JOURNAL OF APPLIED PHYSICS
VOLUME 94, NUMBER 11
1 DECEMBER 2003
Suppressed pinning field of a trapped domain wall due to direct
current injection
T. Kimuraa) and Y. Otani
Quantum Nano-Scale Magnetics Laboratory, RIKEN FRS, 2-1 Hirosawa, Wako, Saitama 351-0198
and CREST, Japan Science & Technology Corporation, Japan
I. Yagi, K. Tsukagoshi, and Y. Aoyagi
Semiconductor Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
共Received 20 June 2003; accepted 25 August 2003兲
We investigate the influence of the dc current injection on trapped domain walls in magnetic
nanostructures designed for high precision anisotropy magnetoresistance measurements. The results
obtained for a simple strip with no trapped domain wall are compared with those for the strip with
the trapped domain wall. The depinning field of the domain wall decreases significantly when the
electron current is applied along the direction of the domain wall propagation. On the other hand,
the switching field only shows a small reduction when the electron current is opposed to the domain
wall propagation. The origin of this behavior can be explained by considering Joule heat as well as
an additional pressure exerted on the domain wall due to the transfer of the spin angular momentum
from the spin-polarized current to the local magnetic moment. © 2003 American Institute of
Physics. 关DOI: 10.1063/1.1618941兴
I. INTRODUCTION
tion processes of the domain wall. Therefore, the spin injection into the domain wall may influence the magnetization
process. Grollier et al.6 recently, using the giant magnetoresistance effect, succeeded in detecting a small change in resistance attributable to the spin current-induced domain wall
displacement in a Ni–Fe/Cu/Ni–Fe/CoO ferromagnetic layered strip. In this structure, however, most of the current
flows through the highly conductive Cu layer, whereby the
current induced Oersted field may have given an additional
contribution to the domain wall displacement, as suggested
in their article. More recently, Kläui et al. performed an experimental study on the current induced domain wall displacement in ferromagnetic ring structures.7 In the present
study, we investigate the pure effect of the applied dc current
on the confined domain wall in the ferromagnetic nanostructure. For this purpose we use a 200 nm wide Ni–Fe wire
attached to a 1 ␮ m⫻2 ␮ m rectangular pad as shown in Fig.
1. In this system, a domain wall is generally nucleated in the
pad, followed by pinning at the mouth 共i.e., the connection
between the pad and the wire兲, and then pushed into the
wire.8
Recent nanofabrication techniques made it possible to
realize magnetic nanostructures for spin electronic devices as
well as magnetic patterned media. Precise control of the
magnetization direction or the domain structure is a key issue
for developing such magnetic devices. The magnetization reversal is usually achieved by applying the external magnetic
field. The size reduction of the magnet down to nanoscale
causes an increase in the switching field, resulting in disadvantageously high energy consumption.
The magnetization in small ferromagnets was recently
shown to be reversed by spin-angular-momentum transfer
from a spin-polarized current to the local magnetic
moment.1–3 This phenomenon can be used in the nanomagnetic devices once the driving current density is lowered below 106 A/cm2 . So far the spin-current-induced magnetization reversal has been experimentally demonstrated mainly
in a magnetic multilayered system. The periodical domain
structure in a magnetic thin film resembles the magnetic multilayered structure. The similar momentum transfer is thus
expected to take place in the domain structure. Berger and
Hung investigated such an effect in Ni–Fe films using pulsed
current, and observed the domain-wall drag due to s – d interaction, i.e., an interaction between the polarized conduction electrons and the local magnetic moment.4,5 However, in
earlier works, almost all the experiments were performed
without examining detailed domain structures.
We are able to control the magnetic configuration in
nanostructured magnets using the geometrically induced
magnetostatic interaction. The magnetization switching in
such structures is governed by the nucleation and propaga-
II. EXPERIMENT
The narrow wire was fabricated by a conventional liftoff
technique as follows. An electron-beam lithographer was
used to define the wire pattern in a trilayered resist structure
with an undercut profile. A Ni–Fe layer with thickness t
⫽40 nm was then deposited on the patterned substrate in the
electron-beam evaporator with a base pressure of 2
⫻10⫺9 Torr. Subsequently, the Cu leads for the resistivity
measurement were formed into the dimensions of 500 nm in
width and 50 nm in thickness by using similar liftoff techniques. The magnetoresistance 共MR兲 was accurately measured at 4.1 K by a low-noise four-terminal dc measurement
a兲
Author to whom correspondence should be addressed; electronic mail:
t-kimu@postman.riken.go.jp
0021-8979/2003/94(11)/7266/4/$20.00
7266
© 2003 American Institute of Physics
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J. Appl. Phys., Vol. 94, No. 11, 1 December 2003
Kimura et al.
7267
FIG. 1. Schematic illustration of the fabricated magnetic wire with pad. The
inset shows the scanning electron microscope image of the fabricated Ni–Fe
wire in the vicinity of the mouth 共the connection between the pad and wire兲.
system in the range of the external magnetic field H from
⫺100 to 100 mT along the wire. This system can detect the
change in MR ratio smaller than 10⫺5 due to a slight change
in domain structure.
III. RESULTS AND DISCUSSION
Figure 2 shows a typical longitudinal MR of the wire
with the pad at 4.1 K. As indicated by arrows, a MR curve
exhibits small and large jumps during the magnetization reversal. This can be understood as an anisotropic MR effect
associated with magnetization reversal. The small jump at
H⬇16 mT and the large one at H⬇50 mT correspond to the
magnetization switching of the wide pad and that of the narrow wire, respectively. The domain wall is therefore pinned
FIG. 2. Typical longitudinal magnetoresistance of the fabricated wire measured at 4.1 K together with the calculated magnetic configurations which
correspond to the magnetoresistance indicated by letters in the figure. The
arrows indicate the resistance jumps due to the magnetization reversals
FIG. 3. Longitudinal magnetoresistances measured at 4.1 K with: 共a兲 I
⫽1.0, 共b兲 I⫽⫺0.2, and 共c兲 I⫽1.0 mA.
at the mouth while the external field H is inbetween 16 and
50 mT. Then the wall penetrates into the wire at H
⬇50 mT. Such a two-stage demagnetization process is also
reproduced in the micromagnetic simulation performed using
the object-oriented micromagnetic framenetwork 共OOMMF兲
software.9 The cell size, the saturation magnetization M S ,
and the damping parameter ␣ are 4 nm, 1 T, and ␣ ⫽0.01,
respectively. The cell size in the calculation is chosen to be
close to the spin-diffusion length of the Ni–Fe alloy.10 Figures 2共a兲–2共d兲 show the calculated magnetization configurations adjacent to the mouth between the pad and the wire. As
seen in Figs. 2共b兲 and 2共c兲, the domain wall is confined in the
vicinity of the mouth. The calculation shows that the switching fields of the pad and the wire are 14 and 46 mT, respectively. The values are in good agreement with those of the
experiment. It should also be noted that almost all the spins
lie in the plane.
We now discuss the influence of the dc current on the
domain wall on the basis of the measured MR curves with
different injection currents I. Figure 3 shows the longitudinal
MR curves measured with different currents I⫽1.0, ⫺0.2,
and ⫺1.0 mA. The switching field of the wire for I
⫽1.0 mA is 49 mT, and takes a value slightly smaller than
that for I⫽⫺0.2 mA. Once the current I is decreased down
to ⫺1.0 mA (⬇1.25⫻107 A/cm2 ), the switching field remarkably diminishes. In this measurement, to be sure about
reproducibility, the switching field is determined by averaging five measurements for each injection current. The switching field distribution at each injecting current is found to
much less than 5%. Figure 4 summarizes the switching field
of the wire with pad as a function of the injection current.
The switching field decreases by increasing the current negatively. As shown in Fig. 1, the electron spin current is injected from the pad into the domain wall when the electric
current is negative. Such a spin current should exert the pressure on a pinned domain wall into the wire, resulting in the
reduced depinning field. If we apply similar consideration to
the case for the positive current, the switching field should
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7268
Kimura et al.
J. Appl. Phys., Vol. 94, No. 11, 1 December 2003
FIG. 4. The reduced switching field (H SW /H SW0 ) as a function of the injection current. Solid circles and open squares correspond to the simple wire
and the wire with pad, respectively.
increase with increasing current. However, we did not observe such a tendency.
In order to understand the above asymmetric variation of
the depinning field with respect to the current polarity, we
have to consider the Joule heat because the current-induced
Oersted field has no component to drive the domain wall
propagation. The Joule heat due to the high current density
causes the reduction of switching field as the depinning field
decreases with increasing temperature. The amount of Joule
heat is given by I 2 R ␶ in Joules, where R is the resistance of
the system and ␶ is the characteristic time. The Joule heat
may be equivalent to the magnetic energy in Joules M s H v ,
where v is the volume of the system. It is thus deduced that
the contribution to the switching field is proportional to I 2 .
Therefore, the current dependent switching field H SW is
given by
H SW⫽H SW0 ⫹aI⫹bI 2 .
共1兲
In this equation, H SW0 is the switching field in the absence of
the current I, where a and b are the conversion coefficients
from the current to the field due to the spin-transfer effect
and the heating, respectively. Fitting Eq. 共1兲 to the experimental results in Fig. 4 yields a⫽6.35 mT/mA and b⫽
⫺10.23 mT/mA2 .
For comparison, the coefficient a is calculated separately
as follows. We first examine the detailed micromagnetic
structure around the pinned domain wall to evaluate the effective field due to spin-momentum transfer. Figures 5共a兲–
5共d兲 show the calculated micromagnetic structures near the
mouth for the external magnetic fields H ex⫽30, 45, and 46
mT. According to the time resolved calculation of the mag-
FIG. 5. Detailed magnetic configuration around the mouth obtained from
micromagnetic simulation: 共a兲, 共b兲, and 共d兲 correspond to the stable states at
H ex⫽30, 45, and 46 mT, respectively. 共c兲 is a snapshot during the domain
wall propagation at H ex⫽46 mT. The domain surrounded by the dotted line
corresponds to the corner domain.
netization reversal, the magnetization configuration near the
mouth hardly changes in the field range of 30 mT⭐H ex
⭐45 mT. Notice that the domain wall penetrates into the
wire when the moment ␮C at the corner, indicated by the
dotted square, switches the direction. This implies that the
moment ␮C governs the depinning process. If we consider
the spin momentum transfer from the conduction electron
spins of neighbors to the moment ␮C , the torque T between
the moment ␮C and the induced spin moment Sns due to the
transferred spins is expressed as S 兵 n␮C⫻(ns⫻n␮C) 其 , 11
where S is the transferred spin momentum per unit time
given by (ប/2e) ␩ JA with the spin polarization ␩, the applied current density J, and the cross sectional area A, ns is
the unit vector of the averaged neighbor spins, and n␮C is the
unit vector of the moment ␮C .
For the following calculation, the unit vectors n␮C and ns
are, respectively, given by (cos ␾␮C,sin ␾␮C,0) and
(cos ␾s ,sin ␾s ,0) because the perpendicular components in
the present lateral structure are found negligible in the simulation. Here, ␾ ␮ C and ␾ s are, respectively, the tilting angles
of the ␮C and the induced moment Sns from the wire. The
induced torque T can then be calculated as
T⫽⫺
ប ␩ JA
sin共 ␾ ␮ C ⫺ ␾ s 兲 e␾␮ ,
2e
C
共2兲
where e␾␮ is the unit vector normal to ␮C in the cylindrical
C
coordinates. This equation means that the local magnetic moment ␮C rotates toward the direction of the induced moment
Sns . The angle between the Sns and the moment ␮C is about
50°, yielding the effective torque. The effective torque only
changes its sign when the current flow is altered.
If we assume that the torque T is given by the first derivative of the free energy of the moment ␮c subjected to the
effective field H eff with respect to the angle ␾ ␮ C ⫺ ␾ s , the
effective field H eff can be deduced from Eq. 共1兲 as
H eff⫽
ប␩J
关 1⫺cos共 ␾ ␮ C ⫺ ␾ s 兲兴 .
2el sfM S
共3兲
Using typical values for permalloy: ␩ ⫽0.37, 12 M S ⫽1 T,
l sf⫽4 nm, and J⫽1.25⫻107 A/cm2 , we obtain the conversion coefficient a from the current to the field as 2.87 mT/
mA. This value is smaller than the experimentally obtained
value. This may be due to the fact that the value of ␩ is larger
than 0.37.
The MR curves for different injected currents in a simple
Ni–Fe wire measured for comparison show that single jump
appears at the nucleation field of the domain wall at the wire
edge, which is larger than that of the wire with the pad. Solid
circles in Fig. 4 represent the dependence of the H SW on the
dc current for the simple wire together with that of the wire
with the pad. The value of H SW0 for the simple wire is 64
mT. The switching field shows a slight reduction of about 1%
at I⫽1.0 mA in both polarities of the injected current. This
means that the magnetization reversal initiates at the edge of
the wire where the current does not flow. The origin of the
slight reduction in the wire without the pad is Joule heat.
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Kimura et al.
J. Appl. Phys., Vol. 94, No. 11, 1 December 2003
IV. CONCLUSION
We have investigated the influence of the dc current injection on the trapped domain wall by using the submicron
scale magnetic structure consisting of the large pad and the
wire. The depinning field of the trapped domain wall is reduced drastically when the electrons flow from the pad to the
wire, i.e., negative current. On the other hand, the behaviors
for the positive current differ from the expectation from a
simple torque model. Such behaviors can be understood by
combining the spin–momentum transfer and the Joule heat.
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