Applied Physics Express 8, 073002 (2015)
http://dx.doi.org/10.7567/APEX.8.073002

Current-induced dynamics of bubble domains in perpendicularly magnetized TbFeCo wires
Masaaki Tanaka1*, Hiroki Kanazawa1, Sho Sumitomo1, Syuta Honda2, Ko Mibu1, and Hiroyuki Awano3
1

Graduate School of Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan
Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan3
Information Storage Materials Laboratory, Toyota Technological Institute, Nagoya 468-8511, Japan2

Received March 25, 2015; accepted May 29, 2015; published online June 15, 2015
We investigated the bubble-domain dynamics in TbFeCo wires with perpendicular magnetization under electric current ﬂows. In TbFeCo wires withrelatively low saturation magnetization (Ms), the current pulse caused the bubble domains to collapse without moving. In TbFeCo wires withrelatively high Ms, however, the bubble domains grew in the current direction. We explain these shape changes by assessing the Ms-dependent
forces caused by the exchange ﬁeld and magnetostatic ﬁeld. We also found that we could control the current-induced behaviors of the bubble
domains by using an external magnetic ﬁeld. © 2015 The Japan Society of Applied Physics

ecently, there has been much interest in electric
current-induced movements of magnetic domains or
domain walls in magnetic wires in terms of theirfundamental physics and their potential as new spintronics
devices.1–3) The magnetic domains of systems with perpendicular magnetic anisotropy have been predicted to move at
low current densities because of their thinner domain wallsand their more eﬃcient spin-transfer torque than in in-planemagnetization systems,4) and several experimental approaches have been reported so far.5–8) However, when adomain wall forms across both wire edges, the edge
roughness sometimes aﬀects the domain wall movement.4)
Such unstable domain wall pinning is an issue to be solved
for the domain wall movement. Bubble domains (BDs), used
for magnetic-bubble memory and magneto-optical disks,9,10)
are also interesting in terms of both spintronics applications
and fundamental research. They can be generated in perpendicularly magnetized ﬁlms, and their domain walls do notreach the wire edges, and so they are expected to be drivable
without inﬂuence from the edge roughness.
In this study, we investigated the BD dynamics in perpendicularly magnetized wires with diﬀerent saturation magnetizations (Ms) exposed to current ﬂow. For the perpendicularly
magnetized material, we used TbFeCo, an amorphous rareearth transition-metal alloy and a kind of speri-magnet.9) In
TbFeCo, the magnetic moment of Tb takes on a random conearrangement whose net magnetization direction is oppositethat of Fe and Co. Because of this opposition, the magnitude
of saturation magnetization can be adjusted by changing thealloy composition. We found that the current-induced BD
dynamics depended on the magnitude of Ms and that it wascaused by diﬀerences in the eﬀective forces acting on the BD
walls from the exchange ﬁeld, as well as on the magnetostaticﬁeld. We also controlled the current-induced BD dynamics
using an external perpendicular magnetic ﬁeld.
Using electron-beam lithography and lift-oﬀ, we fabricated10-µm-wide and 80-µm-long TbFeCo wires with electricpads on both sides on thermally oxidized Si substrates. 10nm-thick TbFeCo layers with 2-nm-thick Pt cap layers weregrown by sputtering. The Pt layers protected the wires fromoxidization. We prepared TbFeCo wires of two diﬀerent
compositions whose saturation magnetizations were 40 and
200 emu=cm3. Polar Kerr hysteresis loops showed that themagnetization of each sample was on the transition-metaldominant side. Current pulses with durations of 10 ms wereapplied to the wires. Joule heating in the TbFeCo wires wasnegligible under the conditions of the present study.11) ToRElectric current
TbFeCo wire

Bubble domain()

10 µm

Pulse generator
Fig. 1. A magneto-optical Kerr micrograph of a BD in a TbFeCo wire andan illustration of the experimental setup.

directly observe the current-induced BD dynamics, we usedpolar-magneto-optical Kerr eﬀect (MOKE) microscopy indiﬀerential imaging modes. In the ﬁgures here, the white andblack regions in the magnetic wires correspond to the upwardand downward magnetized regions, respectively. Figure 1
shows a MOKE micrograph of a BD in the TbFeCo wire andan illustration of the current-induced measurements. The BDs
were generated in the wires as follows.12) First, a magnetic
ﬁeld of more than 3 kOe was applied upward and perpendicular to the substrate plane in order to align the magnetization of the wires in one direction. The centers of theTbFeCo wires were heated for 0.5 s using a 407-nm laser at
8 mW with a magnetic ﬁeld of approximately 1 kOe applied
downward and perpendicular to the substrate plane. This
produced a downward magnetized BD at the center of each
TbFeCo wire. Subsequently, we adjusted the diameters of theBDs to approximately 2 µm by using a perpendicular magnetic ﬁeld without heating. Using MOKE microscopy, we
found that the laser heating caused no permanent damage tothe wires.
Figure 2(a) shows the BD dynamics of a TbFeCo wirewith Ms = 40 emu=cm3 for a single current pulse (2.0 × 1010
A=m2) without an external magnetic ﬁeld. Under this current,
the BD collapsed instantly. Through further experiments, wefound that BDs collapsed from this current ﬂow in TbFeCowires with Ms = 40–60 emu=cm3. In contrast, in the TbFeCowire with Ms = 200 emu=cm3, the BD grew in the current
direction at a threshold current density of 4.6 × 1010 A=m2
without an external magnetic ﬁeld, as shown in Fig. 2(b).
The right edge of the BD expanded with an oblique angle
after 30 pulses, whereas the left edge was pinned at theoriginal position. The BDs in the TbFeCo wires with Ms =150–200 emu=cm3 grew in the direction of the current ﬂow(i.e., opposite the electron ﬂow). Several groups have claimed
that the reverse or transverse forces with respect to the073002-1© 2015 The Japan Society of Applied Physics

Appl. Phys. Express 8, 073002 (2015)(a))
Electric current(b) M =200 emu/cm3
S

5(c)
(d)

Jth(1010 A/m2)

Electric current(a) M =40 emu/cm3
S

Bubble domain(M. Tanaka et al.

4(b)

32

Hbias

1
Electric current
0-600 -400 -200 0CollapseMove
Growth200 400 600

Magnetic field Hbias(Oe)Electric current(b)

Bubble domain()

Fig. 2. Magneto-optical Kerr micrographs of the current-induced eﬀect on
the BDs in TbFeCo wires. The changes are shown in TbFeCo wires with(a) Ms = 40 emu=cm3 after application of one current pulse at 2.0 × 1010
A=m2 and (b) Ms = 200 emu=cm3 after application of 30 current pulses at
4.6 × 1010 A=m2.

electron ﬂow can act on the usual magnetic domains anddomain walls in perpendicular magnetic wires by the Rashba
eﬀect, the Dzyaloshinskii–Moriya (DM) interaction, or thespin Hall eﬀect of the Pt cap layer.13–18)
We also investigated current-induced BD dynamics in theTbFeCo wires with Ms = 200 emu=cm3 by applying perpendicular magnetic ﬁelds (Hbias). Here, we deﬁne downward
Hbias as the positive ﬁeld. Figures 3(b)–3(d) are MOKE
micrographs showing the current-induced eﬀect for BDs
in TbFeCo wires in a magnetic ﬁeld of −200 Oe with one
current-pulse injection, in −20 Oe with ﬁve current-pulse
injections, and in +200 Oe with one current-pulse injection.
Applying Hbias of −20 Oe perpendicular to the plane produced stable BD movement by a current ﬂow, as shown in
Fig. 3(c). These results clarify that the current-induced BDdynamics can be controlled by Hbias. Figure 3(a) shows how
the threshold current density, i.e., the lowest current density
needed to change the BD shape, depended on Hbias in
TbFeCo wires with 200 emu=cm3. By applying Hbias downward and perpendicular to the plane, the BDs grew in thecurrent direction. As the magnitude of Hbias increased, thethreshold current density decreased. By applying negative
Hbias under −100 Oe, the BDs collapsed instantly with thecurrent pulse.
We performed micromagnetic calculations of the currentinduced BD dynamics in a nanowire with perpendicular magnetic anisotropy based on the Landau–Lifshitz equation.19,20)@m¼ jjm  Heff  jj½m  ðm  Heff Þ@tm  ðm  rjs Þ;
Ms

ð1Þ

where m is a unit vector along the local magnetic momentof each small cell and γ is the gyromagnetic constant of−1.76 × 107 rad=(s·Oe). The magnetization (Ms) was set to40, 100, or 120 emu=cm3 and the damping constant (α) wasset to 0.1. The eﬀective magnetic ﬁeld (Heﬀ) is a combinationof the static, exchange, and uniaxial magnetic anisotropy
ﬁelds. The exchange magnetic ﬁeld was calculated by using
the exchange stiﬀness constant (A) of 1.0 × 10−8 erg=cm.

Bubble domain()

Hbias=-200 Oe
Electric current(c)

Bubble domain()

Hbias=-20 Oe
Electric current(d)

Bubble domain()

Hbias=200 Oe

Fig. 3. (a) Dependence of the threshold current density, Jth (for BD shapechange), on the perpendicular magnetic ﬁeld in TbFeCo wires with 200
emu=cm3. The inserted ﬁgure shows the experimental setup. Also shown are
MOKE micrographs showing the eﬀect of current on the BDs in TbFeCowires with magnetic ﬁelds of (b) −200 Oe after one current-pulse injection,(c) −20 Oe after ﬁve current-pulse injections, and (d) +200 Oe after one
current-pulse injection. The dotted circles show the initial positions ofthe BDs.

A perpendicular anisotropy energy (Ku) of 1.0 × 105 erg=cm3
was used to estimate the magnetic anisotropy ﬁeld, which isperpendicular to the plane of the wire. We calculated thespin-polarized current density ( js) from a current of −2.0 ×
1011 A=m2 and a spin polarization (P) of 0.5. The sizes of thesmall cell and the wire were 5 × 5 × 5 nm3 and 500 × 200 ×
10 nm3, respectively. The initial BD diameter was set toapproximately 35 nm. We could not reproduce the currentinduced BD dynamics in calculations using the Ku and A
parameters reported in the literature,21) possibly because
the speri-magnet TbFeCo is assumed to be a ferromagnet.
Because of this inconsistency, we tuned the parameters togive reasonable results; the current-induced BD dynamics
must be calculated in a system close to the experimentalconditions. With this in mind, we simulated the time dependence of the BD shape for ﬁlms with diﬀerent values of Ms
under continuous DC current. Figure 4(a) shows the initial
BD state, in which the magnetic moments around the domain
wall tilt slightly. In these simulations, we set the initial BDs
to have smaller areas than those in the experiments, and sothese simulations show the Ms dependence of the currentinduced BD dynamics over a short time scale. Figures 4(b),073002-2© 2015 The Japan Society of Applied Physics

Appl. Phys. Express 8, 073002 (2015)

M. Tanaka et al.

(a)

(a)

FBack

FFront

FDW
FI

(b)

FDW

FI

Low MS|FBack|>|FFront|(b)FFront(c)

FBackFIHigh MS

FDW

FDW
FI
|FBack|<|FFront|(d)Bubble domain area (arb. unit)

Fig. 5. Schematics of the total force acting on the rigid front end (FFront)and the rigid back end (FBack) of the domain walls of the BDs for ﬁlms with(a) low and (b) high saturation magnetization. FFront and FBack include thecurrent-induced force (FI) and the Ms-dependent force (FDW).

5(e)432MS(emu/cm3)
120
10040(d)
(c)

1(b)

002

4

6

810Time (ns)Fig. 4. Time dependence of the current-induced BD dynamics from themicromagnetic calculation. BD shapes are shown for (a) the initial state,(b) the ﬁlm with Ms = 40 emu=cm3 after 2 ns, (c) the ﬁlm with Ms = 100
emu=cm3 after 10 ns, and (d) the ﬁlm with Ms = 120 emu=cm3 after 5 ns.
(e) Time dependence of the BD area in a DC current ﬂow for diﬀerent
values of Ms.

4(c), and 4(d) show the calculated results of the BD shapewithout an external magnetic ﬁeld in the ﬁlm with Ms =40 emu=cm3 after 2 ns, in the ﬁlm with Ms = 100 emu=cm3after 10 ns, and in the ﬁlm with Ms = 120 emu=cm3 after 5 ns.
Figure 4(e) is the time dependence of the BD area in continuous current ﬂow for magnetic wires with diﬀerent valuesof Ms. In the magnetic wires with Ms = 40 emu=cm3, thesimulated BD disappeared while moving in the electron ﬂow
direction. In the wire with Ms = 120 emu=cm3, the simulated
BD grew while moving in the electron ﬂow direction. In thewire with Ms = 100 emu=cm3, however, the simulated BD
moved in the electron ﬂow direction while maintaining itsarea. All calculated BDs moved in the electron direction,
which conﬂicts with the experimental results. This diﬀerenceoccurred because the calculation did not consider the reverseor transverse forces from the Rashba eﬀect, the DMinteraction, or the spin Hall eﬀect of the Pt cap layer. The
point in this simulation is that the Ms-dependent BD-shapechanges are quantitatively consistent with the experimentalresults.

Based on our results, we propose a simple model for BD
shape changes in ﬁlms with diﬀerent values of Ms in Fig. 5.
In this model, we assume that the torque acting on the magnetic moments of a domain wall produces an eﬀective inplane force acting perpendicular to the domain wall of theBD. We also assume that the domain wall was moved by thiseﬀective force regardless of domain wall type. We consider
a current-induced eﬀective force (FI) and an Ms-dependent
force (FDW). FFront and FBack, shown in Fig. 5, are the sum of
FI and FDW for the front and back ends, respectively. Thefront and back ends of the BDs are assumed to be rigid. The
current-induced eﬀective force (FI) is deﬁned as the sum of
the eﬀective force caused by the spin-transfer torque, the DMinteraction, the Rashba eﬀect, and the spin Hall eﬀect. TheMs-dependent force (FDW) includes the forces induced by theexchange ﬁeld and the magnetostatic ﬁeld.22) The exchangeﬁeld-induced force compresses the BDs because theexchange energy decreases as the BD radius decreases. The
magnetostatic-ﬁeld-induced force, which decreases as the BD
area increases, expands the BDs. When FDW is smaller than
the threshold force needed to change the BD shape, the BD
holds its shape. For the BDs in ﬁlms with low Ms, the magnetostatic-ﬁeld-induced force is small, and so the exchangeﬁeld-induced force dominates in FDW. Thus, FDW for theBDs acts toward the BD center, as shown in Fig. 5(a). Inﬁlms with low Ms, FDW at the back end acts in the same
direction as FI and FDW at the front end acts in the opposite
direction of FI . Thus, FFront becomes smaller than FBack, andthe back end moves by lower current density than the front
end. In ﬁlms with high Ms, the magnetostatic-ﬁeld-induced
force is larger than that in ﬁlms with low Ms, so FDW actstoward the outside of the BD, as shown in Fig. 5(b). Thus, inthese ﬁlms, the threshold current density of front-end movement is lower than that of the back-end movement. Becauseof these diﬀerences in front- and back-end forces, the BD
shape varied in ﬁlms with diﬀerent saturation magnetizations.
In summary, we investigated current-induced BD dynamics in TbFeCo wires with diﬀerent saturation magnetizations.
We found that the Ms-dependent forces, which include theexchange-ﬁeld-induced force and the magnetostatic-ﬁeld-073002-3© 2015 The Japan Society of Applied Physics

Appl. Phys. Express 8, 073002 (2015)

M. Tanaka et al.

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induced force, aﬀected the current-induced BD dynamics.
We also found that the current-induced behavior of the BDs
can be controlled by applying an external perpendicularmagnetic ﬁeld.

8)
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Acknowledgments This work was supported by JSPS KAKENHI Grant
Numbers 25820135, 24656219, and 24360126. This work was also supported by
the Nanotechnology Platform Program (Nagoya Institute of Technology andToyota Technological Institute) of the Ministry of Education, Culture, Sports,
Science and Technology, Japan.

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