted from domain expansion measurements in a continuous Pt/Co/Pt thin film,
~ 0.04 m/(s Oe), reported in [16].
97
3.6
Summary
Using MOKE polarimetry and VSM, we verify that Co/Pt multilayers, particularly
those deposited on Ta and TaOx buffer layers, exhibit strong perpendicular magnetic
anisotropy. Electron-beam lithography is used to fabricate submicron-wide tracks
(nanostrips) of magnetic thin film, within which DWs can be initialized and moved.
The custom time-resolved scanning MOKE polarimeter - equipped with a focused
laser spot, a high-resolution scanning stage, a high-bandwidth detector, and a substrate temperature controller - allows for flexible and reliable measurements of DWs
propagating along magnetic nanostrips. Using the MOKE technique on a Co/Pt
nanostrip, distinct dynamics of DWs in the thermally activated and viscous flow
regimes are revealed.
98
Bibliography
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Ph.D. thesis (2001).
[2] Beach, G. S. D. The Co_{x}Fe_{00-x} Metal/Native Oxide Multilayer. Ph.D.
thesis, University of California, San Diego (2003).
[3] Blundell, S. Magnetism in Condensed Matter (Oxford University Press, USA,
2001), 1 edn.
[4] O'Handley, R. C. Modern magnetic materials: principles and applications (Wiley, New York, 2000).
[5] Spaldin, N. A. Magnetic materials: fundamentals and device applications (Uk
Cambridge university press, Cambridge; New York, 2003).
[6] Lin, C.-J. et al. Magnetic and structural properties of Co/Pt multilayers. Journal
of Magnetism and Magnetic Materials 93, 194-206 (1991).
[7] Knepper, J. W. & Yang, F. Y. Oscillatory interlayer coupling in Co/Pt multilayers with perpendicular anisotropy. Physical Review B 71, 224403 (2005).
[8] Fukami, S., Suzuki, T., Tanigawa, H., Ohshima, N. & Ishiwata, N. Stack Structure Dependence of Co/Ni Multilayer for Current-Induced Domain Wall Motion.
Applied Physics Express 3, 113002 (2010).
[9] Kanak, J. et al. Influence of buffer layers on the texture and magnetic properties
of Co/Pt multilayers with perpendicular anisotropy. physica status solidi (a)
204, 3950-3953 (2007).
99
[10] Johnson, M. T., Bloemen, P. J. H., Broeder, F. J. A. d. & Vries, J. J. d. Magnetic
anisotropy in metallic multilayers. Reports on Progress in Physics 59, 1409-1458
(1996).
[11] Zhang, B., Krishnan, K. M., Lee, C. H. & Farrow, R. F. C. Magnetic anisotropy
and lattice strain in Co/Pt multilayers. Journal of Applied Physics 73, 6198
(1993).
[12] Allwood, D. A., Xiong, G., Cooke, M. D. & Cowburn, R. P. Magneto-optical
Kerr effect analysis of magnetic nanostructures. Journal of Physics D: Applied
Physics 36, 2175-2182 (2003).
[13] Nistor, C., Beach, G. S. D. & Erskine, J. L. Versatile magneto-optic Kerr effect
polarimeter for studies of domain-wall dynamics in magnetic nanostructures.
Review of Scientific Instruments 77, 103901 (2006).
[14] Beach, G. S. D., Nistor, C., Knutson, C., Tsoi, M. & Erskine, J. L. Dynamics of field-driven domain-wall propagation in ferromagnetic nanowires. Nature
Materials 4, 741-744 (2005).
[15] Hubert, A. & Schafer, R.
Magnetic domains: the analysis of magnetic mi-
crostructures (Springer, Berlin; New York, 1998).
[16] Metaxas, P. J. et al. Creep and Flow Regimes of Magnetic Domain-Wall Motion
in Ultrathin Pt/Co/Pt Films with Perpendicular Anisotropy. Physical Review
Letters 99, 217208 (2007).
[17] Ryu, K.-S., Thomas, L., Yang, S.-H. & Parkin, S. S. P. Current Induced Tilting
of Domain Walls in High Velocity Motion along Perpendicularly Magnetized
Micron-Sized Co/Ni/Co Racetracks. Applied Physics Express 5, 093006 (2012).
100
Chapter 4
Thermally Activated Domain-Wall
Motion in Co/Pt Multilayers
Multilayers consisting of thin Co (<1 nm) embedded in Pt are prototypical out-ofplane magnetized materialsystems, which has been used for a few decades as magnetooptical and perpendicular-recordingmedia, as well as components in spin valves and
magnetic tunnel junctions more recently.
Current-induced domain-wall motion in
Co/Pt multilayers have also been studied in hopes of attaining enhanced efficiencies
of spin-transfer torques. However, experimental results have been inconclusive up to
now, as summarized in Sec. 2.6. An obvious route to enhance spin-transfer effects
is to direct a larger fraction of current into the ferromagnetic Co layers, thereby
increasing the effective spin polarization of the driving current. In this chapter, we
investigate domain-wall dynamics in two Co/Pt multilayers with different Co-layer
thicknesses. Surprisingly, no spin-transfer torque is evidenced in the multilayer with
the thicker Co layers, suggesting a spin-torque mechanism distinct from conventional
spin-transfertorques may be dominant in Co/Pt-based materials.1
2
'The contents of this chapter has been submitted for publication as:
Emori, S., Umachi, C. K., Bono, D. C., & Beach G. S. D. Thermally activated domain-wall motion
in Co/Pt multilayers: Beyond conventional creep scaling and spin-transfer torques.
2
The Arrhenius analysis of thermally activated DW motion was originally developed in:
Emori S. & Beach G. S. D. Roles of magnetic field and electric current in thermally activated domain
wall motion in a submicrometer magnetic strip with perpendicular magnetic anisotropy. Journal of
Physics: Condensed Matter 24, 024214 (2012).
101
4.1
Thermally Activated Domain-Wall Dynamics
In viable solid-state devices, domain walls (DWs) in patterned magnetic strips must
be moved over micrometer-scale distances rapidly and unidirectionally, e.g. through
spin-transfer torques (STTs). Out-of-plane magnetized materials with perpendicular magnetic anisotropy (PMA) have recently gained considerable attention due to
reports of small threshold current densities for continuous DW motion. Rapid DW
motion in the flow regime (Fig. 4-1(a)) with velocities of -10-100 m/s have been
achieved by injecting large current pulses (Je
rents
(IJel
<
~ 10" A/m 2 ). By contrast, low cur-
101 A/M 2 ) typically drive DWs by the thermally activated process of
creep or depinning (Fig. 4-1(a)) through a pinning potential landscape (Fig. 4-1(b)).
The velocity v (or depining rate) of thermally activated DW motion expressed by
the general Arrhenius relationship
=
v Voexp
(,kB
(4.1)
kBT
where
kB
is the Boltzmann constant, T is the sample temperature, and vo is the
pre-exponential factor. Because of this exponential relationship, the DW velocity (or
depinning rate) is sensitive to even small variations in temperature. The activation
energy EA depends on the effective driving field Heff, which can be generalized to
include both an externally applied magnetic field H and current-induced spin-torque
effects. Nonadiabatic STT pushes a DW directly in the direction of the spin-polarized
electron flow, and acts as a field-like term proportional to the current density Je. Adia-
batic STT distorts a DW within a pinning potential and facilitates DW displacement
irrespective of the current polarity, so that its influence can be modeled as
Je 2 .
When these are combined, the effective field takes the form Heff = H + EJe + cJe2
where c and c are coefficients related to the nonadiabatic and adiabatic STT, respectively. The efficiencies of spin-torques may be extracted by examining the functional
dependence of the activation energy barrier on the driving current.
This is often
performed by analyzing the DW velocity within the framework of a particular creep
scaling model. However,
EA
can also be extracted directly from Eq. 4.1 through an
102
(a)(b
depinning
flo
'0000
o
0.
CL
0
driving force (H and/or J.)
DW
~10 nm
DW position
Figure 4-1: (a) Three distinct regimes of domain-wall (DW) dynamics, driven by
external magnetic field H or injected electron flow Je. (b) Cartoon of thermally
activated DW motion through a nanoscale defect (pinning) potential landscape.
Arrhenius analysis, i.e. fitting ln(v) against T- 1 , from which its dependence on driving forces can be evaluated empirically without assuming a particular model of creep
scaling. 3
We present a comprehensive study of field- and current-driven thermally activated DW motion in out-of-plane magnetized Co/Pt multilayers. From temperaturedependent measurements spanning up to 8 decades in DW velocity, we directly extract
the activation energy over a wide range of driving field, from deep in the creep regime
up to the viscous flow regime. Further analysis of the activation energy as a function of
driving field reveals a nontrivial dependence on the Curie temperature of the sample.
By incorporating this newly found temperature contribution, we empirically derive a
modified Arrhenius-like relationship that determines the DW velocity as a complete
function of driving field and temperature. From this Arrhenius-like relationship and
the current dependence of the activation energy, we quantify the effects of current on
DW motion as an effective driving field. Our results demonstrate limitations of the
universal creep scaling law and the robustness of the direct analysis of the activation
energy.
Furthermore, the spin-torque efficiencies for Co/Pt multilayers with different Co
layer thicknesses resolve the disparity in recent studies of current-induced DW dynamics in Co/Pt, some reporting high spin-torque efficiencies of over 10 Oe/1011
3
Many works on Co/Pt multilayers assume a creep scaling
exponent of p = 1/4, such that
EA ~ H-.
103
A/M
2
while others showing no effects other than Joule heating (as discussed in Sec.
2.6. Our results suggest that the in-plane current through the ultrathin ferromagnetic layers attains a vanishingly small effective spin polarization. Consequently, in
ultrathin Co/Pt-based structures, conventional spin-transfer torques (STTs) within
the "bulk" of the ferromagnets are likely not present, and instead another type of
current-induced torque arising from "interfaces" likely drives DWs.
4.2
Experimental Methods
500-nm wide Co/Pt multilayer strips with electrodes were fabricated using electronbeam lithography, sputtering, and liftoff (Secs. 3.3). The multilayer structure was
Si / Si0 2 (500) / TaOx(40) / Pt(16) / [Co(tco)/Pt(10)12 / Co(tc,)/ Pt(16), where
numbers in parentheses indicate thicknesses in
A. The
Pt layer thicknesses and TaOx
underlayer were optimized in an attempt to maximize current flow through the ferromagnetic Co layers while maintaining strong PMA (see Sec. 3.2.3).
results for to
=
7
A
We present
and 3 A the upper and lower limits, respectively, at which
the remanent magnetization was fully out of plane and the DW nucleation field H,,e
exceeded the propagation field. H,,, was ~230 Oe for t 0 0 =7
A and
~35 Oe for t0 0 =3
A which set the maximum driving field at which the DW velocity could be measured.
The DW velocity was measured as a function of field, current, and temperature
using a high-bandwidth scanning magneto-optical Kerr effect (MOKE) polarimeter
(Sec. 3.4). The measurements tracked DW propagation along a 10-um strip segment
at timescales spanning up to 8 decades, following the procedure described in Sec.
3.4 and illustrated in Fig. 3-11. In some measurements (Sec 4.5), DW motion was
assisted by an in-plane DC current Je injected through the Co/Pt strip. The substrate
temperature T was controlled to an accuracy of ±0.2 K with a thermoelectric module.
For each driving parameter set (H, Je, T), the MOKE transient signal was averaged over at least 100 cycles to account for the stochasticity of thermally activated
DW motion. These averaged MOKE transients (Fig. 4-2) represent probability distributions for magnetization switching due to DW motion. The insets of Fig. 4-2 show
104
(a)
(b)
1.0 -
0.5 -
0
0.0
3
0
0.0
- , -
, , - ,
1.0
0.5
4
8
1.0
t (s)
1.5
0.
U.06-
12
0.0
2.0
0.00
0.0
0.5
4
1.0
1.5
t (Ps)
12
2.0
Figure 4-2: Examples of averaged MOKE transients for the tc,= 7 A strip at T =
300 K and (a) H = 123 Oe and (b) H = 230 Oe. The insets show linear fitting for
average arrival time tO.5 versus probed position.
the average DW arrival time, taken as the time to.5 corresponding to 50% switching
probability, plotted against probed position along the strip. The linear increase in to.5
versus position implies a uniform average DW velocity governed by a fine-scale disorder potential rather than discrete pinning sites. The distinct profiles of the MOKE
transients between Figs. 4-2(a) and (b) indicate a transition from stochastic to deterministic DW propagation (Sec. 3.5) as the driving field is increased beyond the
strength of the pinning potential.
4.3
Field-Driven Domain-Wall Motion
The DW velocity with zero driving current was measured over a range of driving
field and several sample temperatures. The 7-A sample exhibited substantial pinning
strength so that a driving field of over 100 Oe was required to move DWs at v > 106
m/s (Fig. 4-3(a)). By contrast, DW motion was detected at fields <10 Oe in the 3-A
strip (Fig. 4-3(b)). 4 As shown in Figs. 4-3(a) and (b), the measured DW velocity
spanned several decades. The velocity at low driving fields increased by more than
an order of magnitude with a small temperature difference of 24 K for to0 = 7
A and
9 K for tc
0 = 3 A. This large change in the DW velocity with both the driving field
4H was adjusted, taking into account the small out-of-plane remanent field of the electromagnet
core, to generate linear ln(v) versus H-1/ 4 relations in Fig. 4-3(d).
105
10 2
(a)
-2
lu0
(b)
100
10-1
1-2
10-2
~
10
E 10
E 10-4
I
1
3
10 -4
10-6
10
10-8
10 -61
180 322
140
100
5
0
I
I
10
20 30
H (0e)
H (0e)
4
0
(C)
E
>
(d)
--
3
-9
-12-
0.26
0.28
0.30
0.32
N0.4
H1 /4 (Oe)
4 . ...........
0
(e)
0.6
(Oe
0.7
4
0-
(f)
-
-3
E -6
-8
-9
-12
-16
0.5
H1/4
-4-
.
40
E -6-
-
-12
-16
]
K
K
K
K
I
0
-4
-8
306
303
300
-- 297
I .
-12
0.0008
0.0009
HT1/4
1.6
1.2
0.0010
1 (Oe14K)
H-114
2.0
(1030e1/K
2.4
)
Figure 4-3: Field-driven domain-wall velocities in Co/Pt multilayers. (a, b) DW
velocity v as a function of driving field H at zero current at several different sample
temperatures for the to0 = 7 A (a) and 3 A(b) samples. (c, d) ln(v) plotted against
H-1/ 4 in accordance with the conventional creep scaling p = 1/4 for the to0 = 7 A
(c) and 3 A(d) samples. (e, f) ln(v) plotted against H- 1/ 4 T 1 showing the failure of
the conventional creep scaling for the to0 = 7 A (e) and 3 A(f) samples.
and sample temperature is a key characteristic of a thermally activated process.
In Figs. 4-3(c) and (d), the DW velocity curves are plotted against H- 1/ 4 , following the conventional creep scaling in which the activation energy in Eq. 4.1 scales
as EA
-
H-0 with the creep exponent yu = 1/4 [1, 2, 3, 4]. Each mobility curve at
a fixed temperature appears to be well described by a constant slope in ln(v) versus
H-'/4 over several decades of velocity. For the creep scaling of P = 1/4 to be valid,
4.1 implies that the mobility curves at different temperatures should collapse on top
each other if they are re-plotted as ln(v) versus H- 1/ 4 T- 1 . However, this is clearly
106
(a)
4 -'5
be'
1.6
(C)
E ~-H
1.2
0
E -
L 0.8
160 Oe ~
-8135
Oe
~1
E ~H_
0.4
-E
~-(H,-H)
-12-15O.
3.1
3.2
3.3
0.0
3.4
140
100
10 3T (K')
(b)
220
3.0
(d)
0 -270e
20 Oe
2.0
14 Oe
-
180
H (Oe)
E
5;
-
H
1.0
8 ce
EA~H
-93.2
3.3
0.0
3.4
3
0
10
10 T' (K)
20
30
40
H (Oe)
Figure 4-4: Activation energy for field-driven domain-wall motion. (a, b) Extraction
of activation energy by fitting DW velocity against inverse temperature for the to =
0
7 A (a) and 3 A (b) samples. (c, d) Plot of activation energy versus driving field for
the to0 = 7 A (c) and 3 A (d) samples.
not the case, as the mobility curves do not collapse for either to0 = 7 A (Fig. 4-3(e))
or to0 = 3 A (Fig. 4-3(f)). The conventional creep scaling therefore does not apply
in any range of the driving field examined in this study.
Instead of attempting to adjust the scaling exponents to better collapse the data,
we directly extracted the activation energy from the slope of ln(v) versus T- 1 (Figs.
4-4(a) and (b)). The validity of the linear fit confirms our assumption that the
activation energy is invariant with temperature in the measured range, although a
Curie-temperature-dependent correction needs to be incorporated for rigorous analyses as described in Section 4.4. The values of the activation energy plotted in Figs.
4-4(a) and (b) are of similar magnitude with those reported previously for DW depinning [5] and continuous DW motion [6], and decrease monotonically with increasing
field as expected.
107
However, for to, = 7 A, EA does not follow a simple creep power law scaling
with p
1/4, despite the linear isothermal ln(v) versus H-/4 curves in Fig. 2(c).
=
In the lower field range (H < 180 Oe), EA scales instead with an exponent p = 1,
which corresponds to the "random-field" universality class similar to the experimental
and theoretical findings in a GaMnAs ferromagnetic semiconductor, [7] but different
from p = 1/4 ("random-bond") widely used in previous studies of Co/Pt[1, 2, 3, 4]).
Due to its larger thickness, the 7-A Co/Pt multilayer possibly does not behave as a
two-dimensional DW medium, a prerequisite to the creep dynamics with p = 1/4 [1].
The scaling of EA with H in the 3-A strip cannot be described by a single powerlaw exponent, indicating that a single model of creep scaling cannot accurately capture
the DW dynamics. These results suggest that in real samples, the defect potential is
likely more complex than can be accounted for by a simple scaling model. Nonetheless,
the directly extracted activation energy curves in Figs. 4-4(c) and (d) can be taken as
the fingerprint of DW interactions with defects, which allows the thermally activated
dynamics to be described without initially assuming any particular scaling model. We
will show that this empirical approach, developed further in Section 4.4, allows for a
direct quantitative assessment of the influence of current on DW motion as shown in
Section4.5.
At a sufficiently large driving force, the general scaling of creep breaks down
and the activation energy vanishes. Although such breakdown of creep could not
be observed for the 3-A sample due to spontaneous nucleation of magnetic domains
at H
) 35 Oe, the DW dynamics of the 7-A sample indeed deviates significantly
from creep above H _ 180 Oe. Here, the activation energy follows the simple linear
relationship of depinning [8], described by EA = 2VAMs(H, - Heff), where VA is the
activation volume, Ms is the saturation magnetization, and He, is the effective critical
depinning field. Taking Ms = 1700 emu/cm3 (Sec. 3.2.3 and [9]), H, = 220 Oe,
2VAMs = 0.017 eV/Oe (slope from Fig. 4-4(b)), and the effective magnetic thickness
teff = 3tco = 2.1 nm, we obtain a characteristic activation length LA =
\VA/teff
-
62 nm, in line with _50 nm estimated for a similar Co/Pt multilayer strip with t0O = 6
A
[6]). The activation energy vanishes at Hc, = 220 Oe, above which DW motion
108
(a)
30 -
(c)
.
-1.2-
-
20
1.6
- 40
330
0.8 -
10
0.4
0
20
-10
0.0
(b)
1.0
80
2.0
103T-1 (K-')
3.0
100
..............
(d)
140
180
H (0e)
220
3.0
100
60
-80
40
p2.040600<
-
-
E'i~
>20
1.0
0
-20
-20 - . . .
0.0
40 -
1.0
. . .
. . .
.
0.0
-
3.0
2.0
103 T1 (K1)
0
10
20
H (0e)
30
40
Figure 4-5: Failure of the assumption of a constant pre-exponential v,. (a, b) Arrhenius plots displaying the same data as Fig. 4-4, showing the extrapolated fit lines do
not converge at T- 1 = 0 for both the (a) 7-A and (b) 3-A samples. (c, d) Dependence
of ln(v,) with H, which tracks the dependence of EA with H, for both (c) 7-A and
(d) 3-A samples.
is governed by viscous flow rather than thermal activation. This is consistent with
the finding in Sec. 3.5 in which the DW dynamics became viscous and deterministic
above this critical field. The transition from creep to depinning to viscous flow is seen
directly in the activation energy as a function of driving field (Fig. 4-4(c)), whereas
it is not evident in the DW velocity at a fixed temperature (Fig. 4-3(a)).
4.4
Generalized Arrhenius-Like Relation
The pre-exponential factor v, in the Arrhenius relationship (Eq. 4.1) is extracted
from the intercept of the Arrhenius plot at T
1
= 0.
In the analysis described
previously, the pre-exponential was assumed to be a constant with respect to driving
field. However, the extrapolated fit lines of ln(v) versus T
1
at different driving fields
shown in Fig. 4(a, b) diverge significantly at T- 1 = 0, indicating clearly that the
109
2000
to
l
E
L.)
1500
1000
t0 =3A
500 -
01
300 450
T (K)
150
0
600
Figure 4-6: Saturation magnetization as a function of temperature. The solid curves
show fits to estimate the Curie temperature for each sample.
intercept ln(v,) is not constant. Interestingly, as shown in Fig. 4(c, d), ln(v0 ) and the
activation energy plotted as a function of the driving field track each other almost
perfectly when they are scaled linearly with respect to each other. The relationship
between ln(v0 ) and the activation energy can be written as
(4.2)
ln(v,) = a + bEA,
where a and b are linear scaling constants. Substituting Eq. 4.2 into Eq. 4.1, we
derive a generalized Arrhenius-like equation
V = Aexp
-- E(4T3)
1
,(43
where T, = 1/bkB and A = exp(a) is the corrected pre-exponential constant independent of driving field and temperature.
Here, EA is the effective activation energy within a narrow range of measured
temperature such that the Arrhenius plot produces an approximately constant slope,
as shown in Fig.
3.
In reality, the activation energy scales with the saturation
magnetization Ms and must vanish at the Curie temperature Tc.
The corrected
by
activation energy therefore should be EA* = EA(1 - T/TC), which is satisfied
of
Eq. 4.3 if TC = T,. We estimated TC by measuring the temperature dependence
MS with vibrating sample magnetometry on continuous multilayer films. As shown
110
Table 4.1: Parameters in the generalized Arrhenius-like equation (Eq. 4.4) to quantify
effects of current on DW motion
EA
3A
7A
to
(eV)
C
H < 180 Oe
H > 180 Oe
eff
CH 1
Hef)/H4
C(Hcr - Heef)
H < 13 Oe
H > 13 Oe
130 eV Oe
0.017 eV/Oe
CfH
3.5 eV Oe- 1 4
CH23 eV Oe
220
-
-
Hr (Qe)
Tcr (K)
A(m/s)
h(K/[10"A/m
2 2
)
580
340
2.2 x 10 4
2.5
7.4
2.2
in Fig. 6, by fitting the data with a scaling of the form (1 - T/TC)7, where -y is
an empirical fitting exponent, T0 of the 7-A and 3-A samples were estimated to be
620±70 and 360±20 K, respectively. By comparison, the scaling of ln(vo) and EA
(Fig. 4-5 and Eq. 4.2) yielded Tc, = 580 and 340 K for the 7-A and 3-A samples,
respectively. Since these two independently measured quantities are in reasonable
agreement with each other, we conclude that Tcr _ TC and the corrected activation
energy for DW motion is EA* r EA(1
4.5
-
T/TC).
Current-Induced Effects
Using the generalized Arrhenius-like equation derived in the previous section, we
investigated the roles of current on DW motion. To distinguish thermal and spintorque effects, we first quantified Joule heating in the Co/Pt strips. By measuring
the electrical resistance with respect to current density Je and substrate temperature
Teub
set by the thermoelectric module, the sample temperature was found to increase
quadratically with Je from Joule heating as AT = h J2, where h = 2.5 and 2.2 K/[10"
A/M 2] 2 for the 7-A and 3-A samples, respectively. In extracting the activation energy,
the actual temperature of the sample was used so that T = T,,b - AT.
Current-driven DW motion was assisted with background driving fields, whose
values were chosen to investigate each distinct dynamic regime found from field111
driven DW measurements (Fig. 4-4). The driving electron current density Je was
estimated by assuming a uniform current distribution across the total conductive (Co
and Pt) cross-sectional area, and we defined Je > 0 when electron flow was in the
same direction as field-driven DW motion (left to right in Fig. 3-11). The maximum
IJeI was limited to < 10" A/M 2 to minimize electromigration in the multilayers.
We now incorporate the effects of injected current in the Arrhenius-like equation
(Eq. 4.3):
v = Aexp (
[I + h Je2] I
EA1
(kB[Tsub
Tsub.hJe2
cr
(4.4)
_)
Here, the activation energy is expressed a function of the effective driving field Heff
=
H + J, where c is the spin-torque efficiency, and the sample temperature includes the
Joule heating effect. This is a complete equation for thermally activated DW motion
where the DW velocity is a function of field, current, and substrate temperature.
Table 4.4 lists the empirical parameters from the measurements of field-driven DW
motion (Sec. 4.3). These parameters were then substituted into Eq. 4.4, and the
spin-torque efficiency c was extracted by fitting Eq. 4.4 to the DW velocity data.
For the 7-A sample, the DW velocity increased by only 10% in both polarities
in the thermally activated regime (e.g. H = 190 Oe in Fig. 4-7(a)) and exhibited
no systematic change in the viscous flow regime (H = 230 Oe). Fitting the velocity
data with Eq. 4.4 reveals that c is at most -0.2 Oe/1011 A/M 2, with the negative sign
indicating that DW motion was facilitated slightly against the direction of electron
flow. This vanishingly small current-induced effect was verified with the activation
energy for DW motion, which shows no systematic variation with current density (Fig.
4-7(a)). Thus, in the 7-A sample, current increases the DW velocity through Joule
heating but generates a negligible spin-torque effect. Pinning alone cannot explain
the very low spin-torque efficiency because no significant current-induced effect on
DW motion was observed even when the pinning was nullified at H = 230 Oe. The
lack of spin-torque effects in this Co/Pt multilayer instead arises from a vanishingly
small spin-polarized current in ultrathin Co, as shown rigorously by Cormier et al.
[10].
112
(a)
(a
L4-'I
_
Oe
24 -=230
20
L- O0
_r
298K
-
(b)
16
0.0511
H16e
0.04 -
0.03 -1
SH =190 Oe
310 K
300 K
297 K
0
294 K
.0
0.02
304 K
>3
1
V303 K
303K
2
0.01
1
298
1.6
H =115
1.2
0.00
Oe
2.0 - H
~
8 OeI
1.6--
H =16 Oe
<0.8-
w 1.2
H =1900e
0.4
t-=
-1.0
-0.5
Je
H=300e
e-
0.80.0
0.5
1.0
-1.0
2
-0.5
0.0
0.5
1.0
2
J, (1011 A/m )
(1011 A/m )
Figure 4-7: Domain-wall velocity and activation energy versus current density for to0
= 7 A (a) and tc, = 3 A (b). With Je > 0, the electron flow is in the same direction as
field-driven DW motion. Solid curves in the velocity plots are fits using the canonical
equation (Eq. 4.4) with the spin-torque efficiency e adjusted.
On the other hand, as shown in Fig. 4-7(b), a clear shift in the DW velocity with J
was observed in the 3-A sample. This significant change is similar to the exponential
relationship between the DW velocity and driving field (Fig. 4-3(b)), suggesting that
current generates a spin torque on a DW that can be equated to an out-of-plane field.
Fitting of Eq. 4.4 to the DW velocity data produced a spin-torque efficiency of e =
-2.6±-0.8 Oe/10" A/M 2 . Despite this clear current-dependence on the DW velocity,
the variation of the activation energy with current density AEA/AJe was at most
0.1 eV/10" A/M
2
(Fig. 4-7(d)), which is too small to elucidate any nonlinearity in
the activation energy[5] (see further discussion in Sec. 4.7) for the narrow range of
current density in this present study. The activation energy as a function of current
density Je at a fixed driving field H can be approximated to first order, assuming a
113
small EJe so that Heff ~ H:
EA(Heff )IHo=
EA(Je)
Ho
EA|Ho +
dEA
d H
EAH+
dHHo
6
dEA
dHeff
Je
Ho
Je.
(4.5)
Therefore, the spin torque efficiency can be estimated by
AEA
OEA
&HHo '
A Je
where aEA/aHH was calculated from the experimental data (Table 4.4).
(4.6)
Using
Eq. 4.6, we obtain c = -1.2±0.6 Oe/10" A/M 2 . The spin-torque efficiency in the
Pt/(Co/Pt) 3 multilayer with to0 = 3
A
is on the same order of magnitude as the
typical efficiency in permalloy [11], but about an order of magnitude smaller than the
efficiencies reported by some prior studies on Co/Pt structures [12, 13, 14, 15, 16].
4.6
Origin of Current-Induced Torques in Co/Pt
Current-induced DW motion has usually been attributed to adiabatic and nonadia-
batic spin-transfer torques (STTs) [17, 18, 19]. Adiabatic STT drives DWs in thick
(>
1 nm) out-of-plane magnetized structures, e.g. Co/Ni mulitlayers, and its sym-
metry is distinct from an external magnetic field [20, 21, 22, 23, 24]. The mechanism
(or the existence) of nonadiabatic STT is controversial, but its symmetry is known
to be equivalent to an external field that drives a DW [17, 18]. The magnitudes of
adiabatic and nonadiabatic STTs scale with the spin polarization of in-plane current,
which can be large in thick Co/Ni [22, 23] but typically small in Co/Pt due to current
shunting away from Co and spin scattering by Pt [25, 26]. If either of these conventional STTs were responsible for driving DWs in Co/Pt multilayers, the spin-torque
efficiency would be larger in the 7-A sample that is expected to carry a greater spinpolarized current in the thicker ferromagnetic Co layers. Our experimental findings
are contrary to this expectation: the Co/Pt multilayer with atomically thin (3 A)
114
Co layers exhibits a finite spin-torque effect, whereas the multilayer with the larger
Co thickness (7
A) does
not. The spin polarization and therefore conventional STTs
are likely very small in these Co/Pt multilayers, as reported previously by a number
of studies [6, 16, 25, 27, 28]. The current-assisted DW motion in the ultrathin 3-A
structure does not arise from nonadiabatic STT, but rather from another spin-torque
mechanism equivalent to an effective out-of-plane magnetic field.
We also note that in the 3-A structure, DW motion is assisted against the direction of electron flow (Je < 0), opposite to the direction induced by conventional
STTs. A theoretically predicted negative spin polarization [29] or nonadiabatic STT
coefficient [30] may drive DWs against electron flow, but neither of these is applicable
if the absolute magnitude of the spin polarization is vanishingly small. The Oersted
field is not responsible for this anomalous direction of motion, because we observed
the same current-polarity dependence for both possible magnetization configurations
across the DW (down-up and up-down).
DW charging by the extraordinary Hall
effect [31] is negligible in this metallic Co/Pt strip, and hydromagnetic DW drag [31]
should move DWs in the direction of the electron flow.
Current-assisted DW motion opposing electron flow has also been reported in
asymmetric Pt/Co/Pt trilayers with thicker Pt at the bottom layer [4, 16, 32] and in
Pt/Co(ferromagnet)/oxide(insulator) trilayers with Pt at the bottom [27, 33, 34, 35].
A nonuniform current distribution due to the asymmetric layer structure may produce an internal electric potential, which then may generate an effective Rashba field
in the ultrathin ferromagnet [36, 37]. Certain combinations of nonadiabatic STT and
torques due to the Rashba field have been shown theoretically to move a DW against
electron flow [38].
However, the Rashba field scales with the spin polarization of
current [36, 37, 38], so it cannot explain the anomalous direction of motion under a
small spin polarization.
From the experimental findings in this chapter as well as in the previous studies
discussed above, we now have two questions to answer: (1) How does current move
DWs, in some cases with extraordinarily high efficiencies, even though its spin polarization is evidently small in ultrathin ferromagnets? (2) Why do DWs move in the
115
direction opposing electron flow? The experimental findings described in the following chapters reveal the mechanism behind anomalous current-driven DW dynamics
in ultrathin ferromagnets and answer these questions.
4.7
Nonlinear Current-Induced Effects
Current may influence thermally activated DW motion in a number of different ways.
As described in Sections 4.5 and 4.6, the current-induced effective out-of-plane field
modifies the activation energy unidirectionally similar to an applied field (see Eq.
4.6), whereas Joule heating enhances DW motion irrespective of current polarity
through a temperature rise that enters directly into the Arrhenius relation (Eq. 4.4).
Theoretical studies[19, 39, 40] have also predicted that adiabatic STT decreases the
activation energy for motion independent of current polarity, by distorting the DW
configuration within the pinning potential. This effect from adiabatic STT can be
modeled as a quadratic reduction in the activation energy with respect to current [40],
which was reported in a recent experimental study [5]. We show that the generalized
Arrhenius-like equation (Eq. 4.4), which incorporates the temperature dependence of
the activation energy, provides an alternative explanation for this quadratic contribution through Joule heating. Specifically, Joule heating can affect DW dynamics by
reducing the saturation magnetization, which has been considered in a few studies of
high-speed DW motion [22, 41] but never for thermally activated motion.
In Ref. [5], the activation energy E
T
was obtained from the DW depinning time
at a single pinning site, such that Ede=
A_
attempt frequency. After Joule heating T
kBTln(f0
T),
where
f,
= 10' Hz is the
TSb + hJe was included in the analysis,
there still remained a clear quadratic change in the activation energy with current
density EA ~ J,, which was attributed to adiabatic STT. This quadratic contribution from current can originate from reduced saturation magnetization if the measured
depinning energy barrier is of the form
EA7 =EA 1 -
116
)
(4.7)
which takes into account the temperature dependence of the saturation magnetization
(Sec. 4.4). Here, assuming that current generates an effective field through the SHE
(quantified by the spin-torque efficiency E), we approximate E d" at a fixed driving
field H, by substituting Eq. 4.5 into Eq. 4.7
(i
EdP(Je)Ho ~EH
+ dEA
dH
-EA|HOh
Ter
With EA
H,0
H,
2 _
e
I
dEA
dH
sub
Tsub
Je
'cr)
h J3.
H,
(4.8)
Tcr e
1 eV, h ~ 2 x 10-22 K m4 /A 2 , and Tr ~ 500 K, the coefficient of the
quadratic term in Eq. 4.8 is ~ 10-25
-
10-24
eV m4 /A 2 . This estimated magnitude
is on the same order as the quadratic coefficient extracted in Ref. [5], where the
maximum Joule heating was 30 K at IJl = 3.5 x 1011 A/M 2 . Therefore, a quadratic
dependence of the activation energy with current may be accounted for by Joule
heating, instead of adiabatic STT. The current-induced reduction of the saturation
magnetization, and hence the activation energy, may not be trivial and should be
considered in rigorous analyses of thermally activated DW motion.
4.8
Summary
Thermally activated DW motion driven by magnetic field and electric current is investigated in out-of-plane magnetized Pt(Co/Pt) 3 multilayers. From the thermal activation energy barrier for DW motion extracted directly from temperature-dependent
measurements, the distinct dynamic regimes of creep, depinning, and viscous flow are
observed. Further analysis reveals that the activation energy must be corrected with a
factor dependent on the Curie temperature, and we derive a generalized Arrhenius-like
equation governing thermally activated motion. By using this generalized equation,
we quantify the efficiency of current-induced spin torque in assisting DW motion.
Current produces no effect aside from Joule heating in the multilayer with 7-A thick
117
Co layers, whereas it generates a finite spin torque on DWs in the multilayer with
atomically thin 3-A Co layers.
These findings indicate that conventional spin-transfer torques from in-plane spinpolarized current do not drive DWs in ultrathin Co/Pt multilayers.
Instead, an
alternative mechanism must be responsible for anomalously efficient current-driven
DW motion in Co/Pt-based structures reported in the past few years. The following
chapters of this thesis describe studies that elucidate the origin of the anomalous DW
dynamics.
118
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123
124
Chapter 5
Current-Driven Domain Wall
Dynamics in Pt/Co/GdOx
Out-of-plane magnetized thin films with strong perpendicularmagnetic anisotropy are
promising platforms for solid-state magnetic devices based on electrically manipulated domain walls (DWs), because of the narrow widths and lower threshold current
densities for motion of DWs in these material systems.
The previous chapter has
revealed conclusively that Co/Pt multilayers do not exhibit the desired efficiency of
current-driven DW motion. In this chapter and the following ones, ultrathin ferromagnets with asymmetric stack structures are explored as alternatives. DWs in these
structures indeed move extraordinarilyefficient under current, and the origin of this
anomalous dynamics is investigated.1
5.1
Expected Strong Rashba Effect in Pt/Co/GdOx
Highly efficient current-driven DW motion has been observed in out-of-plane magnetized trilayer structures consisting of an ultrathin (<1 nm) ferromagnetic layer embedded between a heavy-metal Pt underlayer and an insulating overlayer such as Al-oxide
'This chapter consists of materials from the following publications:
Emori S., Bono, D. C., & G. S. D. Beach. Interfacial current-induced torques in Pt/Co/GdOx.
Applied Physics Letters 101, 042405 (2012).
Emori S. & Beach, G. S. D. Assessment of Rashba field effects in ultrathin Pt/Co/GdOx submicrometer strips. IEEE Trans. Magn. 49, 3113 (2013)
125
(AlOx) [1, 2, 3], Mg-oxide (MgO) [4], and Ta-nitride (TaN) [5], with maximum DW
velocities exceeding 100 m/s and spin-torque efficiencies (equivalence ratios of out-ofplane field to in-plane current-density) approaching 100 Oe/1011 A/M 2 . The conventional adiabatic and nonadiabatic spin transfer torques (STTs) cannot account for the
high efficiencies or the current polarity-dependence of DW motion, which occurs in
the direction opposing electron flow, in these Pt/ferromagnet/insulator (Pt/FM/IN)
strips. Moreover, because the spin polarization of in-plane injected current may be
small in such a thin ferromagnetic layer [6, 7], conventional STTs are expected to
be weak. Instead of the conventional STTs within the "bulk" of the ferromagnet,
current-induced torques arising from interfacial effects are likely responsible for DW
motion.
One interfacial effect that may contribute to highly efficient current-induced DW
motion in Pt/FM/IN is the Rashba effect [8]. In an asymmetric out-of-plane electric
potential profile (i.e. one side bounded by a heavy metal and the other by an oxide),
conduction electron spins are canted in an effective Rashba magnetic field HR arising
from spin-orbit coupling, and these conduction spins exert a torque on the magnetization within the ultrathin magnetic layer. The direction of HR is in-plane and
transverse to the strip, and its magnitude was initially reported by Miron et al. to
reach
JHRJ
~ 10 kOe per 1012 A/M
2
of injected current [8]. According their follow-up
study, this large HR could lock the configuration of moving DWs and allow highspeed DW motion by preventing turbulent processional motion (Walker breakdown)
that limits the velocity of DWs propelled by large driving forces. The existence of
the Rashba field was reported by other groups independently in Pt/Co/AlOx [9] and
Ta/CoFeB/MgO [10], although the magnitudes reported by these studies are smaller
at ~3 kOe/(101 2 A/M 2 ). Another study on Pt/Co/AlOx has reported a negligible
Rashba field of <130 Oe/(101 2 A/M 2) [11].
If current-driven DW motion is indeed facilitated by the Rashba effect, further
enhancement may be expected in material systems with stronger spin-orbit coupling,
which often occurs at metal surfaces interfaced with heavy elements or oxides. For
example, large Rashba splitting has previously been observed at the surface of oxidized
126
Gd [12]. This suggests that strong Rashba spin-orbit coupling may also arise at the
interface of a ferromagnet such as Co and Gd-oxide (GdOx). Our recent studies on
ultrathin Pt/Co/GdOx films have demonstrated that an electric field applied across
the GdOx layer can modify magnetic anisotropy (thereby controlling DW motion) [13,
14], implying that significant spin-orbit coupling exists at the Co/GdOx interface.
Therefore, a Rashba effective field comparable to - or even in excess of - that reported
in Pt/Co/AlOx may be expected in Pt/Co/GdOx.
5.2
Experimental Details of Pt/Co/GdOx Films
and Measurements
The thin-film stack had the form Si/SiO 2 (50)/Ta(4)/Pt(3)/Co(0.9)/GdOx(3) (numbers in parentheses indicate thicknesses in nm). The Ta underlayer enhanced perpendicular magnetic anisotropy in Pt/Co/GdOx and adhesion between the substrate and
Pt. The metal layers were deposited by DC magnetron sputtering under 3 mTorr of
Ar at a background pressure of ~1 x 10'
Torr. The GdOx films were grown by DC
reactive sputtering of a metal Gd target in an oxygen partial pressure of ~ 5 x 10-5
Torr. Using vibrating sample magnetometry, the hard-axis (in-plane) saturation field
was determined to be HK ~ 0.8 T. The room-temperature saturation magnetization
was close to the bulk value at ~1300 emu/cm 3 , indicating minimal oxidation of the
Co layer.
To examine DW dynamics in these structures, 500 nm wide Pt/Co/GdOx strips
with Ta(3)/Cu(100) electrodes were patterned with electron beam lithography and
liftoff as shown in Fig. 5-1(a).
DW motion was detected with a high-bandwidth
scanning magneto-optical Kerr effect (MOKE) polarimeter (Sec. 3.4), with a focused
beam spot size of ~3 pm positioned with a high-resolution sample scanning stage.
DWs were initialized by the Oersted field from a 25 ns-long current pulse (~100
mA) injected through the Cu line orthogonal to the magnetic strip. The DW was
then driven along the strip under combinations of out-of-plane magnetic field and an
127
in-plane current injected along the strip as shown in Fig. 5-1(a). Current densities
below - 1 x 1011 A/M
2
were applied with a high-impedance DC current source. The
higher current densities used in the fast DW measurements described in Sec. 5.5 were
injected with a voltage pulse generator turned on 50 ns before the DW initialization
pulse and maintained just long enough for the DW to traverse the strip (up to 20 ps)
to prevent electromigration. In all cases the injected current was monitored using an
oscilloscope. The substrate temperature
Tub
was controlled using a thermoelectric
module stable to t0.1 K, and was maintained at 308 K unless otherwise noted.
We first characterized the effect of current on the DW propagation field Hp,,op.
MOKE hysteresis loops were measured at a fixed position ~7 pm away from the DW
initialization line using a triangular field sweep waveform with a frequency of 17 Hz.
During each field cycle, a DW was initialized at the zero-field crossing on the rising side
only using a 25 ns-long nucleation pulse as described above. The positive switching
field thus corresponds to the propagation field Hprop of the initialized DW, whereas
the negative switching field is the nucleation field Hnuc to form a reverse domain at
a random location. Figure 5-1(b) shows magnetization switching in a Pt/Co/GdOx
strip at three current densities 2 Je = -0.61, 0 and +0.61 x 1011 A/M
2
,
each with 70
cycles averaged to account for stochasticity. H,,c is independent of Je, while Hp,,op
increases significantly with electron flow along the field-driven propagation direction
(J, > 0), and decreases when Je is reversed.
5.3
Spin-Torque Efficiency in the Thermally Activated Regime
The variation of Hp,,op with Je is plotted in Fig. 5-1(c).
Measurements were re-
peated on three nominally identical strips yielding an average field-to-current ratio
57 ± 3 Oe/10 1 1 A/M 2 . As observed in other Pt/Co systems [1, 3, 15,
16], DW propagation is facilitated in the direction opposite to electron flow. This beAHprop/A Je
=
2
The reported current density is the average value through the Pt and Co layers, assuming a
current distribution in the Ta/Pt/Co stack based on the bulk resistivities of the individual layers.
128
(a)
PG1
(b)
DC-1
PG2
8PNor
Scope
,
I,
,
(C)
Prop
Nuc.
SP
,
Pt/Co/GdOx
40
40 A Pt/Co/Pt/GdOx
20 0 Pt/Co/Pt
-D
0
0
o
+
-
-20
-40
-500 -400
0
100 200
-0.8 -0.4 0.0
0.4
0.8
Je (1011 Am 2)
HZ (Oe)
Figure 5-1: Experimental scheme. (a) Micrograph of a 500-nm wide Pt/Co/GdOx
strip and measurement schematic. With Je < 0, the current is in the same direction as
(and electron flow opposes) field-driven DW motion. (b) Hysteresis loops showing the
DW propagation field changing and nucleation field invariant with injected DC current
densities (J = -0.61, 0, and +0.61 x 10" A/m 2 ). Note the breaks in the horizontal
scale to show details. (c) Plot of the DW propagation field change AHprop against
the injected DC current density in Pt/Co/GdOx, Pt/Co/Pt/GdOx, and Pt/Co/Pt
strips (whose zero-current propagation fields are 170, 250, and 160 Oe, respectively).
havior is contrary to the typical behavior under STT, which assists DW propagation
along the direction of electron flow. Identical results were obtained with the opposite
configuration of magnetization across the DW, realized by reversing the polarities of
the driving field and initialization pulse. This demonstrates that the Oersted field
from the injected current cannot play a significant role.
As shown in Fig.
5-1(c), when a thin Pt layer of 4 A was inserted between
the Co film and the GdOx overlayer, AHp,,op/AJe dropped to 33 ± 2 Oe/10" A/M2 .
Moreover, no current-induced effects were observed in symmetric Pt(3)/Co(0.9)/Pt(3)
strips, which were identical to Pt/Co/GdOx except for the topmost layer.
These
results suggest that the Co/GdOx interface plays a role in generating the observed
large current-induced torque.
The DW propagation field depends on temperature and the timescale over which
reversal is probed, and is therefore an indirect probe of thermally activated DW
motion through the defect potential landscape. The DW velocity in the thermally
129
(a)
'b)
10
000
1
0000
-
0
w
0
E
*so0
0*
0
4.
1
02468
10
xx(,M)
0
200 300
HZ (Oe)
100
20
10 15
t (ms)
5
400
10 0
1
1
(c)
I
(d)
V
.- I
AO
V
0
E 10 0-3
10-4
VAo*
*.
A
.*
*
v 324K
A
U
v 324K
316K
308K
300K
A
316K
*
*
308K
AT
*
"
.
*
300K
0.9
0.8
(D
0.7
-
0.6
(e)
05
n.
100
(f)
0
14 ) 180
H (Oe)
220
-1.0 -0.5 0.0 0.5 1.0
Je (10" A/m2 )
Figure 5-2: Effect of current on thermally activated domain-wall motion in
Pt/Co/GdOx. (a) Averaged DW transients probed at several positions at Tesb =
2
324 K, Hz = 169 Oe, Je = +1.05 x 1011 A/M . The inset is a plot of average DW arrival time t4/ 2 against probed position, with the linear fit indicating a uniform average
velocity. (b) Purely field-driven DW velocity spanning more than 5 decades at Tsb
= 308 K. (c, d) DW velocity at several substrate temperatures versus applied field
with Je = 0 (c) and versus current density with H, = 169 Oe (d). (e, f) Activation
energy versus applied field (e) and versus current density (f).
activated regime follows an Arrhenius behavior v
v exp(-EA/kBT), where the
thermal activation energy barrier EA directly reflects the influence of the driving
field and/or current on the DW dynamics. To access EA directly, we have measured
thermally activated DW velocities as a function of field, current, and temperature,
and used an Arrhenius analysis to unambiguously assess the influence of current on
EA, as done in Chap. 4.
130
Average DW velocities were extracted using a time-of-flight technique as described
in Sec. 3.4. Starting from the saturated state, a reversed driving magnetic field H and
current density Je were applied, and a reverse domain was then generated by a 25ns current pulse in the transverse nucleation line. Time-resolved MOKE transients
were then acquired as a function of position along the strip. Fig. 5-2(a) shows
time-resolved MOKE transients (magnetization reversals) averaged over 150 cycles
at several positions along the strip. The exponential tail of each averaged transient,
whose breadth increases with increasing DW displacement, reflects the stochastic
nature of thermally activated DW motion (Secs. 3.4 and 4.2. The average DW arrival
time, taken as the time
t1/ 2
at which the probability of magnetization switching was
0.5, increases linearly with distance from the DW nuclcation line (inset of Fig. 52(a)). These data show that DWs propagate with a uniform average velocity along
the strip, governed by motion through a fine-scale disorder potential. The average
DW velocity increases exponentially with driving field (Fig. 5-2(b)), as expected for
thermally activated propagation.
The DW velocity at four different substrate temperatures Tusb as a function of H,
(at J, = 0) and Je (at H,, =169 Oe) is shown in Figs. 5-2(c) and (d), respectively. The
DW velocity increases by nearly an order of magnitude with J parallel to the fielddriven propagation direction and decreases similarly when Je is reversed, in agreement
with the trend in Hp,,op versus Je (Fig. 5-1(c)). Notably, a temperature increase of
just 24 K also enhances the DW velocity by an order of magnitude, highlighting the
importance of accounting for even weak Joule heating in such measurements. In Figs.
5-2(e) and (f), we have extracted EA at each driving condition, taken as the slope of
ln(v) versus T-'
where Tstrip
= Tusb
+ AT and AT is the temperature increase due
to Joule heating. AT was measured by comparing the strip resistance versus Tsb at
Je = 0 to the strip resistance versus Je at constant Tusb, giving a small correction
AT = hJ.2 with h = 0.8 K/[10 1 A/m 21 2 .
The data in Figs. 5-2(e) and (f) show that EA is lowered with increasing H, and
with increasing Je parallel to DW motion. This strong variation of EA with Je in
the Pt/Co/GdOx strip is in contrast with our previous results on symmetric Co/Pt
131
multilayer strips, in which EA was insensitive to current (Sec. 4). The linear scaling
of EA with field and current is consistent with the depinning regime of thermally activated DW motion, corresponding to the intermediate regime separating DW creep
and viscous flow dynamics previously identified in this velocity range 4). By comparing the slope of EA versus H, to that of EA versus Je, we arrive at a field-to-current
ratio of 67 ± 8 Oe/1011 A/m 2 , in reasonable agreement with the ratio derived above
from the change in Hp,,op with Je. This analysis indicates that the slope A Hprop/AJe
provides an accurate assessment of the efficiency of current-driven DW motion.
5.4
Assessment of Rashba Field Effects
The results in the previous section (Sec. 5.3) establish that DWs in Pt/Co/GdOx
are driven efficiently in the direction opposing electron flow, similar to what has been
observed in Pt/Co/AlOx [1, 3]. The question now is whether a strong Rashba field HR
is also generated in Pt/Co/GdOx. If so, in the thin-film strip geometry of Fig. 5-3(a),
the in-plane transverse HR from current injected along the strip axis should cant the
strip magnetization away from the easy out-of-plane axis. To quantify HR, the tilting
of magnetization as a function of injected DC current was characterized by measuring
the MOKE signal at the center of a Pt/Co/GdOx strip, which is proportional to the
out-of-plane component M, of the magnetization vector. As illustrated in Fig. 5-3(a),
a current-induced transverse Rashba field should reduce M from its zero-current
value of M,, from which the magnitude of HR can be determined if the out-of-plane
anisotropy field Hk is known.
This Pt/Co/GdOx strip (different from those measured in Sec. sec:efficiencyTPCG)
exhibited a square hysteresis loop (Fig. 5-3(b)) with its coercive field H"", ~ 300
Oe governed by reverse domain nucleation. A square field waveform of amplitude
Hz = 360 Oe was applied to reverse the strip magnetization alternately, generating a
step response in the MOKE signal as shown in Fig. 5-3(c). The amplitude of the step,
proportional to M, was measured as a function of injected current density J,. To
attain a sufficient signal-to-noise ratio in the step data, the bandwidth of the MOKE
132
KE
lase
rb
(a)
-MZ
HR
D 1FC
-400-200 0 200 400
H( (e)
0
10 20 30 4
t (s)
Figure 5-3: Experimental scheme for measuring current-induced magnetization tilting
in Pt/Co/GdOx. (a) Schematic of magnetization tilting measurement. The out-ofplane magnetization M;, is measured using the magneto-optical Kerr effect (MOKE).
The injected DC current IDC may generate a transverse Rashba field HR, which may
tilt the magnetization and reduce M;,. The out-of-plane applied field H, switches M,'
between up and down. (b) MOKE hysteresis loop measured at DC = 0 by sweeping
out-of-plane H e (c) Examples of MOKE signal upon magnetization switching for
zero and nonzero (DC The magnitude of the MOKE signal is proportional to M-.
system was limited to 30 kHz and 100 switching cycles were averaged. For each value
of injected current density, at least three sets of averaged MOKE step signal were
obtained after re-centering the laser spot to gain statistics that accounted for drift
in the MOKE signal. Each presented data point is the mean of these multiple measurements, with the corresponding error bar showing the standard deviation. The
maximum injected current was 1.6 mA, which corresponds to a current density of
Je = 8 x 10" A/m
2
averaged across the combined Pt and Co cross section, assuming
a current distribution in the Ta/Pt/Co stack based on the bulk resistivity of each
individual layer.
Fig. 5-4(a) plots the reduction of M, with increasing injected current density. At
current density Je
=
8 x 10" A/m
2
, M reaches 91 ± 3% of the zero-current M_ value.
133
(Z)
(b)
SMz(AT(J))
1.00
-
0
0
MS(AT)
Gooo~
* 0.95
N
-
0.90
00+00
L .
0
z 0.85
0
2
4
6
8
Je (1011 A/m 2)
0 102030405060
AT (K)
Figure 5-4: Quantification of current-induced magnetization tilting and reduction of
saturation magnetization. (a) Decrease of the out-of-plane magnetization M, with
increasing injected current density Je in the patterned device. (b) Decrease of M, with
increasing sample temperature resulting from Joule heating at a constant substrate
temperature (308 K) in the strip (Mz(AT(J)), filled squares), and decrease of M,
from increasing substrate temperature in the continuous film (M(AT), open circles).
This observed reduction of M, could be attributed to two sources: (1) the tilting of
the magnetization away from the perpendicular axis due to the transverse Rashba
field, and/or (2) the decrease in the saturation magnetization M, from Joule heating.
To isolate the two sources, we independently quantified both the current-induced
Joule heating in the device and the temperature dependence of the saturation magnetization. Measurements of electrical resistance versus injected current at a fixed
substrate temperature, and resistance versus substrate temperature at a low sense
current, revealed a quadratic increase in the device temperature with current density,
AT
=
hJ,2 with h = 0.84 ± 0.06 K/(10" A/M 2) 2 . Using this relation, the decrease in
M, is re-plotted with respect to the device temperature rise AT in Fig. 5-4(b). The
reduction of M, with increasing substrate temperature from 308 to 373 K, also plotted
in Fig. 5-4(b), was measured with the MOKE technique on a saturated Pt/Co/GdOx
continuous film (instead a patterned device, to eliminate spurious effects from thermal
drift).
The decrease of M, with current closely follows the decrease of M, with temperature. Therefore, Joule heating alone can completely account for the observed
current-induced reduction of M, in the Pt/Co/GdOx strip within the measurement
134
uncertainty. We extract an upper limit for the transverse field by taking the lower
end of the error bar at Je = 8 x 10" A/M 2 (AT = 55 K), where the normalized
Mz decreases to 88% of the zero-current M, and Joule heating alone reduces Mz to
92%. In this case, the magnetization tilting angle from the perpendicular axis is 0
arccos(88/92)
=
17 . Neglecting the effect of the applied field Hz that is much smaller
than the anisotropy field HK, the transverse Rashba field is
1HR1
- HKsinO
=
2300
Oe at Je = 8 x 10" A/M 2 . Thus, the estimated magnitude of the current-induced
Rashba field in Pt/Co/GdOx is HR= 0 ± 3 kOe/101 2 A/M 2, where the large error
bar is related to the weak dependence of Mz on tilting angle for small angles. Our
measurement is statistically consistent with the values reported by [9, 10, 11] and is
at least a factor of 3 smaller than that reported by
5.5
[81.
High-Speed Domain-Wall Dynamics
The efficiency of current-induced DW motion in Pt/Co/GdOx is found to be large
and comparable to Pt/Co/AlOx, but the magnitude of the Rashba field was may be
very small, or at most 30% of the value reported initially by Miron et al.
[8]
If a strong
Rashba field is present in Pt/Co/GdOx, it should be possible to observe its effect on
rapidly propagating DWs. In particular, because the Rashba field scales with in-plane
current density, the DW mobility should change qualitatively from low to high current
destinies with the larger transverse Rashba field keeping the DW increasingly rigid.
Here, we examine the dynamics of DWs, measured using the time-resolved MOKE
technique described in 3.4 and illustrated in Fig. 5-5(a), driven by combinations of
applied out-of-field and in-plane current. The strip measured for this experiment had
a nucleation field of H,,c a 500 Oe, which set the maximum applied field for driving
a single initialized DW.
DW velocity-versus-field curves at several injected current densities are shown
in Fig. 5-5(b).
With increasing current in the same direction as the field-driven
DW motion (defined as Je < 0), the velocity increases. Because the DW velocity
increases nonlinearly with driving field (or current) and was found to depend weakly
135
(a)
WU
0
0
100 200 3$0
t (ns)
250 (b)
(c)
J =-6.5x10
200 -
-5.2
-3.9
-26
150 -v
100 --
E
T
-1.3
0 050 -4
50
A/m
+1.
.
0
0
100
200 300 400 500
HZ (0e)
300 400 500 600 700 800
Hf (0e)
Figure 5-5: Equivalence of high-speed domain-wall motion driven by field and current. (a) DW velocity measurement scheme. The top image is a scanning electron
micrograph of a 500-nm wide patterned device, with illustrations of the DW initialization pulse (yellow solid arrow) and DW motion direction (white dotted arrow). The
bottom figure shows MOKE signal transients from DW propagation at different locations of the magnetic strip. (b) DW velocity versus applied out-of-plane field H_ at
different current densities Je. (c) DW velocity versus effective field Heff = H, + EJe.
The solid curve is a guide for the eye to represent the common dynamic scaling of
DW velocities for all driving currents.
on temperature in separate measurements, DW motion shown in Fig. 5-5 is still
in the thermally activated regime, despite the large velocities exceeding 1 m/s and
approaching 200 m/s in the fastest cases.
In typical magnetic materials 3 , DWs driven by field greater than the Walker
3
By "typical," we mean materials in which magnetostatics, ferromagnetic exchange, and
anisotropy determine the equilibrium configuration of DWs under no external fields. It will be
shown later that Pt/Co/GdOx and other similar ultrathin film structures with structural inversion
asymmetry do not fall into the "typical" magnetic materials. In these structures, the anisotropic
exchange, also called the Dzyaloshinskii-Moriya interaction, influences the DW configuration and
dynamics under driving field and current.
136
(a)
-
35-
--
30.
25
-
(b)
om, T*300K 4=0
sM. T300K, 4-02
s,300K0pOA
.
M TWO. p
- -1M. T-0,
D.00: e10'"o9n
%4
Two
-&
20
D
.0 0, TWO
D,uOn. on.wOG"~,T
'~~
D,u3nm.%wO,="W~mTO30
-epD-0,u3nnk%-wIr"VrmT-30K
150
0.4
20
100
505
0
0
0.00
0.05
0.10
0.15
0.20
0.25
A
0.0
0.30
-
. ..
....
.nB
........
...............
..
0.2
0.4
0.6
0.8
1. D
2
a (A/pm )
ja (NIm 2)
Figure 5-6: (a) Micromagnetically computed ("yuM") current-driven domain-wall mobility curves for a 120-nm wide nanostrip with edge roughness (roughness parameter
D = 3 nm). Here, no Rashba field is included in the calculations. Adapted from [17].
(b) Micromagnetically computed current-driven domain-wall mobility curves for a
120-nm wide nanostrip with edge roughness (D = 3 nm, blue and red). Here, a large
Rashba field (with Rashba parameter aR = 10-11 eVm) is included in the calculations.
Adapted from [18].
threshold (estimated by [19] to be ~100 Oe in ultrathin Pt/Co/Pt) move by precession, i.e. continuously transforming between the Bloch and N~el configurations.
Similarly, a finite-temperature micromagnetics study by Martinez [17] shows that
fast (v > 1 m/s) thermally activated DW propagation in an out-of-plane magnetized
nanostrip occurs by DW precession. This occurs because a DW can more readily
overcome the pinning potential energy barrier by exploiting both the translational
and precessional degrees of freedom. A related study [18] shows that a strong transverse Rashba field (there taken as 10 kOe/(10" A/m 2 ) as suggested by [8]) increases
the threshold driving force required for sustained DW motion by suppressing DW
precession. Comparing Figs. 5-6(a) and (b), the current density above which the DW
dynamics escape the creep regime increases by a factor of 4 in the presence of the
Rashba field (Fig. 5-6(b)) compared to the zero-Rashba field case (Fig. 5-6(a)). With
the large transverse field strongly favoring the Bloch configuration while raising the
energy penalty for the Neel configuration, the low-energy precessional mode is disabled and the DW can propagate only by rigid translation at higher driving currents.
137
In the thermally activated regime, this leads to a decrease in the DW velocity at a
given driving force.
The computational studies by Martinez [17, 18] (shown in Fig. 5-6) , though
based on conditions quantitatively different from our measurements, indicate that the
Rashba effect should have a qualitatively observable influence on current-driven DW
dynamics. Specifically, if there was a strong current-induced transverse Rashba field,
the velocity of thermally activated DW motion at a fixed driving field might decrease
abruptly at a large current density corresponding to the onset of rigid translation
(stabilization against precession). Such a drop in the DW velocity at high current
densities is not apparent in the data of Fig. 5-5(b), suggesting that the Rashba
field is insufficient to prevent precessionally-assisted DW creep motion up to the
maximum current densities applied. The lack of a transition in DW dynamics brought
on by an in-plane transverse Rashba field is made more evident by plotting the DW
velocity against the "effective out-of-plane field" Heff
efficiency c
=
=
Hz+EJe, with the spin-torque
-63 Oe/(10" A/m 2 ) equating the effect of current to an additional
out-of-plane field. As shown in Fig. 5-5(c), all DW velocity data plotted against
Heff converge to a common curve, which indicates that the effect of current can be
entirely explained as an effective out-of-plane field without an additional in-plane
Rashba field. Joule heating at high currents can account for small deviations from
the common curve, as we observed in separate measurements that a temperature
rise of 20 K increased the DW velocity in this regime by as much as a factor of -2.
This convergence also reveals that even when a DW is driven by a large current and
vanishingly small field, its mode of motion is the same as when it is driven by a large
field and vanishingly small current. In other words, there is no evidence of a Rashba
field altering DW dynamics from precession to rigid translation.
The analysis so far as assumed that DWs in Pt/Co/GdOx driven by large fields
(and current) move by precession. However, it will be shown in later chapters that
DWs in heavy-metal/ultrathin-ferromagnet/insulator structures take on unusual configurations due to an interfacial phenomenon, i.e. the Dzyaloshinskii-Moriya interaction (DMI), arising from spin-orbit coupling. The possibility of the DM1 governing
138
DW dynamics in these ultrathin ferromagnets was first suggested by Thiaville et
al. [20]. They pointed out that the field-driven DW velocity in Pt/Co/AlOx in [3]
was around 5 times greater than that in similar Pt/Co/Pt in [19], and that DWs
in Pt/Co/AlOx could not be undergoing precessional motion to attain such high velocities. Our experimental and computational studies indeed indicate that DWs in
heavy-metal/ultrathin-ferromagnet/insulator are not typical Bloch DWs governed by
magnetostatics [21], but instead Neel DWs with a fixed chirality. Because these chiral "Dzyaloshinskii DWs" do not undergo precessional dynamics (unless driven by an
exceedingly large field), the analysis of DW dynamics in Pt/Co/GdOx in this section
is not entirely accurate.
Nevertheless, the conclusion that there is no appreciable in-plane transverse Rashba
field to alter current-driven DW dynamics still holds. Furthermore, the equivalence of
out-of-plane field and in-plane current in driving DWs, which holds both in the slow
thermally activated regime and faster near-flow regime, provides a hint for the symmetry of current-induced torques responsible for anomalously high efficiencies. This
equivalence is suggestive of extraordinarily strong nonadiabatic spin-transfer torque
as reported in [2], but this mechanism cannot be dominant given the small spin polarization of current in ultrathin ferromagnets [6, 7]. As described in Chaps. 6 and 7,
an entirely different phenomenon, i.e. the spin Hall effect arising from the nonmagnetic heavy metal underlayer, turns out to be responsible for the high efficiency and
symmetry of the observed torques in driving DWs.
5.6
Summary
Current-driven DW motion is investigated in Pt/Co/GdOx nanostrips with perpendicular magnetic anisotropy. This ultrathin film structure is similar to Pt/Co/AlOx
exhibiting highly efficient current-driven domain wall (DW) motion, which has recently been attributed in part to the Rashba effect. Measurements of the propagation field and the energy barrier for thermally activated DW motion reveal a large
current-induced torque equivalent to an out-of-plane magnetic field of ~60 Oe per
139
10" A/M 2 . This same field-to-current scaling is shown to hold in both the slow thermally activated and fast near-flow regimes of DW motion, and there is no evidence of
a large current-induced Rashba field modifying DW dynamics. The current-induced
torque decreases with 4
A of Pt
decorating the Co/GdOx interface and vanishes en-
tirely with Pt replacing GdOx, suggesting that the Co/GdOx interface plays a role in
efficient current-driven DW dynamics. Injecting in-plane current into Pt/Co/GdOx
reduces the out-of-plane component of the magnetization, but this reduction can be
entirely attributed to decrease in the saturation magnetization due to Joule heating,
rather than magnetization tilting due to an in-plane transverse Rashba field. The
efficient current-driven DW dynamics in Pt/Co/GdOx (and other similar ultrathin
ferromagnets) does not arise from the combination of the Rashba field and nonadiabatic spin-transfer torque as suggested initially, and an alternative explanation is
required.
140
Bibliography
[1] Moore, T. A. et al. High domain wall velocities induced by current in ultrathin
Pt/Co/AlOx wires with perpendicular magnetic anisotropy. Applied Physics
Letters 93, 262504 (2008).
[2] Miron, I. M. et al. Domain Wall Spin Torquemeter. Physical Review Letters
102, 137202 (2009).
[3] Miron, I. M. et al. Fast current-induced domain-wall motion controlled by the
Rashba effect. Nature Materials 10, 419-423 (2011).
[4] Koyama, T. et al. Current-Induced Magnetic Domain Wall Motion in a Co/Ni
Nanowire with Structural Inversion Asymmetry.
Applied Physics Express 6,
033001 (2013).
[5] Ryu, K.-S., Thomas, L., Yang, S.-H. & Parkin, S. S. P. Current Induced Tilting
of Domain Walls in High Velocity Motion along Perpendicularly Magnetized
Micron-Sized Co/Ni/Co Racetracks. Applied Physics Express 5, 093006 (2012).
[6] Cormier, M. et al. Effect of electrical current pulses on domain walls in Pt/Co/Pt
nanotracks with out-of-plane anisotropy: Spin transfer torque versus Joule heating. Physical Review B 81, 024407 (2010).
[7] Tanigawa, H. et al. Thickness dependence of current-induced domain wall motion
in a Co/Ni multi-layer with out-of-plane anisotropy. Applied Physics Letters 102,
152410-152410-4 (2013).
141
[8] Miron, I. M. et al. Current-driven spin torque induced by the Rashba effect in a
ferromagnetic metal layer. Nature Materials 9, 230-234 (2010).
[9] Pi, U. H. et al. Tilting of the spin orientation induced by Rashba effect in
ferromagnetic metal layer. Applied Physics Letters 97, 162507-162507-3 (2010).
[10] Suzuki, T. et al. Current-induced effective field in perpendicularly magnetized
Ta/CoFeB/MgO wire. Applied Physics Letters 98, 142505 (2011).
[11] Liu, L., Lee, 0. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. CurrentInduced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin
Torque from the Spin Hall Effect. Physical Review Letters 109, 096602 (2012).
[12] Krupin, 0. et al. Rashba effect at magnetic metal surfaces. Physical Review B
71, 201403 (2005).
[13] Bauer, U., Emori, S. & Beach, G. S. D. Electric field control of domain wall
propagation in Pt/Co/GdOx films. Applied Physics Letters 100, 192408-1924084 (2012).
[14] Bauer, U., Emori, S. & Beach, G. S. D. Voltage-gated modulation of domain
wall creep dynamics in an ultrathin metallic ferromagnet. Applied Physics Letters
101, 172403-172403-4 (2012).
[15] Kim, K.-J. et al. Electric Control of Multiple Domain Walls in Pt/Co/Pt Nanotracks with Perpendicular Magnetic Anisotropy. Applied Physics Express 3,
083001 (2010).
[16] Lee, J.-C. et al. Universality Classes of Magnetic Domain Wall Motion. Physical
Review Letters 107, 067201 (2011).
[17] Martinez, E. The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness. Journal of Physics: Condensed
Matter 24, 024206 (2012).
142
[18] Martinez, E. Micromagnetic analysis of the Rashba field on current-induced
domain wall propagation.
Journal of Applied Physics 111, 033901-033901-6
(2012).
[19] Metaxas, P. J. et al. Creep and Flow Regimes of Magnetic Domain-Wall Motion
in Ultrathin Pt/Co/Pt Films with Perpendicular Anisotropy. Physical Review
Letters 99, 217208 (2007).
[20] Thiaville, A., Rohart, S., Ju6, E., Cros, V. & Fert, A. Dynamics of Dzyaloshinskii
domain walls in ultrathin magnetic films. EPL (Europhysics Letters) 100, 57002
(2012).
[21] Koyama, T. et al. Observation of the intrinsic pinning of a magnetic domain
wall in a ferromagnetic nanowire. Nature Materials 10, 194-197 (2011).
143
144
Chapter 6
Spin-Orbit Torques from
Nonmagnetic Heavy-Metals
In out-of-plane magnetized ultrathinferromagnets sandwiched between a nonmagnetic
heavy metal and insulator, current-inducedDW motion is anomalously efficient. This
observation has been widely attributed to a Rashba effective field that stabilizes Bloch
DWs against deformation, permitting high-speed motion through conventional nonadiabatic spin-transfer torque (STT). However, a number of recent findings suggest
that STT contributes negligibly to DW dynamics in these ultrathin structures and
that interfacialphenomena are instead responsible. The spin Hall effect (SHE) in the
adjacent heavy metal has emerged as a possible alternative mechanism. The SHE produces a spin current from charge scattering in the heavy metal, and the resulting spin
accumulation at the heavy-metal/ferromagnet interface generates a Slonczeswki-like
torque strong enough to drive magnetization. This chapter presents results and anal-
yses that indicate that the SHE is indeed responsible for driving DWs in the ultrathin
ferromagnets.1
'This chapter consists of materials from the following publication:
Emori, S., Bauer, U., Ahn, S.-M., Martinez, E., & G. S. D. Beach. Current-driven dynamics of
chiral ferromagnetic domain walls. Nature Materials 12, 611616 (2013).
145
6.1
Pt- and Ta-Based Ultrathin-Ferromagnet/Oxide
Structures
We characterized current-induced torques and DW dynamics in out-of-plane magnetized Pt/CoFe/MgO and Ta/CoFe/MgO stacks that are nominally identical except
for the heavy-metal underlayers, whose spin Hall angles are large and of opposite
sign [1, 2, 3]. By comparing the polarities of the DW motion and torques, the goal was
to draw a correlation between the observed polarities and the SHE. The stack structure of Pt/CoFe/MgO was Ta(3 nm)/Pt(3 nm)/CosoFe 2o(0.6 nm)/MgO(1.8 nm)/Ta(2
nm), and that of Ta/CoFe/MgO was Ta(5 nm)/CosoFe2O(0.6 nm)/MgO(1.8 nm)/Ta(2
nm). Both were deposited on Si/Si0 2 (50 nm) substrates. The metal layers were deposited by DC magnetron sputtering at 2 mTorr Ar (for Pt, 3 mTorr Ar), and MgO
was RF sputtered at 3 mTorr Ar. The deposition rates were <0.1 nm/s,calibrated
with X-ray reflectivity. Co 80 Fe2O was chosen, instead of pure Co, to attain sufficient
perpendicular magnetic anisotropy on both Ta and Pt underlayers. The bottom Ta(3
nm) layer in Pt/CoFe/MgO served as a seed layer to enhance perpendicular magnetic
anisotropy and adhesion between Pt and the substrate. The Ta(2 nm) capping layer
protected the MgO layer in each structure. Vibrating sample magnetometry on continuous films revealed full out-of-plane remanent magnetization and in-plane (hardaxis) saturation fields of _5 kOe for Pt/CoFe/MgO and ~3 kOe for Ta/CoFe/MgO.
The saturation magnetization was
_700 emu/cm 3 , approximately half of the bulk
value, suggesting a magnetic dead layer due to roughness or oxidation. Both films
exhibited weak DW pinning, with DW propagation at fields <20 Oe.
500-nm wide nanostrips and Hall crosses were fabricated using electron beam
lithography, magnetron sputtering, and liftoff (Sec. 3.3).
Electrical contacts con-
sisting of Ta(2 nm)/Cu(100 nm) were placed with a second layer of electron beam
lithography. To estimate the current density through these devices, current was assumed to flow only through the ultrathin CoFe layer and the adjacent heavy metal
layer, so that the effective conductive thickness was 3.6 nm for Pt/CoFe/MgO and 5.6
nm for Ta/CoFe/MgO. We neglected current shunting in the bottom Ta seed layer in
146
(a)
(b)
propagation
nucleation
-
*
I 4-Je>0
L0
0
I
I
1:
-1
0
y
-60 -40 -20
Z(
0
20
40
60
Hz (0e)
x
Figure 6-1: Experimental scheme for measuring domain-wall propagation field. (a)
Schematic of the domain wall propagation field measurement superposed on a scanning electron micrograph of a nanowire. The focused laser spot is placed halfway
along the nanowire for magneto-opical Kerr effect (MOKE) measurements. (b) Exemplary MOKE hysteresis loops on a Pt/CoFe/MgO device at under polarities of
2
current densities (here, JeJ = 0.07 x 10" A M ). A domain wall is initialized only
on the rising side of the positive applied field, so that here the positive coercive field
is the DW propagation field while the negative coercive field is the reverse domain
nucleation field.
the Pt/CoFe/MgO, as sputtered Ta (-phase)
typically has a much higher resistivity
than Pt. The resistance of the Ta/CoFe/MgO device was 3.5 times greater than the
Pt/CoFe/MgO device, and the Ta layer was estimated to be 5 times more resistive
than the Pt layer. Current shunting through the Ta capping layer, assumed to be
oxidized, was also neglected.
6.2
Heavy-Metal Dependence of Current-Driven
Domain Wall Motion
DW motion was characterized in 500-nm wide, 40-m long nanowires overlaid with
an orthogonal DW nucleation line and lateral contacts for current injection (Fig. 61(a)). All measurements were conducted at a constant substrate temperature of 308
K, maintained to within ±0.1 K with a thermoelectric module. We first examine
the dependence of the threshold field Hp,,p for DW propagation on electron current
density Je. DW motion was detected using our custom scanning magneto-optical
147
Kerr effect (MOKE) system (Sec. 3.4) with a 3 pm focused laser beam placed at
a fixed position midway along the nanowire. For each value of Je injected through
the nanostrips, MOKE hysteresis loops were obtained under an applied out-of-plane
field H, with a triangular waveform of amplitude 150 Oe and frequency 12.5 Hz.
After saturating the magnetic nanowire (e.g. uniformly magnetized down), a reverse
domain (e.g. up) was nucleated using a 25-ns, 50-mA nucleation pulse just after the
field zero-crossing. With the increasing H, expanding the reverse domain, a DW
propagated away from the nucleation line, and magnetization switching was detected
by MOKE as the DW passed through the laser spot. After saturating the magnetic
nanostrip by domain expansion, H. was swept in the other direction. For this side of
field sweep, no DW was initialized so that magnetization switching occurred through
domain nucleation at random locations in the nanowire. At a sufficiently large Hz,
the magnetization was saturated again in the initial direction. This measurement
cycle was repeated at least 50 times and an averaged hysteresis loop was obtained
to attain a sufficient signal-to-noise ratio and take into account the stochasticity of
magnetization switching. The DW propagation field Hprop was taken as the field
at which the normalized MOKE signal (Fig. 6-1(b)) crossed zero. As seen on the
positive side of H, in Fig. 6-1(b), we observed a clear shift of Hprop even at small
currents < 10 A (|Je < 101 A/M 2 ), resulting in a linear correlation between Hprop and
driving current as shown in Figs. 6-2(c)(d) and 6-3(c)(d). No systematic variation in
the nucleation field (switching field in the absence of an initialized DW) was observed
with respect to current, as shown on the negative field side of H, in 6-1(b).
As shown in Fig. 6-2, DW propagation is hindered in the electron flow direction in Pt/CoFe/MgO and assisted along electron flow in Ta/CoFe/MgO. This remarkable difference, produced simply by changing the nonmagnetic metal in contact
with the ferromagnet, was independent of the sense of magnetization (up-down or
down-up) across the DW (Fig. 6-3). The spin-torque efficiency, taken as the slope
of Hprop versus Je, was -120 Oe/1011 A/M 2 for Pt/CoFe/MgO and +170 Oe/101"
A/M
2
for Ta/CoFe/MgO. Here, the signs indicate the polarity, with AHrop/AJe > 0
denoting DW motion assisted along electron flow. These large magnitudes of effi148
(a)
(b)
current-induced
motion 'N
current-induced
motion \
Je
- (c)
30
.
20
0
I
10
0
-0.10
-0.05
0.00
0.05
0.10
-0.10 -0.05
JO (1011 A m- )
2
-100
E 10
10-
E
-
2
10o3
0.10
0
0
50
Hz (0e)
100
150
(f)e
0
>
0.05
J(10 A m)
(e)
101
(1)
Hz (Oe)
-50
0.00
field-driven
current-driven
-
o field-driven
* current-driven
I
-1.0
0.0 0.0
-0.5
Je (1011
2
A m- )
0.5
1.0
J (101 A m2)
Figure 6-2: Effect of current on domain wall motion in Pt/CoFe/MgO and
Ta/CoFe/MgO. (a, b) Illustrations of the direction of current-driven domain wall
motion in the Pt/CoFe/MgO (a) and Ta/CoFe/MgO (b) nanostrips. Electron current Je is defined positive when conduction electrons flow away from the nucleation
line, from left to right in the micrograph in Fig. 6-1(a). (c, d) Domain wall propagation field Hp,,op as a function of driving electron current density Je for Pt/CoFe/MgO
(c) and Ta/CoFe/MgO (d). The slope of the linear fit extracts the spin-torque efficiency for each structure. (e, f) Domain wall velocity as a function of Je and applied
out-of-plane field Hz for Pt/CoFe/MgO (e) and Ta/CoFe/MgO (f). The field-driven
data are scaled by a field-to-current ratio so that they are directly on top of the
current-driven data.
149
(a)
field-induced motion
current-induced
magnetic field
motion
up-down
domain wall
electron flow, J.
(b)
down-up
domain wall
40
(c)
(d)
30-
a)
0
20
10
0
-0.10 -0.05
0.00
Je (10
11
0.05
0.10
-0.08
2
A m- )
-0.04
0.04
0.00
J (1011 A m2 )
0.08
Figure 6-3: Current-induced domain-wall motion independent of magnetization sense.
for
(a, b) Direction of current-induced motion in Pt/CoFe/MgO and Ta/CoFe/MgO
an up-down domain wall (up domain expanding under an upward applied field) (a)
and a down-up domain wall (down domain expanding under a downward applied
field) (b). (c, d) Domain wall propagation field H,,p as function of driving electron
current density Je exhibiting the same trend for up-down (filled symbols) and down-up
domain walls (empty symbols) in Pt/CoFe/MgO (c) and Ta/CoFe/MgO (d).
150
(a)
j
10 m
(c)
2.0-- 1.5-
A.N.
(b)
1.0
0.5
S0
0
0.0
jA
-1
0
5
10
15 20
V____ Iposition
-1
0
1
Time (ps)
2
25
(pm)
30
35
3
Figure 6-4: Experimental scheme for measuring domain-wall velocity. (a) Scanning
electron micrograph of a 500-nm wide nanowire. The current pulse on the left initializes a domain wall, which is then driven to the right by an applied field or injected
current. (b) Magneto-optical Kerr effect signal showing magnetization switching due
to domain wall propagation at different positions along the nanowire. (c) Domain wall
arrival time plotted against position along the nanowire. The domain wall velocity is
extracted by linear fit.
ciencies are comparable to those observed in Pt/Co/AlOx [4, 5], Pt/Co/MgO [6] and
Pt/Co/GdOx (5.3). High-speed DW motion against electron flow was also reported
in Pt/Co/Ni/Co/TaN [7], suggesting that the insulating overlayer does not need to
be an oxide to attain the high efficiency. Furthermore, in Ta/CoFeB/MgO, DWs
were reported to move in the direction along electron flow [8].
Our experimental
findings, combined with these reports, indicate that a universal mechanism governs
current-driven DW motion in heavy-metal/ferromagnet/insulator.
In Figs. 6-2(e)(f), we directly compare field-driven and current-driven DW velocities, measured using a time-of-flight technique (Sec. 3.4). This was carried out
by first driving a DW away from the nucleation line with the out-of-plane field pulse
and then injecting the current to drive the DW (Fig. 6-4). The field-driven DW
velocity was measured by first ramping the field to the setpoint driving level (because
of the slow rise-time of the magnet ~100 ps) and then initializing a DW, which was
subsequently driven to the other end of the nanostrip by the constant driving field.
The DW arrival time was extracted from MOKE signal versus time averaged over
151
at least 50 measurement cycles, and the velocity was obtained by linearly fitting the
plot of the arrival time at several positions along the nanowire, as shown in Fig. 6-4.
Again, DWs moved against electron flow in Pt/CoFe/MgO (Fig. 6-2(e)) and along
electron flow in Ta/CoFe/MgO (Fig. 6-2(f)).
The maximum field was limited by
random domain nucleation, and the exponential dependence of velocity on H, and J
indicates thermally activated motion (Secs. 3.5). The field-driven and current-driven
velocities exhibit the same dynamical scaling across three decades in velocity when
je is scaled by a constant (110 Oe/1011 A/M 2 for Pt/CoFe/MgO and 160 Oe/10 11
A/M
2
for Ta/CoFe/MgO). These field-to-current ratios closely match those extracted
from Figs. ld,e. We therefore conclude that the effect of current on DW motion is
phenomenologically equivalent to an out-of-plane field, as observed in [4] and Sec.
5.5. This equivalence between driving in-plane current and out-of-plane magnetic
field reveals the symmetry of the current-induced torque acting on DWs, as discussed
later in this chapter.
In Fig. 6-5, we present the velocity of DWs up to Je larger than the range shown
in Fig. 6-2. Interestingly, with Jej > 1 x 10" A/M 2, the DW velocity is higher
in Pt/CoFe/MgO than in Ta/CoFe/MgO, despite the smaller spin-torque efficiency
and spin Hall angle exhibited by Pt/CoFe/MgO. This paradox suggests that the
50
40
E
30
*
-U
PtICoFe/MgO
-U
-3
-2
-1
0
JO (10" A
Figure
6-5:
Ta/COFeIMgO
U-
20
10
*
Domain-wall
velocity
at
Pt/CoFe/MgO and Ta/CoFe/MgO.
152
1
m2
higher
2
3
)
electron
current
densities
in
DW velocity is not necessarily an accurate metric of the current-induced torque,
and that caution must be used when relying on velocity data alone to compare the
current-induced torques in different materials. This surprising trend also indicates
that another physical mechanism governs DW dynamics at higher currents.
6.3
Current-Induced Switching of Uniform Magnetization
In addition to robust DW motion, current enables switching between uniformly magnetized "up" and "down" states with the assistance of a constant in-plane magnetic
field [1, 9, 10]. This switching phenomenon was demonstrated in 1200-nm wide Hall
crosses (Fig. 6-6(a)). A sequence of 250-ms long current pulses with increasing (or
decreasing) amplitude was injected along the x-axis. After the current pulse was
turned off, the out-of-plane component of the magnetization was measured from the
anomalous Hall voltage using a 400-Hz low-amplitude (~109 A/M 2 ) AC sense current and a lock-in amplifier. The out-of-plane magnetization M, from the anomalous
Hall voltage was measured successively in this fashion by stepping through a range
of current pulse amplitudes, producing hysteresis loops as shown in Figs. 6-6(d)(e).
Figs. 6-6(d)(e) plot M, versus Je, under a constant applied longitudinal field H,.
This field tilted the magnetization away from the z-axis by ~4' in Pt/CoFe/MgO
at 500 Oe and ~3' in Ta/CoFe/MgO at 100 Oe, 2 but did not bias M, up or down,
as evidenced by the nearly symmetric switching profile (Figs. 6-6(d)(e)). With sufficiently large Hx and Je in the +x direction, the up magnetized state was favored
in Pt/CoFe/MgO (Fig. 6-6d, solid line), whereas the down state was favored in
Ta/CoFe/MgO (Fig. 6-6e, solid line). When the direction of Hx or Je was reversed,
2
The tilting with respect to the z-axis can be estimated from the first harmonic of the anomalous
Hall voltage. For example, in Fig. S5(c) (or S7(c)) of our Nat. Mater. manuscript, the first harmonic
2
from Pt/CoFe/MgO changes quadratically with in-plane field at 2 x 10-6 AV/Oe , which means the
2
2
first harmonic changes by 2 x 10-6 pV/Oe *(500 Oe) = 0.5 pV at 500 Oe of in-plane field. The
amplitude of the first harmonic at zero in-plane field is approximately 225 AV (voltage for +M,
minus voltage for -M,, divided by 2), so the out-of-plane component of magnetization decreases by
about 0.5/225 = 0.2%. The tilting angle is estimated as arccos(1-0.002), which turns out to be 4
degrees. The same procedure yields a tilting angle of ~_3 degrees for Ta/CoFe/MgO.
153
~
(b)
SL
SL
(C)
M
Z
(a)
77T
electr
(d)-H
----
)(e -
= +500 Oe
H =-500 Oe
1
H =+1o6Oe
----H = -1000Oe
X-
y
0
zt_0
-1
-4
-2
4 -0.6 -0.4 -0.2 0.0 0.2
J. (10" An 2 )
2
0
J. (10" Am-2 )
0.4
0.6
Figure 6-6: Current-induced switching under a constant in-plane longitudinal field.
(a) Scanning electron micrograph of a Hall cross. (b, c) Illustrations of Pt/CoFe/MgO
(b) and Ta/CoFe/MgO (c) in the up magnetization state with the injected electron
current and applied longitudinal field H, in the +x direction. Because of the combination of the current-induced Slonczewski-like torque (producing an effective field
HSL) and the applied longitudinal field, up magnetization is stable in Pt/CoFe/MgO
whereas it is unstable in Ta/CoFe/MgO. (d, e) Out-of-plane magnetization M, (normalized anomalous Hall signal) as a function of electron current density J under a
constant Hx in Pt/CoFe/MgO (d) and Ta/CoFe/MgO (e). The magnitude of Hx
is 500 Oe for Pt/CoFe/MgO (d) and 100 Oe for Ta/CoFe/MgO (e). When Hx is
reversed from +x (solid line) to x (dotted line), the stable magnetization direction
under a given current polarity reverses.
the preferred magnetization direction was also reversed (Figs. 6-6(d) (e) dotted lines).
This switching behavior implies that Je generates an effective field HSL associated
with a Slonczewski-like torque [11], given by
HSL
H
M X (i X
Je).
(6.1)
Here mh, i, and Je are unit vectors along the magnetization, z-axis, and electron flow,
respectively, and HsL parameterizes the torque. The SHE in the heavy metal directly
generates a Slonczewski-like torque, but the Rashba effect can also yield a torque of
this form due to spin-relaxation [12, 13]. Assuming the SHE is the dominant source,
154
justified experimentally below, HOL is related to the spin Hall angle OSH in the heavy
metal through [11],
H
SL
= hOSHIJe
2|e|MstF'
where M, is the saturation magnetization and tF is the ferromagnet thickness. From
the sign of HjL extracted from current-induced switching (Figs. 6-6(b)(c),
OSH
is
positive in Pt and negative in Ta, consistent with [1] and [2].
6.4
Heavy-Metal Dependence of Current-Induced
Torques
We quantified the Slonczewski-like torque by detecting magnetization tilting induced
by AC current using the anomalous Hall voltage as described in [14]. The scaling of
HSL with current is shown in Fig. 6-7. When the magnetization was up and electron
flow Je was in the +x direction, HSL pointed along -x in Pt/CoFe/MgO (Figs. 67(a)(e)) and +x in Ta/CoFe/MgO (Figs. 6-7(b)(f)), in agreement with our analysis
of magnetization switching (Figs. 6-6(b)(c)). The direction of HSL reversed when
the magnetization was oriented down. The linear fit in Fig. 6-7(a) reveals a large
HOL in Pt/CoFe/MgO of magnitude 50 Oe per 1011 A/m
2
, implying
0
SH = +0.06 in
Pt, which agrees well with [1]. The magnitude of HOL in Ta/CoFe/MgO is -200 Oe
per 1011 A/M 2 , implying 0 SH =-0.25 in Ta, twice as large as in [2] and closer to the
value reported for W [3].
The current-induced effective transverse field HFL, often associated with a "fieldlike" torque from the Rashba effect, was quantified similarly. Unlike HSL, the direction of was independent of the magnetization orientation (Figs. 6-7(c)(d)). The magnitude of HFL in Pt/CoFe/MgO (Fig. 6-7(c)) was _20 Oe/10" A/M 2 , two orders of
magnitude lower than reported in [15, 16], although its directionality was the same as
in Pt/Co/AlOx [15, 16]. Since current-induced DW motion had a very high efficiency
and occurred against the electron flow direction in Pt/CoFe/MgO, the fact that HFL
was negligible indicates that the Rashba effect cannot be the source of the extraor155
400
down magnetized
200 - o
0
Ir
(b)
(a)
01
L
(n
-200
~ 0 down magnetized
up magnetized
*
up magnetized
-
-400
400 -(c)
-
(d)
200
(D
-
-
0
0
IrU
-200
-400
L
I
1.0
0.5
0.0
Je (10
2.5
1.5 2.0
A m- 2)
0.2
0.0
11
(o)
(f)
HSL
H
0.6
0.4
J0 (10 11 A m2)
A
-
I
0.8
HFL
FL
z
2
Figure 6-7: Current-induced effective fields from the Slonczewski-like and field-like
torques. (a, b) Current-induced effective longitudinal field HSL, arising directly from
the Slonczewski-like torque, as a function of electron current density Je (from AC
excitation current amplitude) in Pt/CoFe/MgO (a) and Ta/CoFe/MgO (b). (c, d)
Current-induced effective transverse field HFL as a function of Je in Pt/CoFe/MgO
(c) and Ta/CoFe/MgO (d). (e, f) Illustration of the directions of the current-induced
effective fields HSL and HFL in Pt/CoFe/MgO (e) and Ta/CoFe/MgO (f), when the
magnetization is up and the electron flow is in the +x direction.
156
dinary DW dynamics. Furthermore, since any contribution to the Slonczewski-like
torque by the Rashba effect enters as a correction proportional to the nonadiabicity
parameter
3
R
< 1 [12, 13], the fact that HSL is here much larger than
HFL
implies
that the Rashba effect contributes negligibly to the Slonczewski-like torque.
In Ta/CoFe/MgO (Fig. 6-7(d)), HFL was by contrast quite large, ~400 Oe/10 1
A/M 2 , and its direction was the same as in Ta/CoFeB/MgO [14, 17] and opposite to
Pt/CoFe/MgO and Pt/Co/AlOx [15, 16]. The trend of |HFL
>
HSL Iis also observed
in Ta/CoFeB/MgO [14]. This result suggests that in addition to the Slonczewski-like
torque, a strong Rashba field may exist in this Ta-based sample. Alternatively, the
apparent Rashba field may be an artifact of the strong SHE-induced Slonczewski-like
torque combined with the weak perpendicular anisotropy in Ta-based ferromagnets. 3
However, the true origin of the measured HFL is beyond the scope of the present
discussion and will require further investigation.
6.5
Spin-Hall-Effect-Driven Domain Walls
As summarized in Figs. 6-7(e)(f), the current-induced torques are opposite in Pt/CoFe/
MgO and Ta/CoFe/MgO, as are the direction of current-driven DW motion and
the sign of the spin Hall angles in Pt and Ta.
Here we consider in detail the
case of Pt/CoFe/MgO, in which the field-like torque is unambiguously small. Onedimensional (1D) model calculations4 in Fig. 6-8(b) show that Bloch DWs cannot be
driven by the SHE alone, in agreement with prior reports [11] and with the symmetry
of the Slonczewski-like torque, which vanishes for mh aligned along the y-axis. In the
ID model with
OSH >
0 and with no transverse Rashba field, the addition of con-
ventional STT enables sustained DW motion, but its direction is along electron flow
(Fig. 6-8(b)). No combination of the SHE and STT reproduces the experimentally
3
1t is possible that the SHE generates a strong Slonczewski-like torque that pulls the magnetiza-
tion out of the xz-plane (towards the y-axis) in the Ta-based ferromagnets with weak perpendicular
anisotropy, or that the applied transverse field Hy assists the SHE Slonczewski-like torque in reducing
M2-
4
The ID calculations were conducted by Prof. Eduardo Martinez at the University of Salamanca,
Spain. The details and parameters for the calculations are found in [18] and the Methods and
Supplementary Information sections of our Nature Materials manuscript.
157
observed DW motion against electron flow. Moreover, conventional adiabatic and
nonadiabatic STTs are likely absent in the ultrathin thin Co layer, as concluded in
Chaps. 4 and 5 and corroborated by other recent studies indicating vanishing spin
polarization [19, 20]. Thus, a different mechanism is required whereby the SHE alone
- without the aid of any conventional STTs or Rashba field - can drive DW motion.
Neel DWs have an internal magnetization that would align with the nanowire
axis, such that the Slonczewski-like torque would manifest as a z-axis field (see Eq.
6.1) as experimentally observed in Fig. 6-2 and in Chap. 5 for similar Pt/Co/GdOx
nanostrips.5 However, the direction of HSL depends of the sense of the DW magnetization, and the direction of DW motion varies accordingly. In Pt/Co/AlOx [5, 21] and
Pt/Co/GdOx (Chap. 5), both up-down and down-up DWs move in the same direction
(against electron flow). We measured several different nanostrips of Pt/CoFe/MgO,
and current-driven motion was also unidirectional for up-down and down-up DWs
(Fig. 6-3). Fig. 6-8(a) illustrates Neel DWs with oppositely directed internal magnetization for up-down and down-up transitions, exhibiting a left-handed chiral texture
(defined using the same convention as in [22]). Based on the sign of the measured
Slonczewski-like torque (Figs. 6-6 and 6-7), these left-handed homochiral DWs move
against electron flow in Pt/CoFe/MgO (and along electron flow in Ta/CoFe/MgO,
due to the opposite SHE polarity).
Because Bloch DWs with no particular chirality are magnetostatically preferred
in our 500-nm wide nanostrips [23], an additional physical phenomenon is required to
stabilize N~el DWs of the same chirality throughout the thin films of Pt/CoFe/MgO
(and Ta/CoFe/MgO). This phenomenon is the Dzyaloshinskii-Moriya interaction
(DMI). The DMI is a form of magnetic exchange interaction in which adjacent spins
5
A recent report by Haazen et al. [9] on all-metal asymmetric Pt/Co/Pt stacks shows that current
effectively promoted domain expansion or contraction, i.e. up-down and down-up DWs moved in
opposite directions with respect to current under an in-plane longitudinal field. Current could
displace DWs only under a sufficient in-plane longitudinal field that locked the Nel wall configuration.
Adjacent up-down and down-up Nel walls were expected to have opposite chiralities, with their
internal magnetic moments oriented parallel to the longitudinal field, which would result in opposite
directions of motion with respect to current. When the direction of the longitudinal field was
reversed, the direction of motion for each DW was reversed. These results of current-driven DW
motion in Pt/Co/Pt were attributed to the Slonczewski-like torque from the spin Hall effect.
6
sometimes called the anisotropic exchange interaction.
158
(a)
%~\AHQI
z
a
--
vow
down-up DW
J
VDW
up-down DW
(b)
7-
300
200
HE+DMI
SHE+STT0 100
E
0 SHE only.
-10
-5
0
5
10
J. (1011 A m-2)
_140(
(d)
E E 120 0
-
L_
0
'a
E
100
80 0
60
40-
(e)
30-
0
up-down DW
down-up DW
o
E
0X20
00
10 -
0 up-down DW
down-up DW
140 -
p0
(g)
(h)
E 130
120)0
0
E 110> 100
-600 -300
0 300 600
H (Qe)
-600 -300
0 300 600
HY (06)
Figure 6-8: Current-driven dynamics of homochiral Neel domain walls. (a) Lefthanded chiral N~el domain walls in Pt/CoFe/MgO. The effective field HSL moves
adjacent up-down and down-up domain walls with velocity VDW in the same direction.
(b) Domain wall velocity as a function of electron current density J, calculated using
the ID model, with the spin Hall effect only (SHE only), the spin Hall effect and
spin-transfer torque (SHE+STT), and the spin Hall effect and the DzyaloshinskiiMoriya interaction (SHE+DMI). (c, d) Spin-torque efficiency for domain wall motion
in Pt/CoFe/MgO under applied longitudinal field H (c) and transverse field H. (d).
(e, f) Domain wall velocity at a constant current Je = -3.0 x 10" A/M 2 as a function
of H (e) and H. (f). (g, h) Calculated domain wall velocity as a function of H, (g)
and H, (h) using the ID model.
159
prefer to align orthogonal to each other with a certain handedness, in contrast with the
ferromagnetic exchange interaction in which spins prefer to align parallel. In the presence of both the DMI and ferromagnetic exchange, homochiral magnetix textures such
as spin spirals and skyrmions arise. The ingredients required for the DMI are a material with strong spin-orbit coupling and broken symmetry. Both of these are present
in Pt/CoFe/MgO (and similar ultrathin-film heterostructures discussed here), namely
the heavy-metal underlayer and the asymmetric interfaces across the ultrathin ferromagnet. Therefore, the DMI from the heavy-metal/ultrathin-ferromagnet interface
may be the mechanism responsible for stabilizing homochiral DWs in Pt/CoFe/MgO.
6.6
Homochiral Domain Walls
Finally, we assess the rigidity and chirality of the Neel DWs in Pt/CoFe/MgO using
applied in-plane fields. In Figs. 6-8(c)(d), we show that the spin-torque efficiency,
extracted similarly to Fig. 6-2(d), is insensitive to H, up to at least 600 Oe, but
declines significantly with increasing jHyl. This behavior is opposite to that reported
for Bloch DWs in [9], but is precisely what is expected for DMI-stabilized Neel DWs:
H, is collinear with the DW magnetization and exerts no torque, whereas Hy exerts
a torque that rotates the DW magnetization away from the x-axis and reduces the
z-axis-oriented HSL (see Eq. 6.1).
That the sense of internal DW magnetization
could not be reversed at the experimentally available maximum Hx of 600 Oe attests
to the strength of the DMI in this system. 7
We also measured the effects of Hx and H. on the velocity of fast current-driven
DWs (Figs. 6-8(e)(f)), which was reproduced qualitatively by the 1D model with the
SHE and DMI (Figs. 6-8(g)(h)).
Hx modified the velocities of up-down and down-
up DWs with opposite slopes (Figs. 4(e)(g)), whereas Hy modified both velocities
identically (Figs. 6-8(f)(h)). The ID model predicts DW motion reversal under very
large Hx coinciding with reversal of the DW sense, and impeded motion for large Hy
7
1n Chap. 7, we output larger Hx and H., to quantify the magnitude of the DMI in Pt/CoFe/MgO.
In that chapter, we also quantify the DMI in Ta/CoFe/MgO.
160
due to rotation towards a Bloch configuration. Interestingly, the velocity increased
with H, in the direction of the previously reported Rashba field in Pt/Co/AlOx [5, 15,
16], although here
HFL
in Pt/CoFe/MgO was vanishingly small. Our experimental
and computational results indicate that, even without the Rashba effect, H. can
modify the dynamics of N~el DWs driven by the SHE-induced Slonczewski-like torque.
While quantitative discrepancies exist between the 1D model calculations and the
experimental results, the qualitative features based on the symmetries of the currentinduced torques and DMI agree well with the experimental results.
6.7
Summary
We have shown that current alone drives DWs with high efficiency but in opposite
directions in Pt/CoFe/MgO and Ta/CoFe/MgO through the Slonczewski-like torque
due to the SHE. However, the SHE-induced torque alone cannot directly drive the
magnetostatically preferred Bloch DWs in these materials. The DMI provides the
missing ingredient to explain current-induced DW motion in heavy-metal/ ferromagnet/ oxide systems by stabilizing N el DWs with a built-in chirality, such that the
SHE alone drives them uniformly and with high efficiency. Engineering both the
DW spin structure and the current-induced torque simply by selecting the materials adjacent to the ferromagnet presents unprecedented opportunities for designing
current-controlled spintronic devices.
161
162
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[3] Pai, C.-F. et al. Spin transfer torque devices utilizing the giant spin Hall effect
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[5]
Miron, I. M. et al. Fast current-induced domain-wall motion controlled by the
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[6] Koyama, T. et al. Current-Induced Magnetic Domain Wall Motion in a Co/Ni
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[9] Haazen, P. P. J. et al. Domain wall depinning governed by the spin Hall effect.
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[11] Khvalkovskiy, A. V. et al. Matching domain-wall configuration and spin-orbit
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[13] Kim, K.-W., Seo, S.-M., Ryu, J., Lee, K.-J. & Lee, H.-W. Magnetization dynamics induced by in-plane currents in ultrathin magnetic nanostructures with
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[14] Kim, J. et al. Layer thickness dependence of the current-induced effective field
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[16] Pi, U. H. et al. Tilting of the spin orientation induced by Rashba effect in
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[18] Martinez, E. The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness. Journal of Physics: Condensed
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[20] Tanigawa, H. et al. Thickness dependence of current-induced domain wall motion
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165
166
Chapter 7
Statics and Dynamics of Chiral
Dzyaloshinskii Domain Walls
Spin-orbit interactions are rapidly emerging as the key to enabling efficient currentcontrolled spintronic devices. Much work has focused on current-induced spin-orbit
torques that can manifest at heavy-metal/ferromagnet interfaces. However, the importance of the Dzyaloshinskii-Moriya interaction(DMI), arisingfrom spin-orbit coupling and asymmetric interfaces, in determining the spin textures in these materials
is only now becoming apparent. The previous chapter (Chap. 6) indicates that DMIstabilized homochiral domain walls (DWs) can be driven with high efficiency by spin
torque from the spin Hall effect. Here, we exploit the angular dependence of the spin
Hall torque to unambiguously quantify its role in DW motion, while simultaneously
probing the structure of DWs and extracting the magnitude of the DMI. We show
that DWs stabilized by a strong DMI can be driven rapidly by current but also exhibit
distortions that have not been observed before.1
'This chapter consists of materials from the following preprint, submitted for publication:
Emori, S., Martinez, E., Bauer, U., Ahn, S.-M., Agrawal, P., Bono, D. C., & G. S. D. Beach. Spin
Hall torque magnetometry of Dzyaloshinskii domain walls. arXiv:1308.1432.
167
7.1
Domain-Wall Motion Assisted by the Spin Hall
Effect
Experiments were conducted on two similar out-of-plane magnetized thin-film stacks
of MgO-capped 0.6-nm thick Co80 Fe 20 grown on nonmagnetic heavy-metal underlayers
of either Ta or Pt (described in Sec. 6.1. These films were lithographically patterned
into nanostrips that served as conduits for DW motion. Fig. 7-1(a) shows a nanostrip
device and the experimental schematic. A reversed domain was first nucleated with
the Oersted field from a current pulse through the nucleation line (connected to PG1
in Fig. 7-1(a)). A DW was then propagated along the nanostrip by sweeping an
out-of-plane field H, while maintaining a constant driving electron current density J
(output by PG2 in Fig. 7-1(a)). Magnetization reversal was detected locally with the
polar magneto-optical Kerr effect (MOKE). In the absence of nucleation pulses (Fig.
7-1(b)), the switching field corresponds to the threshold field for random domain
nucleation. When nucleation pulses were applied at the zero-crossings of the swept
field Hz (Fig. 7-1(b)), the switching field decreased significantly, corresponding in
this case to the out-of-plane propagation field Hp,,op required to drive the nucleated
DW through the defect potential landscape.
The out-of-plane magnetic field H, to drive DWs was output from an air-coil
directly beneath the substrate. An electromagnet with iron pole pieces output the
in-plane bias field. The in-plane field by itself does not move DWs but may rotate
the the internal DW moment (Fig. 7-2). Current densities were restricted to a range
1Jej < 1010 A/M
2
to minimize Joule heating and to ensure quasi-static DW motion.
Fig. 7-2 show examples of AHp,,op versus Je measured in Ta/CoFe/MgO. AHp,,op
varies linearly with Je, indicating that current acts as an out-of-plane effective field
Hzeff = XJe to assist or inhibit field-driven DW depinning. Here, x parameterizes
the strength and direction of current-induced Hzff, and is obtained from the slope
of AHp,,Op versus Je and the direction of current-assisted motion. x is equivalent in
magnitude to the spin-torque efficiency c quantified in Chaps. 4, 5, and 6; however,
the sign of E denotes the direction of DW motion with respect to electron flow (i.e.
168
(a)
10 pm
PG1
zt
H0
PG2
(b)
I
0
:
-40
0
-20
HZ
20
40
(0e)
Figure 7-1: (a) Illustration of the experimental setup superposed on a micrograph of a
nanostrip device. Pulse Generator 1 (PG1) outputs the domain wall (DW) nucleation
pulse. The DW is propagated by out-of-plane field H, and electron flow J from PG2.
DW motion is detected with the magneto-optical Kerr effect (MOKE). (b) Out-ofplane magnetization hysteresis loop measured with MOKE. The solid hysteresis loop
was obtained with DWs initialized by the nucleation pulse, and the red dotted lines
indicate the DW propagation field Hp,,op. The dotted hysteresis loop was obtained
without initialized DWs, and the magnetization switching is governed by random
reverse domain nucleation.
Je > 0 for DW motion along electron flow), whereas the sign of x denotes the direction
of Hzff.
With no in-plane field (Fig. 7-2(a)), current drives both up-down and down-up
DWs along the electron flow direction. Therefore, the sign of x, hence the direction of
H'ff is opposite for up-down and down-up DWs as illustrated in Fig. 7-2(a). With
a sufficiently large in-plane longitudinal field H. along the -x-direction (Fig. 7-2(b)),
the sign of x reverses for down-up DWs, while it is unchanged for up-down DWs .
Under a transverse field Hy (Fig. 7-2(c)), x is reduced substantially regardless of the
sense of the DW transition. Similar trends were observed in Pt/CoFe/MgO, although
for Hx = Hy = 0 DW propagation was assisted against the electron flow direction,
and much larger in-plane fields were required to modify x.
169
(a)
-6
10
down-up DW
up-down DW
Sup-down DW
0 down-up DW
I,
__4-
jHsH -
0
0
-I
-1.0
0.0
-0.5
j.
(b)
20
(D
10
10
(10
0.5
1. 0
0.5
1.0
0.5
1.0
i,
j,
2
A/m )
-10
-
-20
-1.0
0.0
-0.5
2
je (1010 A/m )
(C) 20
10
0
-4
.
A
-10
-201
-1.0
-0.5
0.0
j. (100 A/m 2)
Figure 7-2: In-plane-field dependence of domain-wall motion driven by the spin Hall
effect. (a) Zero in-plane field. (b) In-p lane longitudinal field H, = -400 Oe. (c)
In-plane transverse field H. = -400 Oe.
170
Fig. 7-3 summarizes the dependence of x on H. and H. for Ta/CoFe/MgO. Fig.
7-4 likewise summarizes the in-plane field dependence of x for Pt/CoFe/MgO. For
both structures the sign of x reversed with sufficiently large H" > 0 (H. < 0) for updown (down-up) DWs, and decreased toward zero with increasing IH. . In the case of
Ta/CoFe/MgO, X saturates at IHl > 200 Oe, whereas saturation in Pt/CoFe/MgO
could not be observed due to random domain nucleation at in-plane fields higher than
those shown. The strong in-plane field dependence of x suggests that the currentinduced effective field depends strongly on the orientation of the internal DW moment.
Conventional nonadiabatic STT acts as an out-of-plane effective field that can
assist DW motion, and would produce precisely the behavior seen in Fig. 7-2(a).
However, the results in Figs. 7-2(b)(c), 7-3, and 7-4) are inconsistent with nonadiabatic STT, because its magnitude and, more importantly, polarity should be independent of H, and H.. If nonadiabatic STT were present, there should be a finite
offset in X against applied in-plane field, due to the STT pushing the DW along electron flow independent of the orientation of the internal DW moment. In the case of
Ta/CoFe/MgO, the offset XSTT can be estimated from the difference in the saturation
level of X for H, > 200 Oe, yielding XSTT= 0.3 ± 0.5 Oe/101 0 A/M 2 . From xos, the
product of the nonadiabaticity parameter 0 and current spin polarization P can be
estimated through [1]
=
2 e M5A
hP
XSTT,
(7-1)
where e is the electron charge, Ms is the saturation magnetization, and A is the DW
width. Taking M, a 700 emu/cm 3 and A ~ 10 nm, we obtain 3 = 0.06 ± 0.1. This
is much smaller than OP > 1 inferred previously from measurements of x in similar
materials [2, 3, 4, 51, where variations under in-plane fields were not considered. The
near-vanishing of nonadiabatic STT is likely due in part to reduced spin-polarized
current expected in the ultrathin CoFe layer.
An alternative mechanism that can readily explain the in-plane-field dependence of
current-induced DW motion is the Slonczewski-like torque, which can be generated by
171
(a)
o down-up DW
1
20
A up-down DW
10
G~
7
E1
m
*
00C:
01
-10 >
3
-1
-20
-600
-400
-200
200
0
400
HX (0e)
600
(b)
01 - 20
0
I
10
0
E 0
-1
0
o
10
0
-20
-600
-400
-200
0
200
400
6
H (0e)
Figure 7-3: Domain-wall orientation under in-plane fields in Ta/CoFe/MgO. The
SHE-induced DW-motion efficiency x is related to the x-component of the DW moment through Eq. 7.3. Open symbols are experimental data obtained
from AHpp
versus Je. Solid curves are obtained from the DW macrospin analytical model (Sec.
7.2.2). Cartoons illustrate the orientation of the DW moment.
the Rashba effect or the SHE in heavy-metal/ferromagnet stacks. Since the Rashbainduced Slonczewski-like torque scales with OP [6, 7] while the SHE-induced torque
is independent of OP [7, 8], here we assume that the Slonczewski-like torque arises
predominantly from the SHE. This spin-Hall torque can be described by an effective
field of the form HSH ~
Ih x
(Z x je), where mi,
i, and Je are the unit vectors in the
directions of the magnetization, out-of-plane z-axis, and electron flow, respectively.
The DW moment lies in the xy-plane in an out-of-plane magnetized film, so HSH
takes the form of a z-axis effective field proportional to the x-component of the DW
172
(a)
down-up DVV
1
E
10 3
0
-1
AAAA
up-down DW
-2000
-1000
0
HX (Oe)
1000
2000
(b)
10
1
Ex
00C:
04+0OO
0 O
-10
-1
-1200
-10
-800
-400
400
0
HY (0e)
800
1200
Figure 7-4: Domain-wall orientation under in-plane fields in Pt/CoFe/MgO. The
SHE-induced DW-motion efficiency x is related to the x-component of the DW moment through Eq. 7.3. Open symbols are experimental data obtained from AHp,,op
versus Je. Solid curves are obtained from the tilted DW analytical model (Sec. 7.2.3).
Solid symbols are obtained from micromagnetic calculations. Cartoons illustrate the
orientation of the DW moment.
173
moment, mX.
Sufficiently large H. rotates the DW to a Bloch configuration, such that HSH
should vanish in the DW, consistent with the results in Fig. 7-2(c). Under sufficiently
large Hx, a Neel configuration is preferred such that, with mx along Hx, the SHE gives
a z-axis field oriented in the same direction for up-down and down-up DWs, which
would drive them in opposite directions (Fig. 7-2(b)). The data in Figs. 7-2(b), 7-3,
and 7-4 then imply that the DWs are spontaneously N~el with left-handed chirality
(Fig. 7-2(a)), for both Ta/CoFe/MgO and Pt/CoFe/MgO, despite the magnetostatic
preference for Bloch DWs in nanostrips of these dimensions [9].
7.2
Quantitative Analysis of Chiral Domain Walls
7.2.1
Spin Hall Angle
In an out-of-plane magnetized film, the expression for HSH derived by Thiaville et
al. [10] is
HSH =
2
H cos
=
2
Hm
,
(7.2)
where (D is the angle between the DW moment iii and the current (x-)axis, and
mnx= cos 1. Comparison to the phenomenological effective field Hf f = XJ, inferred
from the data in Fig. 7-2 leads to the identification
H mX.
x 2 Je
=
(7.3)
Here, HiS is equivalent to HiS defined in Eq. 6.2.
At Hx = HY = 0, we set jmxj = 1, i.e. the DW spontaneously takes a Neel
configuration stabilized by the DMI. In particular, for the DW to be left-handed,
the up-down DW takes mx = -1
whereas the down-up DW takes mx = +1. The
magnitude of the SHE-torque efficiency in Ta/CoFe/MgO is JxK
_ 15 Oe/10 1 0 A/m 2 ,
and in Pt/CoFe/MgO Jx~ 9 Oe/10 10 A/m 2 .2 From Eqs. 7.3 and 6.2 with M, ~ 700
2
The values reported here are ~10% lower than those in Chap. 6, likely because of the difference
in field calibration of the out-of-plane electromagnet and measurement procedure, e.g. difference in
174
Figure 7-5: Spin structure of left-handed Nel domain walls. J indicates the direction
of electron flow, and VDW indicates the direction of DW motion driven by the effective
spin Hall effect field HSH-
emu/cm 3 , we obtain 0OSHI ~ 0.11 for Ta and
0
SHI ~ 0.07 for Pt. These estimated
spin Hall angles are in excellent quantitative agreement with [11] and [8], although
0
SH for Ta is smaller than inferred from magnetization tilting measurements in Chap.
6.
7.2.2
Dzyaloshinskii-Moriya Interaction in the Weak Limit
Eq. 7.3 shows that X can be used to probe the static orientation of the DW moment
as a function of H. or H., from which the angular-dependent internal DW energy
terms can be quantified, in analogy with conventional magnetometry. We propose to
call such quantification of these DW energy terms "spin Hall torque magnetometry,"
because it relies on the measurement of quasi-static DW motion driven by the spin
Hall torque, described in Sec. 7.1. Here, we model the behavior of the DW moment
under in-plane bias fields, assuming that it can be described as a single macrospin
mX.
Fig. 7-5 shows schematically the structure of left-handed homochiral Neel DWs
stabilized by the interfacial DMI. These Dzyaloshinskii DWs have their internal moment pointing along -x for up-down DWs and along +x for down-up DWs. The DMI
can be modeled as an effective field HD that points along the DW normal. The sign
field sweep rate.
175
z
Figure 7-6: Rotation of the DW moment parameterized by angle 1 in the rigid DWline assumption.
of HD is opposite for up-down and down-up DWs. Here, for the left-handed chirality,
HD < 0 for the up-down DW, and HD > 0 for the down-up DW. The current-induced
spin Hall effective field HSH is shown corresponding to the case of a Pt/CoFe/MgO
nanostrip with electron flow along -x; for the case of Ta/CoFe/MgO, the effective
field directions are opposite due to the opposite sign of the spin Hall angle.
Fig. 7-6 shows a DW described as a single macrospin canted away from the xaxis along the nanostrip by an angle 1. Canting can occur under a transverse field
Hy, or under a sufficently large longitudinal field Hx opposing HD so that the DW
is forced towards the opposite chirality. The spin Hall effective field HSH is related
to 4D as described in Eq. 7.2. The easy axis of this macrospin is orthogonal to the
DW normal (defined by the shape anisotropy field of the DW, which prefers a Bloch
configuration), and the DMI enters as a hard-axis bias field. The DW surface energy
density is written [10]:
-= 2AK, cos2
4
- 7r D cos(4) + 4 /AK
1
,
(7.4)
where K, is the magnetostatic in-plane shape anisotropy of the DW (magnetostatic
energy barrier between the Bloch and Ndel configurations), D is the DMI constant,
A is the exchange stiffness, K 1 is the effective out-of-plane uniaxial anisotropy, 3 and
A is the DW width. The last energy term on the right-hand side of Eq. 7.4 is
independent of the canting angle (D. This is the conventional "self-energy" of a DW
3Kj_ = K
-
M 8 2 /2 with K
the uniaxial perpendicular magnetic anisotropy constant, M, is the
saturation magnetization
176
from the ferromagnetic-exchange and uniaxial-anisotropy energy penalties of having
a DW.
We can re-write Eq. 7.4 in terms of effective fields. The effective fields for the
energy terms of shape anisotropy Hk, DMI HD, and self-energy H 1 shown in [10]
are4 :
2Ks
(7.5)
M8
D
HD
If
(7.6)
MSD
MsA'
=
2K-L
(7.7)
H1 should be close to the in-plane saturation field of the out-of-plane magnetized
film (~3 kOe for Ta/CoFe/MgO and ~5 kOe for Pt/CoFe/MgO).
The DW energy in terms of the above effective fields is
2AM8
-Hkcos2
k
2
D - -HDcos 4 + H 1 .
(7.8)
2
We can include the effects of an external in-plane longitudinal field H. and transverse
field H., by introducing Zeeman energy terms,
2AM3
1k
2
2
HD cos 4)-
7TH,,cos(4D) -
2
7THy
2 '
sinI4)+HL
H1
(7.9)
Without applied fields, the DW takes a Neel form with m, along ±x corresponding to
P = 0, 7, whenever
IHDI
>
!Hk
. In the presence of applied in-plane fields, however,
(D may rotate away from the x-axis.
Minimizing a- with respect to 1, i.e. d-dI = 0, yields the zero-torque condition
and allows us to calculate equilibrium 1, hence the internal DW moment, as a function
4
In SI units, M, is multiplied by a factor of po.
177
of H. or Hg. Under H. (and H, = 0), the X-component of the DW moment mx is
mn = cos4 =
±1,
(HD +HX)
(HD + Hk)/(2Hk),
-!Hk
+1,
(HD + Hx) < -_ Hk
> 2Hk
HX) <
< (HD +
2Hk
(7.10)
Similarly, the solution for m under H. is
-Hkm
-
1--HmD2 -Hymx
2
= 0.
(7.11)
With Hk and HD adjusted, the above equations (7.10 and 7.11) adequately reproduce the experimentally observed DW rotation in Ta/CoFe/MgO, as shown by the
solid curves in Fig. 7-3. The best fit to the experimental data yields Hk =110 Oe
and
JHDJ
= 80 Oe, with HD oriented along -x for up-down DWs and +x for down-
up DWs, indicating left-handed chirality. Writing Hk in terms of the demagnetizing
factor Nx for a N~el DW in the thin film limit [12]
Hk
MsNx
Mst In (2)
Mltl
,A
(7.12)
we deduce a DW width A _ 11 nm for this sample. The expression for HD (Eq. 7.6)
then yields D _ -0.053 mJ/m 2 , where the sign indicates the left handedness of the
DW. Although HD in Ta/CoFe/MgO is larger than the threshold
7
1Hk
necessary to
stabilize Dzyaloshinskii DWs [10], the DW moment can be easily reoriented with weak
in-plane applied fields. The close correspondence between the macrospin calculation
and the data in Fig. 7-3 shows that when 4D rotates, the DW itself remains rigid and
its configuration is well-described by the single parameter <1.
7.2.3
Dzyaloshinskii-Moriya Interaction in the Strong Limit
In Pt/CoFe/MgO, a much larger longitudinal field jHxj
reverse x and mx, as shown in Fig. 7-3(a).
178
4 2000 Oe is required to
The reversal is much more gradual
weak DMI
strong DMI
E1 IE
0
Figure 7-7: Rotation of the DW moment under a torque in a material with weak DMI
and strong DMI.
than the narrow transition width ~lHkl for m, predicted by the rigid DW macrospin
model. These observations indicate that the DMI is much stronger in Pt/CoFe/MgO,
and that the model governed by Eq. is insufficient to account for the response of the
DW to externally applied torques. To capture the observed static DW configuration
with respect to in-plane fields in Pt/CoFe/MgO, another degree of freedom must be
introduced into the model.
When an in-plane field is applied in a direction other than HD, the Zeeman energy
tends to align the DW moment with the applied field, while the DMI prefers the
moment to remain normal to the DW plane. If the DW remains rigidly fixed in
position, then 4D rotates progressively away from HD towards the applied field at
the expense of the DMI energy term. However, if the DW itself is free to rotate
in the xy-plane, the DW moment can follow the applied field with a reduced DMI
energy penalty (see Fig. 7-7). Although there is an associated energy cost due to the
increased DW length, the net energy should be lowered by DW tilting if the DMI is
sufficiently strong.
We have modeled this behavior by modifying the analytical to parameterize the
DW by two angles: qr,which describes the inclination of the DW moment away from
the DW normal, and 0, the tilting angle of the DW normal away from the x-axis. We
assume that the DW remains straight, so that the DW moment is everywhere inclined
179
L - 1/cos0
Figure 7-8: Definitions of the two angles to parameterize DW moment rotation in the
macrospin model. The length L of the DW scales with 1/cos 9.
by an angle 4) = q +0 from the x-axis. The governing energy equation, modified from
Eq. 7.13, now reads
2z\M 8
cos(
7r
S1 _
1
-H COs2 - -HDCos7---Hx
cos(71+9) -- H, sin (27 +)
2
2
2
2
+ H1 )
(7.13)
Minizing o with respect to r and 0 (i.e.
- = 0) produces the zero-torque
_=
condition. From this, we obtain r and 0 at equilibrium and thus the DW moment
orientation <D = r7 + 9 as a function of Hx or Hy.
Under Hx (and Hy = 0), we obtain
sin0 =
' Hx sin 77
2
Hk cos2 -q+
s
HDcos27- H 1
(7.14)
and
sin y7 = 7 Hsin(7+)
HD
Hkcos 7-
(7.15)
For Hx far from Hx = -HD, the physical solutions are 7 = 0, 7r, and 0 = 0. This
corresponds to the DW moment orienting along the x-axis (mx = t1) with no tilting
of the DW normal.
Similarly, for the H. case, we have
sin 0
2Hx
=
I Hk cosS2
-
180
cos7
HDcosq + H 1
(7.16)
i(a)
Hx<O
X
(b)
Hy>0
X
(d)
'U)'
A
120
90
*0
60
PM
Y~
pMi
-
1DO
V
60
90
30
0
-30
1D "
CO-60
30
-3000
-2000
-1000
0
Hx (Ce)
1000
2000
I
-90
a
".-
-1500
3000
-1000
-500
0
HY (0e)
500
1000
1500
Figure 7-9: Micromagnetic snapshots of equilibrium DW structure for parameters
appropriate to Pt/CoFe/MgO. Red (blue) corresponds to M > 0 (M2 < 0). Results
are shown for longitudinal field H, against the DMI internal field (a) and under
increasing transverse field Hy (b). The angle of the DW moment inclination from the
DW normal, q, and the tilt of the DW normal away from the x-axis, 0, and their sum,
<b, are plotted versus Hx (c) and H. (d) for micromagnetic simulations (symbols) and
the analytical model (solid lines).
and
sin1 7=
'TH,
cos (,q + 0)
Hkcosr7- 'HD
.
(7.17)
The solid curves in Fig. 7-4 were obtained by solving Eqs. 7.14 - 7.17 and identifying
effective field parameters that yielded best fits to the data. Fig. 7-4 shows the results
for IHD
=
2800 Oe and H1 = 6300 Oe. The value of H1 was in close agreement with
the in-plane saturation field measured on continuous films. Note that HD is larger
than the longitudinal field required to null mx, because as the DW tilts, 4D = wF/2 is
reached before 7 = 7r/2.
DW tilting under in-plane fields was verified by full micromagnetic simulations
181
as summarized in Fig.
7-9.
Material parameters appropriate for Pt/CoFe/MgO
were used,5 and D was varied to best match the data in Fig. 7-4.
shown correspond to D = -1.2
The results
mJ/m 2 . Under increasing H, antiparallel to the
DW moment (Fig. 7-9(a)), there is a rotation of r/ and 0 until the DW chirality
reverses and the tilting abruptly vanishes. Under a transverse field Hy (Fig. 7-9(b)),
4D likewise rotates continuously towards 7r/2 through a combination of DW moment
and surface-normal tilting until, above a critical field, the DW plane rotates abruptly
to wr/2 and runs along the length of the nanostrip. The micromagnetically computed
(mX) taken as an average along the centerline of the DW shows excellent agreement
with the experimentally-measured X in Fig. 7-4, and the analytically computed tilt
angles match well to the micromagnetics results (Figs. 7-9(c)(d)). Interestingly, for
HY > 1000 Oe, DW propagation along the nanostrip could no longer be detected
experimentally, which is consistent with the fully rotated domain structure predicted
in Fig. 7-9.
Here DW tilting is induced by in-plane applied fields. However, this phenomenon
is expected to be a general feature of strong Dzyaloshinskii DWs whenever torques
are present that tend to rotate the DW moment in the plane. Under conditions of
dynamic DW propagation, driven by an applied field Hz, or the effective out-of-plane
field induced by the SHE, the (effective) field applies a torque to the DW moment
causing a rotation about the z-axis. In the ID model of DW dynamics [10], the canting
angle <D increases with increasing driving field (current). For Dzyaloshinskii-DWs
with strong DMI, this rotation is expected to be taken up in part through rotation
of the DW line profile for the reasons outlined above. Indeed, a recent publication
by Ryu et al. [13] reported unexplained tilting of DWs driven by current pulses in
Pt/Co/Ni/Co/TaN. This tilting is entirely consistent with the expectations for SHEdriven motion of Dzyaloshinskii DWs, suggesting that tilting may be universal in
material systems with strong interfacial DMI.
5
A = 10-11 J/m, M, = 7 x 10
5
A/m, Ku = 4.8 x 10
182
5
J/m 3 , A =
A/(Ku - jPoM 2 ) = 7.6 nm.
7.3
Dynamics of Chiral Domain Walls under Weak
and Strong Dzyaloshinskii-Moriya Interactions
The different magnitudes of the DMI, quantified by HD or D, in Ta/CoFe/MgO
and Pt/CoFe/MgO should reflect in their DW dynamics. The DW velocity v in the
one-dimensional model [10] is
'yA7
2
HD
1 + (aHD/HSH 2
(7.18)
with a the Gilbert damping. The effective SHE field HSH scales with the electron
current density Je.
At low Je, HSH< aHD so that
-yIA7
2
HSH
oz .
(7.19)
aHD, v saturates toward
By contrast, at higher Je such that HSH
2
2
HD-
(7.20)
Fig. 7-10(a) shows v versus Je for Ta/CoFe/MgO and Pt/CoFe/MgO. The maximum
Je
was limited by random nucleation, and the relatively low velocities suggest the
dynamics do not fully reach the flow regime. Nonetheless, the essential qualitative
features are evident. Taking a = 0.3, as justified below, the transition between HSHlimited (Eq. 7.19) and HD-limited (Eq. 7.20) velocities should occur at - 2 x 1010
A/M
2
for Ta/CoFe/MgO and - 1 x
1012
A/M
2
for Pt/CoFe/MgO. This explains the
contrasting behaviors in Fig. 7-10(a), where v saturates at a 4 m/s for Ta/CoFe/MgO
due to the small HD. By contrast, v increases remarkably and does not saturate in
Pt/CoFe/MgO up to the highest accessible Je ~ 3 x 1011 A/M 2 .
In the simple ID model that disregards the tilting of DW line, H, modifies Eq. 7.18
as HD -
HD + H.. v should depend strongly on H, in the HD-limited regime (Eq.
7.20), but weakly in the SHE-limited regime where v oc J. The strong Hr-dependence
183
40
(a)
Pt/CoFeMgO
A-1000 Oe
" Oe
30
20
0 +1000
10
-
A
Oe
+300
0
4
Oe
A
-)
0
>
Ta/CoFe/MgO
A -300 Oe
U Oe
-0
-10
-20
-2
-3
-1
(d)
(b) 15
A up-down DW
0 down-up DW
10
-
A
-
>5
0
-2000
-1000
20
0
1000
Aje
-20
A AA
'p
60
40
*@
AA
3
2
1
0
Je (1011 A m-2)
-20
-401
-60 0
2000
0
0 0W
A
J_____________
I
-400
-200
H (0e)
(e)
(c) 15
200
0
HX (Oe)
400
6
5-
-k
4-
10
>5
3-
4*1
2
I
1
0
-_
-2000
-1000
0
HY (0e)
1000
0-
-600
2000
600
Al
-400
-200
a
0
200
H (0e)
400
600
Figure 7-10: Current-driven dynamics of Dzyaloshinskii domain walls. (a) Velocity
of up-down domain walls as a function of electron current density Je under different
in-plane longitudinal fields H,. (b,c) Domain wall velocity in Pt/CoFe/MgO as a
function of in-plane longitudinal field H. (b) and transverse field H, (c) at a fixed
2
electron current density Je = +0.9 x 10" A/M . (c,d) Domain wall velocity in
Ta/CoFe/MgO as a function of H (d) and H, (e) at Je = -1.8
184
x
10" A/M 2
for Ta/CoFe/MgO (Fig. 7-10(d)), and the weak dependence for Pt/CoFe/MgO (Fig.
7-10(b)), agree qualitatively with these expectations.
From [10, 14], the velocity under H. is most conveniently written
_
HSH
hY|A7r
2oa y/1+± (( HsH + aHY)/ciHD)2
(.1
which is equivalent to Eq. 7.18 when H, = 0. This form shows that v should exhibit
a peak at H. = -HSH/a and tend toward zero for large IH. . The peak in v versus
H. in Pt/CoFe/MgO at H.,
350 Oe (Fig. 7-10(c)) indicates a
0.3, which agrees
with pump-probe measurements in similar Pt/Co/AlOx films [15] . The data for
Ta/CoFe/MgO (Fig. 7-10(e)) also show the expected asymmetry, but in this case
with a broad plateau.
Quantitatively, the ID model has significant shortcomings in describing these
data, due largely to the effects of pinning from disorder that leads to slower, thermally activated DW dynamics. However, even without disorder, deviations from iD
dynamics are expected due to DW tilting under strong DMI. Fig. 7-11 shows micromagnetic simulations for Pt/CoFe/MgO depicting the static DW state and the
steady-state propagating DW structure under Je = -1.8
rotates counterclockwise by 0
At an even higher current Je
0
x 1011 A/m 2 . The DW
20', so that compared to the ID model, 1D is larger.
=
-2.5 x 1012 A/M 2, micromagnetic modeling shows
) 450 , and the obtained velocity of 320 m/s is -25% lower than in the ID model.
The larger tilting of the DW away from the current (x-)axis reduces the efficiency of
the SHE, HSH, in driving DWs, thereby decreasing the DW velocity compared to the
ID model that disregards DW tilting. The tilted DWs observed in micromagnetics
are also consistent with a recent publication reporting unexplained DW tilting under
large current pulses in Pt/Co/Ni/Co/TaN [13]. This tilting is naturally explained as
resulting from strong DMI.
Current-driven DW dynamics in such systems have been previously attributed to
the Rashba field together with strong nonadiabatic STT, whose magnitude scales with
the product of nonadiabatic parameter
# and current
185
spin polarization P. Our obser-
Figure 7-11: Micromagnetically computed domain-wall line tilting driven by spin-Hall
torque, at various current densities Je and applied longitudinal field H,.
vations suggest theories based on large OP must be carefully considered in systems
where this term is demonstrably small. Although our experiments do not preclude
a transverse Rashba field HR, since
significant only for
acHR/HSH
=
HRJ
HR
modifies Eq. 7.18 as H-
> HSH and acts simply to rescale
+
Hy + HR, it is
v at large Je. The case
-1 is notable, however, because then there would be no net torque to
tilt the DW. Under this special case, DWs could propagate at high speeds without
distortion at v
=
(4yjA7r/2a)HH)
even under weak DMI, so long as HD exceeds
the magnetostatic threshold to stabilize N~el DWs over Bloch. While initial estimates [16, 17] of HR in Pt/ferromagnet/oxide stacks have been revised significantly
downward by subsequent experiments [8, 14, 18], there are indications that in some
materials [14, 19, 20] HR may be comparable to HSH. The Rashba effect could potentially enhance DW dynamics if the ratio HR/HSH could be optimally tuned.
7.4
Summary
Current-induced domain wall motion in the presence of the Dzyaloshinskii-Moriya
interaction (DMI) is experimentally and theoretically investigated in heavy-metal/
ferromagnet bilayers, where the heavy metals are Ta and Pt. The angular dependence of the current-induced torque from the spin Hall effect and the magnetization
structure of Dzyaloshinskii domain walls are described and quantified simultaneously
186
in the presence of in-plane fields. While the spin Hall angles in Ta and Pt are similar
in magnitude, the DMI is more than 20 times stronger in the Pt-based ferromagnet.
We show that efficient current-driven motion requires both a large spin Hall effect
and strong DMI, but the latter leads to wall distortions not seen in conventional
materials. These findings provide essential insights for understanding and exploiting
chiral magnetism for emerging spintronics applications.
187
188
Bibliography
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[2] Miron, I. M. et al. Domain Wall Spin Torquemeter. Physical Review Letters
102, 137202 (2009).
[3] Boulle, 0. et al. Nonadiabatic Spin Transfer Torque in High Anisotropy Magnetic
Nanowires with Narrow Domain Walls. Physical Review Letters 101, 216601
(2008).
[4] San Emeterio Alvarez, L. et al. Spin-Transfer-Torque-Assisted Domain-Wall
Creep in a Co/Pt Multilayer Wire. Physical Review Letters 104, 137205 (2010).
[5] Lee, J.-C. et al. Universality Classes of Magnetic Domain Wall Motion. Physical
Review Letters 107, 067201 (2011).
[6] Wang, X. & Manchon, A. Diffusive Spin Dynamics in Ferromagnetic Thin Films
with a Rashba Interaction. Physical Review Letters 108, 117201 (2012).
[7] Kim, K.-W., Seo, S.-M., Ryu, J., Lee, K.-J. & Lee, H.-W. Magnetization dynamics induced by in-plane currents in ultrathin magnetic nanostructures with
Rashba spin-orbit coupling. Physical Review B 85, 180404 (2012).
[8] Liu, L., Lee, 0. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. CurrentInduced Switching of Perpendicularly Magnetized Magnetic Layers Using Spin
Torque from the Spin Hall Effect. Physical Review Letters 109, 096602 (2012).
189
[9] Koyama, T. et al. Observation of the intrinsic pinning of a magnetic domain
wall in a ferromagnetic nanowire. Nature Materials 10, 194-197 (2011).
[10] Thiaville, A., Rohart, S., Ju , E., Cros, V. & Fert, A. Dynamics of Dzyaloshinskii
domain walls in ultrathin magnetic films. EPL (Europhysics Letters) 100, 57002
(2012).
[11] Liu, L. et al. Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum.
Science 336, 555-558 (2012).
[12] Tarasenko, S., Stankiewicz, A., Tarasenko, V. & Ferr6, J. Bloch wall dynamics
in ultrathin ferromagnetic films. Journal of Magnetism and Magnetic Materials
189, 19-24 (1998).
[13] Ryu, K.-S., Thomas, L., Yang, S.-H. & Parkin, S. S. P. Current Induced Tilting
of Domain Walls in High Velocity Motion along Perpendicularly Magnetized
Micron-Sized Co/Ni/Co Racetracks. Applied Physics Express 5, 093006 (2012).
[14] Emori, S., Bauer, U., Ahn, S.-M., Martinez, E. & Beach, G. S. D. Current-driven
dynamics of chiral ferromagnetic domain walls. Nature Materials 12, 611-616
(2013).
[15] Schellekens, A. J. et al. Determining the Gilbert damping in perpendicularly
magnetized Pt/Co/AlOx films. Applied Physics Letters 102, 082405-082405-4
(2013).
[16] Miron, I. M. et al. Current-driven spin torque induced by the Rashba effect in a
ferromagnetic metal layer. Nature Materials 9, 230-234 (2010).
[17] Pi, U. H. et al. Tilting of the spin orientation induced by Rashba effect in
ferromagnetic metal layer. Applied Physics Letters 97, 162507-162507-3 (2010).
[18] Garello, K. et al. Symmetry and magnitude of spin-orbit torques in ferromagnetic
heterostructures. Nature Nanotechnology 8, 587-593 (2013).
190
[19] Kim, J. et al. Layer thickness dependence of the current-induced effective field
vector in TajCoFeBlMgO. Nature Materials (2012).
[20] Fan, X. et al. Observation of the nonlocal spin-orbital effective field. Nature
Communications 4, 1799 (2013).
191
192
Chapter 8
Conclusions and Outlook
8.1
Summary of this Thesis
Control of magnetization by electric current, rather than by magnetic field, is essential for scalable low-power devices in memory-storage applications. Since domain-wall
(DW) motion is a convenient way to control stored magnetization in many proposed
devices, enhancing electrically-driven DW dynamics is of great technological interest.
Out-of-plane magnetized thin films, patterned into nanostrips, are great platforms
for these devices, because DWs in such films are compact and can be moved by relatively low currents. Taking advantage of strong spin-orbit coupling in out-of-plane
magnetized heavy-metal/ferromagnet multilayers is an especially promising route to
generate robust current-induced torques. We demonstrate extraordinarily efficient
current-driven DW motion in an ultrathin ferromagnetic metal, sandwiched between
a nonmagnetic heavy metal and oxide, and pinpoint the physics responsible for the extraordinary dynamics. The important contributions emerge not from the ferromagnet
itself, but from the nonmagnetic heavy metal interfaced with the ferromagnet.
The conventional mechanisms of current-induced DW motion are spin-transfer
torques, which rely on angular momentum transfer between spin-polarized conduction
electrons and gradients of magnetic moments (i.e. DWs) within the ferromagnet.
Although spin-transfer torques have been shown to drive DWs in "thick"
(> 1
nm)
ferromagnetic films, we reveal that in ultrathin ferromagnets spin-transfer torques are
193
Pt
Co
Pt
electron flow, Je
3dOx
no current-induced motion
efficient motion against electron flow
40
40-
20-
W20-0
0
-20 -
-20
-40
-40
-
-1.0 -0.5 0.0 0.5
J. (10" A/m 2)
-1.0 -0.5
1.0
0.0
0.5
1.0
J (1011 A/m 2)
Figure 8-1: Current-induced domain-wall motion in Pt/Co/Pt and Pt/Co/GdOx.
Data show the change in domain-wall propagation field AlHprop
as a function of
injected electron current density Je.
negligible and alternative interfacial phenomena instead contribute to domain-wall
motion. For example, a symmetric multilayer of Pt/Co(O.9 nm)/Pt does not exhibit
current-induced DW motion, whereas a similar asymmetric Pt/Co(O.9 nm)/GdOx
multilayer exhibits highly efficient motion by current (Fig. 8-1).
However, the Rashba field, often reported in materials with strong interfacial spinorbit coupling, does not contribute to the observed efficient DW motion. Instead,
we reveal that the spin Hall effect generates the strong spin torque on DWs, as
evidenced by opposite directions of DW motion in similar ultrathin ferromagnets on
heavy metals with opposite spin-Hall-angle polarities (Fig. 8-2). In this case, the
source of the torque is a spin current generated from spin-orbit-derived scattering in
the nonmagnetic heavy metal, rather than the spin-polarization of current within the
ferromagnet. This mechanism enables robust tuning of magnetization dynamics in a
ferromagnet by engineering an adjacent nonmagnetic material.
Uniform motion of DWs by the spin Hall effect requires a spiral configuration with
a fixed chirality for all DWs in the ferromagnet. We find that such homochirality arises
from a combined effect of spin-orbit coupling and broken symmetry in the multilayer namely, the Dzyaloshinskii-Moriya interaction (DMI) at the heavy-metal/ferromagnet
194
MgO
CoFe
MgO
CoFe
electron flow, J.
Ta
Pt
spin current (eS
spin current (SH > 0)
<0)
30
20
along electron flow
against electron flow
M
U
10 P
U
U
U
N
01
-2
M*
M
-1
0
3
2
1
Je (10d A/rr)
Figure 8-2: Current-induced domain-wall motion in Pt- and Ta-based ultrathin ferromagnets. Data show the change in domain-wall propagation field JAHp,,op as a
function of injected electron current density Je.
AQt
I zyaloshinskii-Moriya interaction:
homochiral spin e
ultrathin
~(ferromagnet
0*S
nonmagnetic
heavy metal
~VDW
VDW
spin Hall effect: driving torque
Figure 8-3: Two key interfacial spin-orbit effects
Moriya interaction.
195
spin Hall effect and Dzyaloshinskii-
interface, which biases magnetic moments to curl with a certain handedness. All DWs
in the ultrathin ferromagnet are thus left-handed Neel walls, which, as illustrated in
Fig. 8-3, can be driven in the same direction
(VDW)
by the effective spin Hall field
(HSH)-
The strength of the DMI depends on the heavy metal, and we quantify the DMI
to be more than 20 times stronger in the Pt-based ferromagnet than in the Ta-based
ferromagnet. The stiffer chiral spin texture stabilized by the strong DMI allows the
spin Hall torque to be transmitted more efficiently to DWs at large currents, which
accounts for the significantly higher current-driven DW mobility in the Pt-based
ferromagnet (data in Fig. 8-2).
However, stiff DMI-stabilized DWs under a large
torque also exhibit stretching and tilting of the wall line, not observed for DWs in
conventional ferromagnets. This finding highlights the qualitatively distinct nature
of DM1-stabilized DWs and the necessity for further experimental and computational
investigations for device applications.
8.2
Outlook on Future Developments
8.2.1
Towards Viable Domain-Wall Devices
In addition to the high efficiency of current-driven DW motion, a nanostrip of the
heavy-metal/ultrathin-ferromagnet/insulator multilayer is a convenient structure for
device applications. For example, an additional ferromagnetic metal layer directly
on top of the insulator layer of a multilayer nanostrip would constitute a magnetotunnel junction, which could ne used to read the magnetic bit in the nanostrip, as
part of a racetrack-memory device. By injecting an out-of-plane current through this
tunnel junction, it might also be used to re-write magnetizatic bits in the ultrathin
ferromagnet by spin torque from the top ferromagnet.
An in-plane current through the nanostrip moves all DWs uniformly (through the
combination of the spin Hall effect and homochirality stabilized by the DMI, Fig.
8-3), which enables shifting of magnetic bits while retaining all stored information.
196
Figure 8-4: Nanostrip device with a magneto-ionic domain-wall trap controlled by
gate voltage. Adapted from [1].
The effective spin Hall field acting on DWs has a similar symmetry as an out-of-plane
driving magnetic field. Therefore, it is possible to decrease the threshold current
density (power) required to move DWs by reducing the pinning field - or defects in the nanostrip. Attaining smoother nanostrip edges by advanced lithography as
well as employing ultrahigh-vacuum sputter deposition and optimized annealing may
reduce pinning defects considerably.
On the other hand, strong pinning of DWs is required for nonvolatile memory storage, so that DWs separating magnetic bits remain stable against stray magnetic fields
and thermal fluctuations (Sec. 1.3). Strong pinning can be introduced, while keeping
low inherent pinning in the nanostrip, through voltage-gating as demonstrated in
[1].
Narrow gates transverse to the nanostrip are activated by gate voltage, such that ions
(or oxygen vacancies) migrate in the oxide gate material and locally modify magnetic
anisotropy at the ferromagnet/oxide interface. This "magneto-ionic" effect, generating pinning sites through anisotropy change, remains even after the gate voltage is
turned off, and the pinning can be removed by applying a voltage of opposite polarity.
Therefore, DWs can be pinned strongly while the pinning gates are activated, and
walls can be displaced with a small current when the gates are deactivated. Again,
the insulating layer of the multilayer is convenient, because it can be an engineered
197
ionic conductor with a fast response to the gate voltage.
8.2.2
Implications of the Spin Hall Effect
The spin Hall effect was originally proposed by Dyakonov and Perel in 1971 [2], but
it was first reported experimentally more than 30 years later in 2004 [3]. Dyakonov
discusses the utility of the spin Hall effect in his review article on the spin Hall effect
published in 2010 [4], within a section tiltled "What is it good for?":
"So far, nobody knows. My personal opinion is that the Spin Hall Effect
is one of the many physical phenomena
[...],
which do not have any prac-
tical applications. Still, it is good that we know and understand them,
because such phenomena may help to determine some material parameters and, more importantly, because based on this knowledge we may be
able to understand other things, and this eventually might lead to some
applications.
"However, virtually every paper devoted to this subject start with the
standard mantra: 'Implementing electrical manipulation of the spin degree of freedom is an essential element for the emerging field of spintronics,' or something to this effect. Whether such manipulation (with useful
consequences) will ever be possible, or not, still remains to be seen. There
are no indications to that so far."
Only three years after the above review, we now use the spin Hall effect for "electrical manipulation of the spin degree of freedom" in ways relevant to future device
applications. In particular, as shown in this thesis and recent studies from 2012-2013
(e.g. [5, 6, 7, 8, 9]), we can now use the spin Hall effect to switch uniform magnetization
and drive DWs in ferromagnetic thin films. Moreover, we attain such magnetization
switching and DW motion in multilayer films, consisting of a nonmagnetic heavy
metal and a ferromagnet, which are conducive to industrial-scale fabrication, e.g. by
sputter deposition. Spin Hall effects observed in a variety of such metals systems are
summarized in [10].
198
(a)
w
(b)
W
Figure 8-5: (a) Schematic of the conventional spin-transfer torque for the currentin-plane geometry. The charge current I, and spin current I share the same cross
sectional area w x t. For each electron injected, at most one unit of spin is generated,
i.e. I < I,. (b) Schematic of spin current generation from the spin Hall effect. In
this case, the vertical spin current I is generated across a much larger cross sectional
area w x L. For t < w, L, the spin current pumped into the ferromagnet exceeds the
charge charge current in the heavy metal, i.e. I > I,. Note also that spin torque
from the spin Hall effect is generated even in the absence of magnetization gradient
in the ferromagnet. This is in contrast to the conventional spin-transfer torque that
arises from charge current crossing over a finite magnetization gradient.
The efficiency of the spin Hall effect in driving DW motion can be much higher
than that from conventional spin-transfer torques (STTs). Conventional STTs are
limited by the spin polarization P of charge current injected through a ferromagnetic
metal, and by the fact that the spin current is carried by the charge current through
the same cross sectional area (Fig. 8-5(a)). Thus, in conventional STTs, at most
one unit of spin angular momentum can be generated from each electron, if the spin
polarization is maximized at P = 1. In the case of the spin Hall effect, because the
resulting spin current is orthogonal to the original charge current, the cross sections
for the spin current A, = w x t and the charge current A, = w x L can be very different
(Fig. 8-5(b)). The spin current I, can be much larger than the charge current I, as
indicated by
Is-
_
Ic
As-- Js
Ac Je
L
-(H
t
8.1)
The spin Hall angle is the ratio of the spin current density to the charge current
density, 9 SH
=
J
cJ,.
Even though
9
SH
-
0.1 in heavy metals such as Pt and Ta,
the ratio I/Ic can be greater than 1 depending on the device geometry (Fig. 8-5(b)).
Physically, this fortuitous excess of spin current comes from repeated scattering of
the conduction electrons, i.e. repeated transfer of spin, while they flow through the
199
heavy metal.
It is also possible to increase the spin Hall angle 0BSH by materials engineering.
For example,
0
OSH|
in sputtered /-phase W has been reported to be
0.3 [7], about
twice that of Ta. Even in a metal like Cu, which by itself exhibits a vanishingly
small spin Hall effect,
0
OSHI
can be enhanced to ~0.3 by doping the metal with a
small amount (<1%) of heavy metal, such as Bi [11]. Spin Hall effects in metals have
only been investigated experimentally for the last few years, and we may encounter
new engineered materials exhibiting unprecedentedly large |6 SHI in the coming years.
Because the spin Hall effect is arises from spin-orbit coupling intimately related to the
structure of a nonmagnetic heavy metal, we expect that it can be tuned considerably
with the composition, crystallography, strain, etc. of the heavy metal.
Spin torque from the spin Hall effect does not rely on the spin polarization of
charge current in a ferromagnet. A ferromagnetic insulator, instead of a ferromagnetic
metal, can then be interfaced with a nonmagnetic heavy metal to drive magnetization
dynamics through the spin Hall effect. The use of a ferromagnetic insulator may
be beneficial for applications involving spin wave propagation 1 or an electrostatic
phenomenon from chiral magnetization. 2
8.2.3
Engineering Chiral Magnetism
The possibility of an exchange interaction that would cause spins to form a curl
with a fixed handedness was first proposed in the late 1950s. This interaction is
now widely known as the Dzyaloshinskii-Moriya interaction (DMI). The DMI has
gained attention in the last several years to stabilize homochiral magnetic textures,
which may be potentially useful for low-power device operation (e.g. [15]).
Such
homochiral textures include spin spirals, similar to DWs illustrated in Fig. 8-3, and
skyrmions, which are vortex-like swirls of magnetization (Fig. 8-7). The observation
'Most ferromagnetic insulators exhibit significantly lower damping than metals, thereby allowing
spin waves to propagate over longer distances. Spin waves can assist DW motion [12, 13], and
perhaps spin waves pumped by the spin Hall effect can drive DWs in the ferromagnetic insulator
more efficiently.
2
See brief discussion on "spin flexoelectricity" in Sec. 8.2.3 and [14].
200
(a)
(b)
AJOx
MnSi
Co
Pt
.S1 [112]
..
SiO2
-2m
Figure 8-6: (a) High-resolution transmission electron micrograph (HRTEM) of epitaxially grown MnSi on a Si crystal substrate. Adapted from [16]. (b) HRTEM
of sputter deposited Pt/Co/AlOx on a thermally grown SiO 2 layer. The nominal
thickness of Co is 0.6 nm. Adapted from [20]
and these chiral textures, however, have mostly been limited to noncentrosymmetric
crystals (e.g. MnSi [16]) or epitaxially grown ultrathin films on heavy-metal crystal
substrates (e.g. Fe on Ir [17]) , and required sophisticated characterization techniques
(e.g. spin-polarized scanning tunneling microscopy [17, 18], spin-polarized low energy
electron microscopy [19]) at high applied magnetic fields, cryogenic temperatures,
and/or ultrahigh vacuum.
We have successfully quantified the DMI in sputtered
films, using a relatively accessible magneto-optical Kerr effect (MOKE) polarimeter. 3
The observed homochiral DWs are stable at zero applied field, room temperature,
and atmospheric pressure.
The presence of a strong interfacial DMI in materials that are readily fabricated
and measured has enormous technological implications, beyond the development of
more efficient current-operated DW devices. In particular, the strength of the DMI
in Pt/CoFe/MgO is comparable to what has been observed in atomically-perfect epitaxial layers grown on heavy-metal single crystals [17, 18, 21], despite the highly
disordered interfaces expected in the present sputter-deposited films (Fig. 8-6(b)). It
will be extremely useful to determine how the combination of heavy-metal and ferromagnetic elements and the crystallographic order affect the magnitude and chirality
3
Similar measurements can also be conducted using a MOKE microscope or an anomalous Hall
effect setup.
201
(b)
(a)
Electron
30nm!
(c)
0
0
0
0
0
7 nm
57 nm57nm
5757nm
57 nm
57 nm
0-0
Figure 8-7: (a) A skyrmion in a helical-magnetic crystal Fe0 .5 Co0 .5 Si imaged with
Lorentz transmission electron microscopy. Apated from [23]. (b) Schematic of a spin
torque exerted on a skyrmion. Apated from [24]. (c) Micromagnetically simulated
current-driven motion of skyrmions. Adapted from [25].
of the interfacial DMI.
Our results already suggest the feasibility of realizing more complex chiral features
(spin spirals or skyrmions) in robust thin-film heterostructures. The threshold for
spontaneous formation of complex chiral features in out-of-plane magnetized thin
films is governed by the ratio of the effective DMI field HD and anisotropy field
H 1 [22], such that if
|HDJ >2/7re0.6,
(8.2)
H1
magnetic domains separated by DWs are unstable and skyrmions may form.
In
Pt/CoFe/MgO, IHDJ ~ 2500 Oe and Hi ~ 6000 Oe, not far from the threshold
in Eq.
8.2.
It is then perhaps feasible to form skyrmions in sputtered films at
room temperature by tuning the composition (or crystallographic orientation) and
thickness, i.e. to increase the DMI and reduce the perpendicular anisotropy, of the
heavy-metal/ferromagnetic composite.
Skyrmions are <10-nm diameter packets of spins (Fig. 8-7(a)) that can be pro-
202
pelled by current through spin torques, as illustrated in Fig.
8-7(b).
A train of
skyrmions in a magnetic nanostrip may be an alternative to the DW racetrack memory, with the small size of skyrmions increasing the maximum information storage
density. Moreover, recent theoretical works [25, 26] indicate that skyrmions move at
driving current densities significantly lower than DWs, which should allow for even
lower power consumption. For example, the result in Fig. 8-7(c) demonstrates a
skyrmion velocity of >50 m/s at J, = 5 x 1010 A/M 2 . This current density is an
order of magnitude lower than that required to attain a DW velocity of ~ 50 m/s in
Pt/CoFe/MgO (Fig. 8-2), which suggests that current-driven control of skyrmions
may require significantly less power.
Homochiral magnetic textures may enable other routes of magnetization control
as well. For example, a spin spiral (or Neel DW) in a magnetic insulator with a
sufficiently strong DMI may spontaneously develop an electric polarization, through
an effect called "spin flexoelectricity" [14]. Such electrostatic charging of homochiral
spin textures may allow for pure voltage control - i.e. without power dissipation from
charge current - of DWs (or other features) in device-compatible magnetic structures.
203
204
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