Magnetism on the Move
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Ferromagnetism
Inhomogenous magnetization
Magnetic vortices
Dynamics
Spin transport
US-Spain Workshop on Nanomaterials
Ferromagnetism is rare……
…. but useful
Inductive Write Element
GMR Read Sensor
W
t
B
B = 25 nm (s<3 nm),
W=150 nm, t = 14 nm
data rate ~ GHz
“Compass” that responds to
local magnetic field and
varies the resistance
Head
Disk
Write
Pole2
100 nm
<D> = 8.5 nm
+/- 2.5 nm
Write
Coil
Read
Head
Courtesy of Eric Fullerton
Recording Media
100 nm
<D> = 8.5 nm
+/- 2.5 nm
SNR  N # grains/bit
1000 nm
Courtesy of Eric Fullerton
Why is ferromagnetism neither common nor “perfect”?
Macroscopic
Microscopic
R. Schaefer, Dresden
Magnetostatics (Not as bad as it looks)
Magnetostatics: equilibrium condition
Variational method to find the equilibrium condition
, where
=0
Torque
W. F. Brown, Jr., Micromagnetics (Interscience Publishers, New York, 1963)
Micromagnetics Simulation
Excitations
[Equilibrium State]
[Excited State]
Landau-Lifshitz-Gilbert Equation
[Dynamic motion]
 
g B

= 17.6 GHz/kOe
Spin waves
 Uniform precession (q = 0 spin wave)
 Spin Waves

q
 
Eexch  2 J  Si  S j  J cos ij  Aq2
nn
i j
The simple case (no magnetocrystalline anisotropy)
LE = exchange length = A / 2M s2
K.L. Metlov et. al., J. Magn. Magn. Mater. 242-245 (2002) 1015
Magnetic vortex
Of course there are intermediate cases - such as the S-state
Four different configurations of the vortex state
 Schematic illustration of four different vortex states
P= Polarity (the magnetization direction of the vortex core)
C= Chirality (the winding direction of in-plane magnetization)
The magnetostatic energies are obviously identical….
Magnetic vortices
 Observation of magnetic vortices
1) Lorentz Microscopy
on 200 nm Co disk
2) MFM on 1 m
Permalloy disk
3) SP-STM on 200 nm wide
and 500 nm long Fe island
1) J. Raabe et al. J. Appl. Phys. 88, 4437 (2000)
2)T.Shinjo et al. Science 289, 930 (2000)
3) A. Wachowiak et al. Science 298, 577 (2002)
What about the dynamics?
Vortex-core dynamics (gyrotropic motion)
 Gyromagnetic force acting on a shifted vortex
Landau-Lifshitz-Gilbert Equation:





1 dM

dM
 M  H eff 
M
0
 dt
M s
dt
Equivalent force equation



W ( X (t ))  dX (t )  dX (t )


G
 D
0
dt
dt
X (t )

where W = static force for an applied field H
G = gyrovector (antiparallel to the direction
 of vortex polarity P)
D = magnetic energy dissipation dyadic
A.A. Thiele, Phys. Rev. Lett. 30, 230 (1973).
See also B. Argyle et al., Phys. Rev. Lett. 53, 190 (1984).
When
 P changes sign,
G changes sign!
Gyrotropic Mode
The lowest frequency excitation: Gyrotropic mode
[Will be replaced with
a movie:
Gyrotropic motion in
simulation]
1 s  1 ns
16
Time Scales
10-12 sec
(semiconductors)
10-14 sec
(chemical
reaction
dynamics)
10-9 sec
10-7 sec
(magnetism)
How do you make a movie
on picosecond time scales?
Time-resolved Kerr microscopy (stroboscopic)
What we measure:
Polar Kerr Rotation  Mz
as a function of time delay, probe-beam position, and applied field
[Freeman et al. J. Appl. Phys. 79, 5898 (1996)]
Also Back, Hicken, and others.....This is a stroboscopic technique.
Experimental Setup
Different equilibrium positions
Not at a pinning site
Excitation off
At a pinning site
Pinning potential
20
Large Amplitude: Core Switching
Counterclockwise orbit
Clockwise orbit
1 s  0.5 ns
B. Van Waeyenberge et al., Nature 444, 461 (2006)
21
Core reversal
22
Phase Diagram of Vortex Dynamics

Pinned & Depinned
23
Magnetic Heterostructures
Disk
drives
Magnetic
Random Access
Memory
New Technologies:
• Magnetic Random Access Memory
• Magnetic tunnel junction sensors
• Patterned media
• Semiconductor spintronics
• Highly polarizable materials
Field sensing
(medical devices,
security)
Magnetic Heterostructures
Example: the spin valve
F
•
The electrical response of the device depends
on the magnetic state of two or more
electrodes (field sensors, read heads)
•
The magnetic state of the device can be changed
by an electrical current (memory, oscillators)
F
Integration of ferromagnets with insulators, semiconductors, and
normal metals
Read Head Technology
Pole2
Gap
Write
Shield2
Pole1
MR
Leads
Read
Leads
Shield1
Scale: 50 nm
Compound PtMn
Free Layer
Cu
Pinned Layer
Magnetic Tunnel Junctions
FM 1
Insulator
FM 2
Spin transfer torque oscillators
•
•
•
•
•
MgO-based tunnel junction devices for
maximizing signal and reducing threshold
current
Built-in hard-axis polarizer enhances
output power and allows for zero-field
operation
Influence of CoFeB on damping (with
Data Storage Institute, Singapore)
Modification of CoFeB/MgO interface
anisotropy (with DSI)
Spin transfer torque FMR (with DSI)
J. Appl. Phys. 109, 07D307 (2011)
J. Appl. Phys. 109, 07C714 (2011)
Appl. Phys. Lett. (accepted, 2012)
Wang, Crowell
Materials science of magnetic heterostructures
Electronic Structure
Calculations
Growth and characterization
Co2MnGe
GaAs
TEM
Interfacial
characterization
Simulations
Transport
Spin dynamics
Epitaxial Fe/InxGa1-xAs heterostructures
• Epitaxial structures: low temperature
growth to minimize interfacial reactions
• Transport and modeling techniques
developed by the IRG
• Increase spin-orbit coupling by shifting
to InxGa1-xAs
Palmstrøm, Crowell
Summary
• Magnetism is ubiquitous, although ferromagnetism is relatively rare
• Ferromagnetism is useful if not always easy to understand
• Imperfect magnets are more interesting than perfect ones
• Dynamics are accessible by new tools
• Integration of ferromagnets with other materials yields new physics
and new devices