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Stochastic Nature of Current-Excited Magnetic
Domain and Domain Wall Dynamics Microscopically
Investigated by Lorentz Microscopy
Yoshihiko Togawa1,2, Takashi Kimura3, Ken Harada4,5, Akira Tonomura2,4, Yoshichika Otani2,6
1 Nanoscience and Nanotechnology Research Center, Osaka Prefecture University, Sakai, Osaka 599-8570, JAPAN
2 Advanced Science Institute, Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, JAPAN
3 Inamori Frontier Research Center, Kyushu University, Fukuoka 819-0395, JAPAN
4 Advanced Research Laboratory, Hitachi Ltd., Hatoyama, Saitama 350-0395, JAPAN
5 Department of Materials Science, Osaka Prefecture University, Sakai, Osaka 599-8531, JAPAN
6 Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, JAPAN
Abstract— We microscopically investigate the dynamics of
magnetic domains and domain walls induced by a current pulse
in Permalloy narrow wires by means of Lorentz microscopy and
simultaneous transport measurement. A variety of magnetic
domain and domain wall dynamics are induced as a function of
current density flowing into the wire and wire resistance.
Important finding is that observed magnetic domain wall
displacement and domain nucleation explicitly exhibit stochastic
nature, indicating that the magnetic state in the wire is hardly
controlled by using solely the current pulse. However, the
application of small in-plane magnetic field changes drastically
the nature into deterministic, which effectively improves
controllability of the magnetic domain and domain wall
dynamics using current.
Keywords- magnetic domains; magnetic domain walls;
magnetization dynamics; spin current; spin transfer torque;
Lorentz microscopy
I. INTRODUCTION
Manipulation of magnetic state is a key element in device
operation of electromagnetic, i.e., spintronic devices. Magnetic
domain and domain wall dynamics induced by spin-polarized
current (or spin current) instead of magnetic field in magnetic
wire device gains in importance because it provides basic
physical understanding of underlying mechanism of the
phenomena and great advantages in device miniaturization,
integration and operation with low power consumption.
The spin current plays an essential role to excite the
dynamics of magnetic domains and domain walls. A transfer of
the spin angular momentum from conduction electron spins to
localized electron magnetic moments induces the torque to the
magnetized structure in a flow of electrons. This torque is
called the spin transfer toque [1]–[3], which drives the domain
wall along the electron flow in the wire [4]–[6] and the
magnetization is successively reversed in a region where the
domain wall propagates as shown in Fig. 1(a). When there is
no domain wall in the wire, the spin current narrows the energy
gap of the spin-wave excitation, destabilizes the magnetic
system due to the spin-wave instability [7]–[9], and resultantly
nucleates the magnetic domains in the uniformly-magnetized
state [10]. These dynamics of magnetic domains and domain
walls using current provide useful ways of manipulating the
magnetic state, which will open up novel spintronic device
application such as domain wall logic circuit [11], race track
memory [12] and TMR memory [13].
For reliable manipulation, it is important to understand the
nature of magnetic domain and domain wall dynamics under
the spin current. In this connection, we perform microscopic
investigation of magnetic domain and domain wall dynamics
induced by a current pulse in Permalloy narrow wires by means
of Lorentz microscopy, electron holography and simultaneous
transport measurement [14]–[16]. A variety of changes of the
magnetic state in the wire are systematically observed as a
function of the current density. Importantly, the magnetic
domains and domain walls exhibit stochastic nature, which is a
main focus in this paper. Stochastic nature might impede
manipulating the magnetic state in spintronic device
application. However, it is found that small in-plane magnetic
field application effectively alters stochastic nature into
deterministic and enhances controllability of the magnetic state
using current. This brings a promising technology of
manipulating the magnetic state using current and will lead to a
wide variety of spintronic applications in nano-scaled
electromagnetic devices.
II. EXPERIMENTAL
We employ Lorentz microscopy that enables the real-time
observation using video (30 frames/second) in a high spatial
resolution (down to 10 nm) to clarify microscopic behavior of
an individual magnetic domain and domain wall. Quantitative
distribution of the magnetic flux line is visualized by means of
electron holography if necessary. Permalloy narrow wires with
thickness of 30 nm and width of 500 nm are prepared on a 30-
nm-thickness Si3N4 membrane for transmission electron
Corresponding author: Y. Togawa (e-mail: y-togawa@21c.osakafu-u.ac.jp).
978-1-4244-6890-4/10$26.00 ©2010 IEEE TENCON 2010
122
Figure 1. Magnetic domain wall displacement. (a) Schematic illustration
of domain wall displacement under the spin current. Domain wall moves
along electron flow due to the spin transfer torque. (b) and (c) Domain
wall displacement at threshold current density Jth, observed by Lorentz
microscopy. Jth is 1.98×1011 A/m2 at 300 ns current pulse in (b) and
2.09×1011 A/m2 at 200 ns current pulse in (c). While the domain wall
propagates along electron flow in (b), it moves against electron flow in
(c). These observations indicate stochastic nature of the current-driven
domain wall movement.
Figure 2. Magnetic domain nucleation in presence of small in-plane
magnetic field at 2.00 × 1011 A/m2 at 300 ns current pulse. (a) 0 Oe. (b)
2.5 Oe (leftward). (c) 3.8 Oe. (d) -2.5 Oe (rightward). While the
uniformly-magnetized state appears in most cases at 0 Oe in (a), the
magnetic domain with reversed magnetization is stably formed in the
wire in leftward magnetic field in (c). When the magnetic field is
reversed, just the uniformly-magnetized state appears in the wire in (d).
microscope (TEM) observation by lift-off technique using
electron-beam lithography. The wire device is mounted on a
special TEM holder for the current application, installed into
the column of the 300 kV field-emission TEM above the
objective lens where the magnetic field generated by
electromagnetic lenses in the TEM is negligibly small [17].
While observation, a current pulse with variable amplitude and
duration is applied every one second to the observed magnetic
wires. The current density flowing into the wire and wire
resistance are measured to monitor the wire temperature using
a reference resistance.
III. RESULTS AND DISCUSSIONS
Figures 1(b) and 1(c) shows the domain wall displacement
observed around wire corners in different wires by Lorentz
microscopy. At the threshold current density Jth, the vortex
domain wall displaces over the distance of the wire width in
the wires for the first time by the current pulse application.
Although the vortex domain wall locating at the corner of the
wire propagates over 1 μm along electron flow in Fig. 1(b), the
vortex domain wall moves against electron flow in Fig. 1(c).
Namely, these observations present that the current pulse
displaces the domain walls in an opposite direction.
According to one-directional picture of the domain wall
propagation due to the spin transfer torque, the domain wall
would proceed along the applied electron flow. Thus, the
domain wall behavior of bidirectional displacement observed
in Figs. 1(b) and 1(c) explicitly exhibits stochastic nature of the
magnetic domain walls displacement induced by current pulse
application, which is inconsistent with the simple scenario due
to the spin transfer toque.
The domain wall displacement observed is triggered by the
current pulse application. When a current pulse is applied, the
wire resistance, i.e., wire temperature increases, although it
does not reach the Curie temperature TC. It is natural to
consider thermal excitation effect in addition to the spin
transfer torque. Indeed, the dependence of Jth and the wire
resistance at the threshold Rth on the current pulse duration
shows that Jth and Rth decrease with decreasing
, indicating
that both spin transfer torque and thermal excitation work
cooperatively to drive the domain wall.
Thermally-assisted spin transfer torque efficiently lessens
the pinning potential energy barrier for the domain wall and
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thus helps the domain wall depinning. In addition, the spin
waves, i.e., magnons are excited all along wire under the spin
current and in elevating temperature during current pulse
application, which enables the domain wall to move in
bidirectional direction. Although an exact mechanism to trigger
the bidirectional displacement still remains to be clarified,
stochastic nature of the current-driven domain wall movement
is a matter of importance in the application viewpoints.
Another interesting dynamics is that the current pulse
triggers the magnetic domain nucleation (magnetization
reversal) in the uniformly-magnetized state in quite low
probability. For instance, the uniformly-magnetized state
appears in probability as high as 96% and the magnetic
domains with reversed magnetization appear in very low
probability of less than 1 % in the uniformly magnetized wire
when current pulses are applied at 0 Oe for 2000 times. Thus,
in most cases, the uniformly-magnetized state is observed as
shown in Fig.2(a). Namely, the current-excited domain
nucleation occurs stochastically.
The stochastic nature, which the magnetization dynamics
due to thermal excitation and spin-wave excitation should have
in principle, suggests that the magnetic domain nucleation is
hardly controlled by using solely the current pulse. However,
for improving controllability of domain nucleation, it is found
that applying small in-plane magnetic field along the wire is
very effective to tune the probability of the domain nucleation
induced by the current pulse and to change the stochastic
nature of the current-excited domain nucleation into
deterministic.
Figure 2(c) shows that the current pulse reverses the
magnetization in a part of the wire and nucleates the domain
with reversed leftward magnetization in in-plane leftward
magnetic field of 3.8 Oe. Strikingly, the nucleated domain
remains stable against the subsequent application of current
pulses in small in-plane magnetic field. This contrasts well
with the experimental observation that the nucleated domain is
erased immediately by the current pulse application at high
probability of more than 90% in the absence of applied
magnetic field as shown in Fig. 2(a). Interestingly, in an
opposite magnetic field, the reversed magnetic domain is never
nucleated by the current pulse application as shown in Fig. 2(d).
Thus, observed results support that the current-excited domain
nucleation is predominantly induced (suppressed) when the
magnetic field is applied antiparallel (parallel) to the averaged
magnetization direction. We stress that the applied magnetic
field is too small to change the uniformly-magnetized structure
without the current pulse application.
IV. SUMMARY
We investigate the magnetization dynamics induced by a
current pulse in Permalloy narrow wires with strong shape
anisotropy by means of Lorentz microscopy and simultaneous
transport measurements. A variety of magnetization dynamics
as a function of current density flowing into the wire and wire
resistance is observed below the Curie temperature. The spin-
wave excitation due to the spin current and thermal excitation
affect the nature of the magnetic domain and domain wall
dynamics, giving rise to stochastic nature in these dynamics.
Although an exact mechanism of stochastic nature of the
magnetization dynamics under the current pulse application is
still open question, these experimental findings should help us
enrich the technology of the magnetization manipulation. For
instance, we microscopically demonstrate that small magnetic
field drastically changes the nature of the dynamics into
deterministic and allows stable and selective control of the
magnetic domain nucleation. This could be applicable in
manipulating the magnetic domain walls motion with
stochastic nature using current because small magnetic field
predominantly allows one-directional movement of the domain
wall so as to enlarge the magnetic domain with magnetization
parallel to the direction of applied magnetic field.
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