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Vol.44 No.6
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2020

Power Magnetics
Iron Loss and Hysteresis Properties of Nanocrystalline Magnetic Materials Under High Frequency Inverter
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Excitation

A. Yao, F. Kato, and H. Sato

…129

Tian Li, Takuya Taniguchi, Yoichi Shiota, Takahiro Moriyama, and Teruo Ono…133

Spin Electronics

Chromatic Aberration Eﬀect in Refraction of Spin Waves

Spin Hall Eﬀect in Topological Insulators

広告◇東英工業株式会社

PHAM NAM HAI

…137

44

HP: http://www.magnetics.jp/ e-mail: msj@bj.wakwak.com
Electronic Journal: http://www.jstage.jst.go.jp/browse/msjmag

6

2020

INDEX

Journal of the Magnetics Society of Japan
Vol. 44, No. 6
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTSPower Magnetics
Iron Loss and Hysteresis Properties of Nanocrystalline Magnetic Materials Under High Frequency
Inverter Excitation…………………………………………………………………… A. Yao, F. Kato, and H. Sato

129

Spin Electronics
Chromatic Aberration Effect in Refraction of Spin Waves……………………… Tian Li, Takuya Taniguchi, Yoichi Shiota, Takahiro Moriyama, and Teruo Ono

133

Spin Hall Effect in Topological Insulators………………………………………………… PHAM NAM HAI137

Board of Directors of The Magnetics Society of Japan
President:
K. Nakagawa
Vice Presidents:
S. Sugimoto, S. Matsunuma
Directors, General Affairs:
Y. Miyamoto, H. Saito, H. Yuasa
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K. Ishiyama, H. Takahashi
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S. Nakagawa, T. Kondo
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T. Ono, T. Kato
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M. Nakano, H. Yanagihara
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F. Akagi
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Specially Appointed Director, International Conferences: Y. Miyamoto
Auditors:
R. Nakatani, Y. Takano

INDEX
J. Magn. Soc. Jpn., 44, 129-132 (2020)
LetterIron loss and hysteresis properties of nanocrystalline magnetic materials
under high frequency inverter excitation
A. Yao, F. Kato, and H. Sato
National Institute of Advanced Industrial Science and Technology (AIST), 16-1, Tsukuba 305-8569, Japan, a.yao@aist.go.jp

Recently, wide-bandgap (WBG) power semiconductors made of silicon carbide (SiC) and gallium nitride (GaN) have been widely
developed as high-speed switching devises. Many researchers have studied novel magnetic materials, such as nanocrystalline magnetic
materials (NMMs), for low-loss electric motors and transformers. This study experimentally examines the hysteresis (B–H) curve andiron loss properties of the NMM core excited using a pulse width modulation (PWM) inverter at high carrier frequencies on the orderof MHz with and without the dead time. For comparison, the magnetic properties of amorphous magnetic materials (AMMs) core arealso evaluated. Particularly at high carrier frequencies (approximately 1 MHz), the iron loss of NMM and AMM cores signiﬁcantly
depends on the dead time. Compared with the case of the AMM core, the NMM core suppresses the increasing rate of iron losses
caused by the dead time because the area of minor loops in NMM becomes small, particularly in high-frequency regions.
Key words: Nanocrystalline magnetic materials, iron loss, B–H curve, inverter, high frequency, wide-bandgap semiconductor
1 Introduction
Transformer and motor systems often comprise inverters andcores composed of soft magnetic materials. In motor systems,
pulse width modulation (PWM) inverters are commonly used toperform speed and torque control. Thus, magnetic material cores
are excited using a PWM inverter. The waveform generated using
the PWM inverter exhibits high-order harmonic components andinduces complex hysteresis (B–H) curves in soft magnetic material (motor) cores1–17) . Owing to these complex hysteresis (B–H)
curves of the cores, the iron loss under PWM inverter excitation

have been shown under PWM inverter excitation at high carrier
frequencies on the order of MHz and without the dead time17) .
To use inverters that employ WBG devices, the next step is tounderstand the hysteresis (B–H) curve and iron loss properties of
the NMM core under MHz high carrier frequency inverter excitation with and without the dead time. In the PWM inverter, thedead time is necessary for practical use to prevent a short circuit
between the upper and lower arms.
This study experimentally examines the hysteresis (B–H)
curve and iron loss properties of the NMM core excited using a
GaN inverter at the MHz high carrier frequency. For comparison,

the PWM inverter at the MHz high carrier frequency.

the magnetic properties of the AMM core are also evaluated.
Moreover, the impact of dead time on the magnetic properties of
NMM and AMM cores excited using the high carrier frequency
inverter with and without the dead time is discussed. When theratio of the iron loss caused by the dead time to the total iron loss

Recently, several researchers have focused on motor corescomposed of NMM and amorphous magnetic materials (AMMs)

becomes small, the magnetic material is suitable for high-speed
and high-frequency applications.

increases by approximately 10%–50% compared with that undersinusoidal excitation2) . The objective of this study is to clarify
the complex hysteresis (B–H) curve and iron loss properties ofnanocrystalline magnetic materials (NMMs)18, 19) core fed using

to perform iron loss reduction9, 12, 20, 21) . NMM and AMM have

2 Experimental Method

lower iron loss density than conventional nonoriented (NO)silicon steel11, 12, 21) . Moreover, a previous study has shown

Figure 1 illustrates a schematic of the ring core, single-phasethat the iron loss of the NMM motor is smaller than that of
the AMM motor, and the NMM motor core is expected to besuitable for use in high-speed and high-frequency regions12) .

GaN inverter, and measurement system to obtain the hysteresis(B–H) curve and iron loss properties. The ring core with a thickness of 7 mm, inner diameter of 102 mm, and outer diameter

The iron loss characterization of NMM cores under high carrier
frequency excitation using the inverter is useful for core designin high-speed and high-frequency regions. Therefore, examiningof 127 mm is composed of NMM (FT-3M) laminations11) . For

the fundamental magnetic properties in the NMM core underhigh carrier frequency inverter excitation is necessary.
Wide-bandgap (WBG) power semiconductors made of siliconcarbide (SiC) and gallium nitride (GaN) have been widely developed and studied as high-voltage, low loss, and particularly highcomparison, the ring core with identical geometries of AMM(SA-1) laminations is also used. Both ring laminations (NMM
and AMM) are impregnated with acrylic resin and cut using thesame wire-cutting technique. The stacking factor S f of NMM

speed switching devises10, 11) . Recently, using these WBG de-and AMM ring cores is 0.873 and 0.935, respectively. These tworing cores have two (primary and secondary) coils that are woundusing a wire. Here, the primary (secondary) coil is used as the exciting coil (B-coil to measure the magnetic ﬂux density B). See

vices, magnetic properties of conventional NO silicon steel coresRefs.10, 11, 15, 16) for further explanation of the ring cores.

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GaN-FET inverterto the high-harmonic components, the PWM carrier waveform is
responsible for many minor loops in the hysteresis (B–H) curves(See Refs.10, 11) for the further explanation of the minor loops). In

A/D converter

NMM core

Ref.17) , the hysteresis (B–H) curve and its minor loop of the conventional NO silicon steel core fed using an inverter under carrier
frequencies on the order of MHz without the dead time were ob-

Ring coreFig. 1 Schematic of the NMM ring core, single-phase GaN inverter, and measurement system used to obtain the hysteresis (B–H) curve and iron loss characteristics.
The single-phase inverter with GaN ﬁeld-eﬀect transistors(GaN-FET)10, 17) is used to measure the hysteresis (B–H) curveand iron loss properties of two (NMM and AMM) ring cores.
The frequency f0 of the fundamental sinusoidal waveform is
set to 50 Hz. The carrier frequency fc of the triangular carrier
waveform is varied from 400 kHz to 1.0 MHz in 200-kHz steps.
The modulation index is deﬁned as the ratio of the fundamental
waveform to the carrier frequency waveform amplitude and is
set at 0.7. The maximum magnetic ﬂux density Bmax of two ringcores is set at 0.5 T. The dead time D is set at 0, 10, and 20 ns.
To estimate the magnetic ﬁeld intensity H (= N1 I/l) and the∫magnetic ﬂux density B (= Vdt/(N2 S c S f )) in ring cores, theprimary current I ﬂowing through the primary winding and theB-coil voltage V induced in the secondary winding are measured.
Here, N1 (= 10) denotes the number of turns in the primary coil,l (= 0.36 m) is the magnetic path length of the ring cores, N2 (=10) is the number of turns in the secondary coil, and S c (= 87.5mm2 ) is the cross-sectional area of the cores. To measure I andV, a current probe (HIOKI E.E. Corp., CT6711), a voltage probe(Iwatsu Electric Co., Ltd., SS-320), and a high-performance A/D
converter (NI Corp., PXIe-5163, 14 bit, 1 GS/s) are used. Using
H and B, the iron loss W of the ring cores can be calculated by17)
∫
f0
HdB,
(1)
W=
ρ
where ρ denotes the density of the cores. Here, ρ of NMM andAMM is 7300 and 7180 kg/m3 , respectively.
To clarify the impact of the increasing rate of iron loss causedby the dead time, the ratio ηn of the loss without the dead time tothat with the dead time is discussed. Here, ηn is deﬁned by thefollowing equation:
ηn =

Wn
,
W0

(2)

where W0 denotes the iron loss without the dead time and Wn isthat with the dead time. In this study, n (Wn ) can be set to either
10 or 20 ns (W10 or W20 ).

served. For the ﬁrst time, this study shows that the NMM andAMM cores also have minor loops under inverter excitation at a
relatively high carrier frequency of 1 MHz. As shown in Figs. 2
and 3, the width and area of the minor loops in both NMM andAMM cores increase with an increase in the dead time. It is assumed that owing to the dead time, the return current becomeslarge4) ; then, the change in the minor loop becomes large (SeeRefs.4, 14) for further explanation of the relationship between thedead time and the minor loop.). Under inverter excitation, thewidth and area of the minor loops of NMM become small compared with those of AMM. There are two possible reasons forthese phenomena. First, H of the major loop in the NMM coreis smaller than that in the AMM core; then, the variation in H of
the minor loop of NMM condenses. Second, because the thickness of the NMM sheet (approximately 18 µm) is thinner thanthat of the AMM sheet (approximately 25 µm), the eddy current
loss of NMM becomes small compared with that of AMM; then,the area of the minor loops of NMM becomes small.
Figure 4 shows the carrier frequency dependence of iron losses
in the two ring cores under inverter excitation at D = 0, 10, and 20
ns. Each iron loss (W) is obtained from the average of ﬁve measurements. The error bars (standard deviation) of each measurement are shown. W at D = 0 ns in these two cores decreases withrespect to fc up to approximately 800 kHz and then increases. W
at D = 10 and 20 ns in the NMM core monotonically increases
with an increase in fc . W at D = 10 and 20 ns in the AMM corealmost reaches the minimum value when fc is 600 kHz. These
results indicate that when the dead time increases, the carrier frequency at which the iron loss reaches the minimum value shifts tothe low-frequency side. A previous study has shown that owing to
the skin eﬀect and the distortion of the input voltage, W decreases
and increases with an increase in fc on the order of MHz17) . This
study shows that particularly at such high carrier frequencies ( fc
= approximately 1 MHz), the iron loss of the NMM and AMM
cores not only depends on the skin eﬀect and the distortion of the
input voltage but also signiﬁcantly depends on the dead time.
Finally, the impact of increased iron loss owing to the deadtime of the NMM and AMM cores excited using a PWM inverter
under high carrier frequencies on the order of MHz is discussed.
Figure 5 shows the ratio ηn with respect to fc using Eq. (2). As
shown in this ﬁgure, ηn monotonically increases with an increasein fc . In the high carrier frequency region, the impact of the dead3 Results and Discussion

time on one pulse becomes large; then, the minor loop in the case

Figures 2 and 3 show the hysteresis (B–H) curves at fc = 400

with the dead time increases compared with the case without thedead time, as shown in Figs. 2 and 3. Here, η10 and η20 of the

kHz and 1.0 MHz when the NMM and AMM ring cores are excited using the GaN inverter at D = 0, 10, and 20 ns. Owing
130

Journal of the Magnetics Society of Japan Vol.44, No.6, 2020

INDEXNMM ring core are smaller than those of the AMM core. Thus,
the increasing rate of loss owing to the dead time in the NMM
ring core is smaller than that in the AMM core. It is assumed that
this occurs because under inverter excitation, the area of the minor loops of NMM becomes small compared with that of AMM,
as shown in Figs. 2 and 3. Therefore, for the ﬁrst time, this study
shows that the NMM core can have a low iron loss caused by thefundamental waveform and suppress the increasing rate of ironlosses caused by the dead time compared with the case of theAMM core, particularly in the high carrier frequency region. The
NMM core is expected to be suitable for use in motor and power
converter systems using WBG devices, such as SiC and GaN, in
high-speed and high-frequency regions, in which the inﬂuence ofthe dead time becomes large.

(a)

(a)

(b)

(b)

(c)

(c)

(d)

(d)

(e)

(e)

(f)

(f)

Fig. 2 Hysteresis (B–H) curves of the NMM ring core fed usinga PWM inverter. The left panels show the major loops, and rightpanels show the minor loops, which correspond to the enlarged

Fig. 3 Hysteresis (B–H) curves of the AMM ring core fed usinga PWM inverter. The left panels show the major loops, and rightpanels show the minor loops, which correspond to the enlarged

view of the part of the left panels. (a) fc = 400 kHz and D = 0 ns,

view of the part of the left panels. (a) fc = 400 kHz and D = 0 ns,(b) fc = 400 kHz and D = 10 ns, (c) fc = 400 kHz and D = 20 ns,(d) fc = 1 MHz and D = 0 ns, (e) fc = 1 MHz and D = 10 ns, and(b) fc = 400 kHz and D = 10 ns, (c) fc = 400 kHz and D = 20 ns,(d) fc = 1 MHz and D = 0 ns, (e) fc = 1 MHz and D = 10 ns, and(f) fc = 1 MHz and D = 20 ns(f) fc = 1 MHz and D = 20 ns

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using WBG devices, such as SiC and GaN. In the future, the loss
repartition9, 16) at high carrier frequencies will be quantitatively
evaluated by numerical simulations.
Acknowledgments This work was partly supported by the JSPS
KAKENHI ♯20K14721, the JFE 21st Century Foundation, andthe Nagamori Foundation Research Grant.
References
1) A. Boglietti, P. Ferraris, M. Lazzari, and F. Profumo: IEEE
Trans. Magn., 27, 5334 (1991).
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3) T. Taitoda, Y. Takahashi, and K. Fujiwara: IEEE Trans. Magn.,
51, 1 (2015)4) T. Tanaka, S. Koga, R. Kogi, S. Odawara, and K. Fujisaki:
IEEJ J. Ind. Appl., 136, 110 (2016) (in Japanese).
5) W. Martinez, S. Odawara, and K. Fujisaki: IEEE Trans. Magn.,
Fig. 4 Carrier frequency dependence of iron losses in the tworing cores under PWM inverter excitation at D = 0, 10, and 20
ns: (a) NMM and (b) AMM

53, 1 (2017).
6) A. Yao, K. Tsukada, S. Odawara, K. Fujisaki, Y. Shindo,
N. Yoshikawa, and T. Yoshitake: AIP Adv., 7, 056618 (2017).
7) A. Yao, T. Sugimoto, S. Odawara, and K. Fujisaki: AIP Adv.,8, 056804 (2018).
8) A. Yao, S. Odawara, and K. Fujisaki: IEEJ J. Ind. Appl., 7,298 (2018).
9) A. Yao, T. Sugimoto, S. Odawara, and K. Fujisaki: IEEE
Trans. Magn., 54, 1 (2018).
10) A. Yao, K. Tsukada, and K. Fujisaki: IEEJ J. Ind. Appl., 7,
321 (2018).
11) A. Yao, T. Sugimoto, and K. Fujisaki: IEEJ J. Ind. Appl.,
139, 276 (2019) (in Japanese).

Fig. 5 Ratio ηn of loss without the dead time to that with thedead time as a function of fc using Eq. (2).

4 Conclusions
This study experimentally examined the hysteresis (B–H)
curve and iron loss properties of the NMM core excited using a
PWM inverter at high carrier frequencies on the order of MHz
with and without the dead time. Here, the AMM core wascompared with the NMM core to discuss the magnetic propertiesof the NMM core. For the ﬁrst time, this study showed that the
NMM core suppressed an increasing rate of iron losses causedby the dead time compared with the case of the AMM core
because the area of the minor loops of NMM became small,particularly in the high-frequency region. Thus, it is considered
important to make the main loop small and the thickness ofmagnetic materials thin while developing magnetic materials.
These results provide a path for further research on the iron loss
reduction of magnetic materials under PWM inverter excitation
at high carrier frequencies in motor and power converter systems

13212) A. Yao, T. Sugimoto, and K. Fujisaki: J. Magn. Soc. Jpn.,
43, 42 (2019).
13) A. Yao and T. Hatakeyama: J. Magn. Soc. Jpn., 43, 46 (2019).
14) A. Yao, T. Funaki, and T. Hatakeyama: J. Magn. Soc. Jpn.,
43, 105 (2019).
15) A. Yao: J. Magn. Soc. Jpn., 44, 30 (2020).
16) A. Yao, R. Moriyama, and T. Hatakeyama: J. Magn. Soc.
Jpn., 44, 52 (2020).
17) A. Yao, R. Moriyama, and T. Hatakeyama: J. Magn. Soc.
Jpn., 44, 87 (2020).
18) Y. Yoshizawa and K. Yamauchi: Mater. Trans., JIM, 31, 307(1990).
19) A. Yao, M. Inoue, K. Tsukada, and K. Fujisaki: AIP Adv., 8,056640 (2018).
20) N. Nishiyama, K. Tanimoto, and A. Makino: AIP Adv., 6,055925 (2016).
21) N. Denis, M. Inoue, K. Fujisaki, H. Itabashi, and T. Yano:IEEE Trans. Magn., 53, 1 (2017).
Recieved Jul. 24, 2020; Accepted Sep. 4, 2020

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J. Magn. Soc. Jpn., 44, 133-136 (2020)
Letter

Chromatic aberration effect in refraction of spin waves
Tian Li*, Takuya Taniguchi**, Yoichi Shiota*, Takahiro Moriyama*, and Teruo Ono*, ****Institute for Chemical Research, Kyoto University,

Uji, Kyoto 611-0011, Japan
Garching 85748, Germany**Fakultãt für Physik, Technische Universität München,***Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University,

Japan

Osaka 560-8531,

We numerically investigated the refraction property of spin waves (SWs) at thickness step in films with out-ofplane magnetization, in which the SWs propagate isotropically in the film plane. It was confirmed the isotropic SWs
were refracted at a thickness step by following the Snell's law. We also found that the refraction angle of SWs of thedipole-exchange mode depends on the resonant frequency, indicating that the chromatic aberration effect should betaken into account in designing magnonic devices.
Key words: magnonics, spin waves
Magnonics is a rapidly developing research field, inwhich spin waves (SWs) are utilized to transfer andprocess information1-4). In magnonics, controlling the
propagation direction of SWs is one of the crucial issues59). It has been recently demonstrated that refraction is
also useful for controlling the propagation direction of
SWs12,13,16-18). In optics, the dispersion relation of light isisotropic, and thus, the relation between the incident andrefraction angles is determined by the ratio of therefractive indices. On the other hand, for spin waves inthin films with in-plane magnetization the dispersion
relation is anisotropic, and thus, deviations from Snell’s
law in optics has been reported13, 16). This deviation from
Snell’s law in optics results in the complicated design formagnonic devices11). Thus, isotropic SWs, rather thananisotropic SWs, are expected to be more suitable forapplication. Here, we numerically investigate therefraction property of SWs in thin films withperpendicular magnetization, in which the isotropic SW
propagation in the film plane is expected from thesymmetry. It is found that the refraction of SWs follows
the Snell’s law in optics with the chromatic aberration
effect.
The micromagnetic simulation is performed utilizing
mumax319). In simulation, we use the following material
parameters reported for yttrium iron garnet (YIG); thesaturation magnetization 𝑀𝑀s = 139 kA/m, the exchange
stiffness 𝐴𝐴ex = 4.15 pJ/m , and the Gilbert damping
constant 1 × 10−4 20,21). In this study, two types ofsamples, labeled as sample A and B, are designed. Bothsamples are shaped as displayed in Fig. 1(a) and consistof thicker and thinner regions. The thicknesses of thicker
and thinner areas are set to be 800 nm and 400 nm insample A, and set to be 100 nm and 50 nm in sample B,
respectively. The cell size for the calculation is 200 ×
200 × 200 nm3 in sample A and 50 × 50 × 50 nm3 insample B. Note that the cell size is set to be much smaller
than the wavelength of excited SWs. To avoid the SW
reflections at the edges of calculation area, the damping

constants in the areas of 6 μm width from the left andright edges are set to increase gradually to 1. An external
magnetic field 𝜇𝜇0 𝐻𝐻ext = 200 mT is applied to +z direction,
which is enough to saturate the magnetization to z
direction, and SWs are excited by locally applied rf field𝜇𝜇0 𝐻𝐻rf sin(2π𝑓𝑓𝑓𝑓) along x direction at an antenna in the
thicker area. In this work, we use 𝜇𝜇0 𝐻𝐻rf = 1 mT and thefrequency 𝑓𝑓 of rf field is varied as 𝑓𝑓= 0.9, 1.0, and 1.1
GHz. We analyze the results recorded at 100 ns after the
SW excitation.
Fig. 1(b) shows a typical result, which displays thephase of magnetization precession at each position in xyplane. A SW with wavenumber 𝑘𝑘1 propagates from theantenna to the thickness step with the incident angle 𝜃𝜃1and it is refracted into the other SW with wavenumber
𝑘𝑘2 at the thickness step with the refraction angle 𝜃𝜃2 . The
estimation of 𝑘𝑘1 , 𝑘𝑘2 , and 𝜃𝜃2 is accomplished as follows.
Firstly, we define two areas (A1 and A2) and perform
two-dimensional fast Fourier transform (2D-FFT) on thedata in each area. Results of 2D-FFT are shown in Figs.
1(c) and 1(d). Secondly, we estimate 𝑘𝑘1 , which is theincident wavenumber in +x direction, from the data on
𝑘𝑘𝑦𝑦 = 0 (Fig. 1(c)). 𝑘𝑘1 is given as the second highest peak,
as shown in Fig. 1(e). Thirdly, we linearly fit the 2D-FFT
results of A2 and obtain 𝜃𝜃2 from the slope (Fig. 1(d)).
Finally, 𝑘𝑘2 is estimated from the second highest peak on
the fitted line, as shown in Fig. 1(f).
To confirm that SWs propagate isotropically in both
samples, we plot 𝑘𝑘1 and 𝑘𝑘2 as a function of 𝜃𝜃1 , asshown in Fig. 2. Both 𝑘𝑘1 and 𝑘𝑘2 are almost constantwith respect to 𝜃𝜃1 even if the resonant frequency isvaried from 0.9 GHz to 1.1 GHz. If the SW dispersion
relation is anistropic in the film plane, the wavenumber
should depend on the SW propagating dicrections13).
Therefore, the results shown in Fig. 2 indicates that theSWs propagate isotropically in both thicker and thinner
regions, and Snell’s law in optics, sin 𝜃𝜃1 ⁄sin 𝜃𝜃2 = 𝑘𝑘2 ⁄𝑘𝑘1 ,can be applied in the present system.
It is known that the dispersion relation of SW

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propagating in a film with perpendicular magnetization
can be described as𝜔𝜔2 = (𝜔𝜔𝐻𝐻 +2𝐴𝐴ex 𝛾𝛾𝑀𝑀𝑠𝑠

𝑘𝑘 2 ) [𝜔𝜔𝐻𝐻 +2𝐴𝐴ex 𝛾𝛾𝑀𝑀𝑠𝑠

𝑘𝑘 2 + 𝜔𝜔𝑀𝑀 (1 −1−𝑒𝑒 −𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘)] (1)

where 𝜔𝜔 is the angular frequency of the excited SW,
is the𝜔𝜔𝐻𝐻 = 𝜇𝜇0 𝛾𝛾(𝐻𝐻ext − 𝑀𝑀s ) , 𝜔𝜔𝑀𝑀 = 𝜇𝜇0 𝛾𝛾𝑀𝑀s , 𝜇𝜇0
permeability of vacuum, 𝛾𝛾 is the gyromagnetic ratio,
and 𝑑𝑑 is the film thickness10, 22). Here, both dipole-dipole

interaction and exchange interaction are taken into
account. In the small-k limit (i.e. for magnetostatic SWs),
where 𝑘𝑘 2 is comparatively smaller than 𝑘𝑘𝑑𝑑 , theinfluence of exchange interaction can be ignored. Inthat case, the SW dispersion relation for out-of-planemagnetized films, named as magnetostatic forward
volume wave (MSFVW), is expressed as𝜔𝜔2 = 𝜔𝜔𝐻𝐻 [𝜔𝜔𝐻𝐻 + 𝜔𝜔𝑀𝑀 (1 −1−𝑒𝑒 −𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘

)].

(2)

Fig.1 Example of process of simulation and analysis. The shown results are obtained from sample B when we set
𝑓𝑓 = 1 GHz and 𝜃𝜃1 = 45°. (a) Typical simulation setup. The black and white areas are respectively the thicker andthinner regions. The thickness step (boundary between two regions) is tilted with the angle 𝜃𝜃1 . The rf magnetic field
is applied at the antenna (orange line), which has one-cell width. 𝑘𝑘 and  of incident and refracted SWs are describedby the blue and green arrows, respectively. (b) Simulation result of the SW propagation. The phase of magnetization
precession, 𝜑𝜑, is displayed. The areas A1 and A2 surrounded by white frames are utilized for analysis. (c,d) Results of
2D-FFT from (c) A1 and (d) A2. The black dashed line L1 in (c) is 𝑘𝑘𝑦𝑦 = 0 and L2 in (d) is the result of linear fitting ofintensity in the yellow frame. (e,f) Intensity on (e) L1 and (f) L2.

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Fig.2 Incident angle dependent k1 and k2 in sample A (a,b,c) and sample B (d,e,f). The SWs are excited at threedifferent resonant frequencies; 0.9 GHz (a,d),1.0 GHz (b,d), and 1.1 GHz (c,f). The green markers show k1 and the blue
markers show k2.

Fig.3 The resonant frequency as a function ofwavenumber. Dispersion relation of DEFVW andMSFVW are respectively described by the solid andbroken lines and the simulation results are plotted by themarkers. Purple and green markers represent the SWs
in the film of 𝑑𝑑 = 800 nm and 400 nm, referring to thedata of 𝑘𝑘1 and 𝑘𝑘2 in sample A, respectively. The blue
and red markers represent the SWs in the film of 𝑑𝑑 =100 nm and 50 nm , referring to the data of 𝑘𝑘1 and 𝑘𝑘2
in sample B, respectively.
Fig. 3 shows the resonant frequency as a function ofwavenumber. Symbols show the results by the
micromagnetic simulation, and the calculation results by
Eq. (1) and Eq. (2) are shown by broken lines and solidlines, respectively. While the simulation results in theregions of 400 and 800 nm thicknesses (sample A) are
well reproduced by Eq. (2), those in the regions of 50 and
100 nm thicknesses (sample B) show deviation from Eq.
(2) and can be explained by Eq. (1), indicating that not
only the dipole interaction but also the exchangeinteraction should be taken into account to describe therefraction of spin waves with high wavenumbers.
Figs. 4(a) and 4(b) show the relation between theincident angle 𝜃𝜃1 and the refraction angle 𝜃𝜃2 observedin the samples A and B, respectively. The refraction
angle is independent of the resonant frequency in thesample A. This is due to the specific nature of MSFVW.
According to Eq. (2) for MSFVW, the wavenumber varies
by keeping 𝑘𝑘𝑘𝑘 constant, resulting in the special conditonof 𝑘𝑘1 ⁄𝑘𝑘2 = 𝑑𝑑2 ⁄𝑑𝑑1 . Therefore, Snell’s law, sin 𝜃𝜃1 ⁄sin 𝜃𝜃2 =𝑘𝑘2 ⁄𝑘𝑘1 , is given solely by the thickness ratio of two regions.
On the other hand, in the case of the dipole-exchange
forward volume wave (DEFVW) described by Eq. (1), theratio 𝑘𝑘2 ⁄𝑘𝑘1 depends not only on the thickness ratio but
also on the frequency. Note that similar effect is also wellknown in optics as the chromatic aberration due to thedependence of refractive index on wavelength of light.
The lines in Figs. 4(a) and 4(b) show the calculation
results of Snell’s law based on Eq. (1) and on Eq. (2),respectively, and the simulation results well reproduce
the calculation results, confirming that the refraction ofSWs follows the Snell’s law in optics with the chromaticaberration effect.

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Fig.4 Refraction angle versus incident angle of the SWs propagating (a) in sample A and (b) in sample B. In both
figures, the pink, green, and blue markers correspond to the simulation results of 𝑓𝑓 = 0.9 , 1.0 , and 1.1 GHz ,respectively. (a) Snell’s law of MSFVW is expressed by the black dashed line. (b) The frequency dependent Snell’s lawof 0.9,, 1.0, and 1.1 GHz are shown by the pink, green, and blue solid lines, respectively.

In summary, we performed the micromagnetic
simulations to investigate the refraction of SWs acrossthe thickness step in magnetic thin films with out-ofplane magnetization. It was confirmed that the SWs
propagate isotropically and the Snell’s law in optics canbe applied in the present system, leading to the simple
design of magnonic devices. It was also found that while
the refraction angle is independent of the resonant
frequency in MSFVW it depends on the resonant
frequency in the case of DEFVW, suggesting that thechromatic aberration effect should be taken into accountin designing magnonic devices using spin waves withhigh wavenumbers.

Acknowledgements We gratefully acknowledge fundingof JSPS KAKENHI Grant Numbers 15H05702, 18J22219,
Collaborative Research Program of the Institute for
Chemical Research, Kyoto University, and the
Cooperative Research Project Program of the ResearchInstitute of Electrical Communication, Tohoku
University.
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Received Aug. 27, 2020; Revised Sep. 18, 2020; Accepted Sep. 23,
2020

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J. Magn. Soc. Jpn., 44, 137-144 (2020)<Review>

S p i n Ha l l e f f e c t i n t o p o l o g i c a l i ns ul a t o r s
Pham Nam Hai1,2

1 Department of Electrical and Electronic Engineering, Tokyo Institute of Technology,

2-12-1 Ookayama, Meguro, Tokyo 152-8550, Japan

2 Center for Spintronics Research Network (CSRN), The University of Tokyo,

7-3-1 Hongo, Bunkyo, Tokyo 113-8656, JapanThe giant spin Hall effect (SHE) in topological insulators (TIs) is very attractive for applications to various
spintronic devices, notably spin-orbit torque magnetoresistive random-access memory (SOT-MRAM). In this paper,
we review the recent progress on the giant SHE in TIs, with emphasis on the role of topological surface states. We
discuss current challenges and future prospects for TIs as a realistic material in SOT-MRAM.
Key words: spin Hall effect, topological insulator, spin-orbit torque, MRAM
1 . I n tro d u cti o n(SHE) 1 , 2 )The spin Hall effectin non-magnetic
materials with strong spin-orbit coupling has recently
attracted great interest for its possible applications tovarious spintronic devices, most notably spin-orbit
torque (SOT) magnetoresistive random-access memory(MRAM). In the SHE, a perpendicular pure spin current
density Js can be generated by an in-plane charge
current density Je in a non-magnetic layer, whosecharge-to-spin conversion efficiency is characterized by
the spin Hall angle θSH = (2e/ℏ)Js/Je. This pure spincurrent can be injected into the free magnetic layer of amagnetic tunnel junction (MTJ), and it consequently
exerts a spin torque on the layer for magnetization
switching. The relationship between the injected spincurrent Is and the charge current Ie in the non-magnetic
layer is then given by Is = (ℏ/2e)(L/t)θSHIe, where L is
the length of the magnetic layer, and t the thickness ofthe non-magnetic layer. Because the factor (L/t)θSH canbe much larger than unity, i.e. Is/(ℏ/2) >> Ie/e, the SHE
can be used as an effective way of generating a spincurrent, meaning that a small writing current can beused for magnetization switching. Furthermore, since
there is no charge current flowing into the magnetic
layer, damage to MTJs can be suppressed. Finally, since
the spin-polarization direction of the pure spin current
generated by the SHE is perpendicular to themagnetization direction of the free magnetic layer withperpendicular magnetic anisotropy (PMA), theanti-dampling-like spin torque is maximized and themagnetization can be switched very fast (< ns). 3 )Motivated by these prospects, there have been intensive
efforts put into the research and development of
SOT-MRAM. In particular, very fast switching with low
voltage and no in-plane bias field has been
demonstrated in SOT-MRAM arrays deposited on 300
mm Si wafers, underlying the feasibility of
SOT-MRAM. 4)
Despite these recent developments, the writing
current density in SOT-MRAM is still as large as 108
Acm-2, which is too high for implementing SOT-MRAM
with Si driving transistors. This is because the heavy
metals used for the spin Hall layer in SOT-MRAM, suchas Ta, Pt or W, have a limited spin Hall angle. The
maximum θSH, ~0.4, is obtained with W. 5 ) Even if
taking into account the L/t factor, the driving current in
SOT-MRAM is still one order of magnitude larger thanthat of the conventional spin-transfer torque MRAM. To
solve this bottle neck, it is essential to find newmaterials with spin Hall angles at least one order ofmagnitude larger than that of heavy metals, which
requires θSH > 1. Since the extrinsic mechanism of SHE,
i.e. side-jump or skew scattering, unlikely yields such a
giant θSH, we can rely only on its intrinsic mechanism, 6)
which originates from Berry-phase curvature in the
momentum
space
and
is
an
intrinsic
quantum-mechanical property of the band structure. 7)
Because Berry-phase curvature has a singularity at
Dirac points, we can expect a very large θSH inmaterials with Dirac-like dispersion. Topologicalinsulators (TIs) are promising since they have metallic
surface states with Dirac-point-like dispersion. In fact,
very large θSH, usually higher than 1, have beenroutinely observed in many TIs, which is abreakthrough for SOT-MRAM. In this paper, we will
briefly introduce some fundamental properties of TIs.
Then, we will review recent studies on the giant SHE in
TIs, with emphasis on the role of topological surface
states. Finally, we will discuss the current challenges
and future prospects for TIs as a realistic material in
SOT-MRAM.
2.

Bri e f h i s to ry a n d f u n d a m e n ta l p ro p e rti e s o f
to p o l o gi ca l i n s u l a to rs

TIs are quantum materials having insulating bulk
states and metallic surface states with spin-momentum
locking, as shown in Fig. 1. TIs have had roots inresearch on the quantum Hall effect since the early
1980s. When two-dimensional electron gas at theinterface of a semiconductor heterostructure is
subjected to low temperatures and strong magnetic
fields, its energies are quantized to multiple Landaulevels. If the Fermi level lies in between those Landaulevels, the charge conduction inside the sample issuppressed, and the inside of the sample becomesinsulating with only one-dimensional conduction at the

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INDEXedges of the sample. Thus, electron gas undergoing thequantum Hall effect can be considered as a
two-dimensional TI with one-dimensional edge states.
It was later found that the quantum Hall effectoriginates from the non-trivial topology of thetwo-dimensional electron wavefunctions under strong
magnetic fields. 8) This further led to the prediction of anovel quantum Hall effect without Landau levels(quantum anomalous Hall effect) based purely on
topology arguments by Haldane in 1988. 9) Then, in 2006,
a two-dimensional TI with spin-polarized edge states
was predicted in a heterostructure consisting of a HgTe
quantum well sandwiched by two (HgCd)Te barriers. 10)
For this heterostructure, spin-polarized edge states
were predicted even without a magnetic field (quantum
spin Hall effect), and immediately confirmed. 11) These
theoretical and experimental achievements opened thedawn of TI research. Theories on quantum spin Hall
states were further studied for the two-dimensionalsurface states of three-dimensional TI materials, 12) and
BiSb (Sb composition of 7−22%) was proposed as athree-dimensional TI. 13) The topological surface statesof BiSb and their spin-momentum locking wereconfirmed by using angle-resolved photoemission
spectroscopy, 14 , 15 ) making it the first experimentallyconfirmed three-dimensional TI. This sparked a gold
rush of both theoretical and experimental searches for
new three-dimensional TI materials. Among them,Bi-based chalcogenides, such as Bi2Se3, Bi2Te3, and(BiSb)2Te3, are the most studied for their electronic
properties and possible device applications because they
have a large band gap and a single surface state withsimple Dirac-like band dispersion and because theirthin films can be easily grown on various substrates
using
the
molecularbeamepitaxy(MBE)
technique. 16 - 20 ) Notably, Cr-doped magnetic TI(CrBiSb)2Te3 with PMA was synthesized, in which thequantum
anomalousHalleffectwas
finally
confirmed. 21)

Fig. 1. (a) Typical band structure of TI, having
insulating bulk and Dirac-like metallic surface states.
(b) Spin-momentum locking of electrons on topologicalsurfaces.

138

From this brief history, we can see that TIs inherit
many properties of quantum Hall states and thereby
have been the object of many studies on
low-temperature physics such as the quantum spin Hall
effect or quantum anomalous Hall effect. At the sametime, TIs have many different characteristics fromquantum Hall states that make them attractive forroom-temperature spintronic applications. One featureis that the existence of one(two)-dimensionaledge(surface) states of TIs is ensured by the non-trivial
topology of their band structure and can emerge
without the application of large external magnetic fields.
If the band gap energy is much larger than the thermalenergy at room temperature and the Fermi level isinside the band gap, the edge(surface) states can beelectrically accessed even at room temperature. Anotheris that the surface states have Dirac-like band
dispersion, which promises a large intrinsic SHE. Yetanother feature is the unique spin-momentum locking
feature of the surface states, which prioritizes pure spincurrent generation in the direction perpendicular to thefilm plane. All of these features are very promising for
applications to spintronics, especially their expected
giant SHE.
3 . S p i n Ha l l e f f e c t i n B i 2 S e 3
Bi2Se3 is a TI with a large band gap of about 300 meV
and has thus become one of the most studied TIs. As aresult, the SHE in TIs was first evaluated in Bi2Se3. A.R.
Mellnik et al. cleaned the surface of a MBE-grown
Bi2Se3 layer and deposited NiFe on top of it. They thenused the spin torque ferromagnetic resonance (ST-FMR)
technique to determine the spin Hall angle. 22 ) The
obtained θSH = 2–3.5 was larger than that of heavy
metals by one order of magnitude. This work
immediately generated great interest in the SHE of TIs.
Nevertheless, studies on the SHE in Bi2Se3 face a big
problem. Since Bi2Se3 is a V-VI group compound, strict
control of the stoichiometry is required to obtain theinsulating bulk. In reality, due to the existence ofanti-site Se or anti-site Bi defects during MBE growth,
there are always extrinsic electrons or holes that shift
the Fermi level to either the conduction band or thevalence band, making the bulk of Bi2Se3 a degenerated
semiconductor. Therefore, there can exist parallel
conduction in the bulk and on the surfaces of Bi2Se3. In
such a situation, it becomes impossible to separate theelectric currents flowing in the bulk and on the surfacesof Bi2Se3. The ratio between the surface current and thebulk current may vary from sample to sample,
depending on the growth condition and the thickness of
the Bi2Se3 thin film. Consequently, there has been abroad distribution of reported θSH values for Bi2Se3,
making it difficult to draw a clear conclusion about theorigin of the giant SHE in Bi2Se3, i.e. whether theobserved giant spin Hall angle is real and originatesfrom the surface states or not. For example, Y. Wang et

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al. used the same ST-FMR technique to measure thespin Hall angle in Bi2Se3/CoFeB bilayers, but obtained
only θSH = 0.047 (room temperature) ~ 0.42 (50 K). 23)
Meanwhile, the same group reported θSH = 1−1.75 andsuccessfully
realizedroom-temperature
SOT
magnetization switching in Bi2Se3/NiFe bilayers with acurrent density as low as 6 × 105 Acm−2. 24)
4 . S p i n Ha l l e f f e c t i n ( B i S b ) 2 T e 3(BiSb)2Te3 is a ternary TI that can avoid the bulk
current problem in Bi2Se3. Since Bi2Te3 tends to ben-type while Sb2Te3 tends to be p-type, it is possible toprepare alloy (BiSb)2Te3 thin films with insulating bulk
by adjusting the Sb composition (88−96%). 25) The spin
Hal angle of (BiSb)2Te3 was first evaluated in(Bi0.5Sb0.5)2Te3/(Cr0.08Bi0.54Sb0.38)2Te3 bilayers. 26) Because(Cr0.08Bi0.54Sb0.38)2Te3 is a diluted magnetic TI with a
low Curie temperature, the experiment was performed
at 1.9 K. SOT magnetization switching was realized at avery low current density of 8.9 × 104 Acm−2. The spin
Hall angle was investigated with second harmonic Hallmeasurements. However, the obtained θSH = 140−425
value may have been significantly overestimated due toan artifact from the asymmetric magnon scattering on
the surfaces of (Cr0.08Bi0.54Sb0.38)2Te3. 27) The correctedvalue was obtained later in (BiSb)2Te3/Ti/CoFeB
junctions, which yielded θSH = 2.5 at room temperature.

Fig. 2. (a)(b) Room temperature SOT switching loops of
Bi2Se3/CoTb bilayer, measured under bias field of ±1000
Oe, respectively. (c)(d) SOT switching loop of reference
Pt/CoTb and Ta/CoTb bilayer, respectively. Here, Je ischarge current density inside spin Hall materials.
Reprinted with permission from Ref. 28). Copyright(2017) by American Physical Society.

5 . R o o m te m p e ra tu re SOT m a gn e ti z a ti o n s wi tch i n g b y
to p o l o gi ca l i n s u l a to rs
Room temperature SOT magnetization switching and
its advantage compared with heavy metals was first
demonstrated by J. Han et al. using Bi2Se3, (BiSb)2Te3,
Ta, and Pt/CoTb bilayers. 28) Figures 2(a) and 2(b) show
the SOT magnetization switching loops of the
Bi2Se3/CoTb (4.6 nm) bilayer, while Figs. 2(c) and 2(d)show that of the reference Pt/CoTb (2 nm) and Ta/CoTb(2 nm) bilayer, respectively. The threshold switchingcurrent density in the Bi2Se3/CoTb (4.6 nm) bilayer was
3 × 106 Acm−2, which was much smaller than of Pt/CoTb(2 nm) (40 × 106 Acm−2) and Ta/CoTb (2 nm) (10 × 106
Acm−2).
Figure 3(a) shows the effective spin Hall angle of(BiSb)2Te3, Bi2Se3, Pt, and Ta in junctions with CoTb
measured by the loop shift method. The effective spin
Hall angles of (BiSb)2Te3, Bi2Se3, Pt and Ta were 0.4,
0.16, 0.017, and −0.031, respectively. These values were
smaller than their intrinsic values, which is explainedby the small spin transmissivity of CoTb. Nevertheless,the effective spin Hall angles of (BiSb)2Te3 and Bi2Se3
are clearly larger than those of Pt and Ta. Figure 3(b)compares the power consumption of SOT switching
using (BiSb)2Te3, Bi2Se3, Pt, and Ta, which confirmed
the advantage of TIs.

Fig. 3. (a) Effective spin Hall angles of (BiSb)2Te3,
Bi2Se3, Pt, and Ta measured in junctions with CoTb. (b)Normalized power consumption (with Ta set to beunity) for SOT switching using (BiSb)2Te3, Bi2Se3, Pt,
and Ta. Reprinted with permission from Ref. 28).
Copyright (2017) by American Physical Society.
6 . Ro l e o f to p o l o gi ca l s u rf a ce s ta te s
Although giant spin Hall angles and low SOT
switching current densities have been confirmed invarious TI/ferromagnet bilayers, the origin of the giant
SHE in TIs is still not clear due to the fact that thecurrent may flow on both the surfaces and in the bulk of
TIs. To definitely determine the origin of the giant SHE
in TIs, H. Wu et al. investigated the SHE in(Bi1-xSbx)2Te3
thin
films
with
varying
Sb
compositions. 29) As shown in Fig. 4(a), the Fermi level of(Bi1-xSbx)2Te3 can be tuned by changing the Sb
composition. When the Sb composition is about 93%, theFermi level approaches the Dirac point. Figure 4(b)shows the sheet carrier density and the resistivity of(Bi1-xSbx)2Te3 as a function of Sb composition. Near the
Dirac point, the electron sheet density decreases andthe resistivity reaches the maximum at x = 93%, which

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Fig. 4. (a) Schematic of Fermi level positions for different Sb ratios (x = 0, 0.7, 0.78, 0.85, 0.93, 1.0) of(Bi1−xSbx)2Te3. (b) Sheet carrier density |n2D| and resistivity ρxx as function of Sb composition in(Bi1−xSbx)2Te3. (c) Switching current density |Jc| and SOT-induced effective field |χSOT| as function of Sb
composition. Reprinted with permission from Ref. 29). Copyright (2019) by American Physical Society.
indicates that the Fermi level is inside the band gap
and approaches the Dirac point. Figure 4(c) shows thethreshold switching current density and the
SOT-induced effective field as a function of Sb
composition in (Bi1-xSbx)2Te3/Ti/CoFeB junctions. Near
the Dirac point, the switching current density Jc is at
the minimum, and the SOT-induced effective field is
maximized. This unambiguously demonstrates thesurface state origin of the giant SHE. The Jc of the(Bi0.07Sb0.93)2Te3/Ti/CoFeB junction is reduced to 5.2 ×
105 Acm−2, which is one to two orders of magnitude
smaller than that of the reference Pt,Ta,W/Ti/CoFeB
junctions. Furthermore, θSH = 2.5 was obtained for the(Bi0.07Sb0.93)2Te3/Ti/CoFeB
junctionfromsecondharmonic Hall measurements.
7 . Hi g h e l e c t r i c a l c o n d u c t i v i t y a n d g i a n t s p i n Ha l l
e f f e ct i n Bi Sb
One disadvantage of using TIs as the spin Hall
material in SOT-MRAM is their low electricalconductivity σ of ~104 Ω−1m−1. For example, the σ of
(Bi0.07Sb0.93)2Te3 discussed in the previous section is
only 1.8 × 104 Ω−1m−1, which is significantly smaller
than the 6 × 105 Ω−1m−1 of CoFeB. Therefore, in thejunctions of TI/metallic ferromagnets, most of thecurrent will be shunted by the ferromagnetic layer anddoes not contribute to the generation of a pure spincurrent. For example, in a typical (Bi0.07Sb0.93)2Te3 (sixquintuple layers)/CoFeB (1.5 nm) bilayer, 87% of thecurrent will flow into the CoFeB layer. Therefore,
finding a TI material with both high conductivity and a
giant spin Hall effect is essential. Thus, we have been

140

concentrating on BiSb. 30 ) Although BiSb is the firstexperimentally confirmed three-dimensional TI (Sb of
7−22%), it has a small bulk band gap of ~20 meV andcomplex surface states. Therefore, not much attention
has been paid to BiSb since the discovery of Bi2Se3 andrelated compounds with a much larger band gap of ~300
meV and much simpler surface states. However, as apure spin current source for SOT-MRAM, BiSb is very
attractive because it has multiple surface states andhigh mobility as evidenced by the high bulk electricalconductivity of 4~6.4 × 105 Ω−1m−1. Furthermore,because Bi and Sb are in the same V-group, deviation of
the composition or existence of anti-site defects does not
result in any donors/acceptors that would generate free
carriers and shift the Fermi level to the conduction
band or to the valence band as in the case of Bi2Se3. As
a result, the Fermi level of BiSb is always in the bandgap, making it easier to investigate the origin of theSHE. Motivated by these promising prospects, we grewand characterized Bi1-xSbx thin films on semi-insulating
GaAs(111)A substrates by MBE, with various Sb
concentration ranging from 0 to 100%. By optimizing
the growth condition, we were able to grow single
crystalline Bi1-xSbx thin films on GaAs(111)A substrates,
despite the large and changing lattice mismatch
between Bi1-xSbx and GaAs(111) as the Sb concentration
changes. For thick enough thin films, their conductivity
approached those of bulk values, indicating that the
crystal quality was high. From the temperaturedependence of the electrical conductivity, we confirmed
the existence of the metallic surface states of Bi1-xSbx. 31)

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Fig. 5. (a) Room-temperature electrical conductivity of various Bi1-xSbx thin films with different Sb
concentrations and thicknesses. (b) Temperature dependence of resistivity (normalized by value at room
temperature) in Bi0.89Sb0.11 thin films with thicknesses of 10, 41, and 92 nm. Dots and solid lines show
experimental data and fitting to parallel conduction model of BiSb (inset). (c) Band gap of Bi1-xSbx thin films
with thicknesses around 90 nm, obtained by fitting their experimental temperature dependence of resistivity
to parallel conduction model.30,31)
Figure 5(a) shows the electrical conductivity σ ofvarious Bi1-xSbx samples with different thickness andSb concentrations x. We found that Bi1-xSbx thin films
show electrical conductivity higher than 1 × 105 Ω−1m−1with an average of 2.5 × 105 Ω−1m−1, which is higher
than other Bi-based chalcogenides by one order ofmagnitude. Figure 5(b) shows the temperaturedependence of the normalized resistivity of Bi0.89Sb0.11
thin films with thicknesses of 10 nm, 41 nm, and 92 nm.
For the 92 nm-thick thin film, the resistivity
exponentially increased as the temperature decreased
as expected for an intrinsic semiconductor, but it
approached a constant value at low temperatures. Thisbehavior can be explained by the parallel conduction
model for this sample. At high temperatures, bulk
conduction occurs due to thermally excited intrinsic
carriers in the conduction band and valence band. As
the temperature decreases, the bulk conduction isquenched, and the surface conduction becomesdominant at low temperatures. As the thickness
reduced to 41 nm, the surface state contribution began
to rise significantly. Finally, the 10-nm-thick sample
showed metallic behavior over the wide range oftemperature. This indicates that surface conduction was
dominant for the thinnest sample. Another importantfeature of BiSb is the quantum confinement effect that
adds an extra band gap energy to the intrinsic bulk
band gap. Figure 5(c) shows the band gap of various
Bi1-xSbx thin films with thicknesses around 90 nm,
obtained by fitting the experimental temperaturedependence of resistivity to the parallel conduction
model. Although the bulk Bi1-xSbx only has a band gap
for x = 7−22% with a maximum value of about 20 meVat x = 15%, the actual band gap is enhanced by thequantum confinement effect, which is effective at small
thicknesses. Furthermore, the band gap exists not only
inside the bulk TI regions (0.07 ≤ x ≤ 0.22) but also
outside of the TI region (x < 0.07 and 0.22 < x < 0.35),

which is also due to the quantum confinement effect, as
can be seen in Fig. 5(c). For the 10-nm-thick BiSb (x =15%), the band gap increased to 200 meV, which is large
enough so that most of the current flowed on thesurfaces. The strong quantum confinement effectreflects the high crystal quality of BiSb thin films.
To evaluate the SHE in BiSb, we prepared
Mn0.45Ga0.55 (3 nm)/Bi0.9Sb0.1 (10 nm) bilayers grown on
GaAs(001) substrates. Because MnGa on GaAs(001) has
a cubic crystal structure, BiSb grown on top of MnGa
has a pseudo-cubic (012) orientation. MnGa has a verylarge perpendicular anisotropy field of 40−50 kOe.
However, at the Mn concentration of 45%, themagnetization of MnGa is not perfectly perpendicular,
but tilts toward the in-plane direction. 32) The spin Hall
angle was measured by the loop-shift technique withthe experimental setup shown in Fig. 6(a). The purespin current injected from BiSb to MnGa generated aneffective anti-damping-like SOT field H SO that caneither increase or decrease the coercive force of MnGa,
depending on the current direction. Figure 6(b) shows
the perpendicular hysteresis loops of MnGa measured
under different current densities and polarities. Figure6(c) plots the coercive force of MnGa and its change,
which is equal to the effective SOT field, as a function of
the current density inside the BiSb layer. This data
indicates that the effective SOT field was as large as 2.3
kOe per (106 Acm-2), which yielded θ SH = 52 for the
BiSb(012) orientation. 33) The giant spin Hall angle for
the BiSb(012) surfaces can be understood by the factthat there are multiple Dirac points for the BiSb(012)surface states, compared with only one Dirac point forthe (001) surface states. 34)
Figure 7 shows SOT magnetization switching loops
for a Mn0.45Ga0.55 (3 nm)/Bi0.9Sb0.1 (5 nm) bilayer. The
threshold switching current density is only 1.5 × 106
Acm−2, which is smaller than that of MnGa/Pt,Ta,IrMn
bilayers by two orders of magnitude.35-37)

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Fig. 6. (a) Experimental setup for measuring SHE in Bi0.9Sb0.1 (10 nm) / Mn0.45Ga0.55 (3 nm) bilayer. (b) Hall
resistance of 100-µm × 50-µm Hall bar device of Bi0.9Sb0.1 (10 nm) / Mn0.45Ga0.55 (3 nm) bilayer under slightly
tilting perpendicular magnetic field Hext (θ = 2°), measured with various current densities J = −7.7 − 13.8 × 105
Acm−2 at room temperature. (c) Coercive force Hc of MnGa and its change ΔHc as function of current density
JBiSb in BiSb layer. Inset shows perpendicular effective SOT magnetic field Hso acting on magnetization vector
M at Hext = −Hc (coercive force) in macrospin picture.30),33)

Fig 7. Room-temperature SOT magnetization switching in Bi0.9Sb0.1 (5 nm)/Mn0.45Ga0.55 (3 nm) bilayer. (a) (b)Hall resistance of 100-µm × 50-µm Hall bar of bilayer under 100-ms pulse currents and in-plane magnetic fieldof +3.5 kOe and −3.5 kOe, respectively.33)
8.

Cu rre n t ch a l l e n ge s a n d f u tu re p ro s p e cts

Figure 8 shows the expected writing current andwriting energy of a realistic SOT-MRAM device using
various type of materials for the pure spin current
source, including heavy metals, two-dimensional
materials, and topological insulators. 38) It can be seenthat our MBE-grown BiSb outperformed all othermaterials by several orders of magnitude, because BiSb
shows not only high electrical conductivity but also a
giant spin Hall angle. However, most of the TIs thinfilms studied so far, including BiSb, were epitaxiallygrown on dedicated III-V semiconductor substrates by
the MBE technique, which is not suitable for142

mass-production. Therefore, it is essential to investigate
the performance of non-epitaxial TIs thin films
depositedonsiliconsubstrates
withanindustry-friendly technique, such as sputtering
deposition. Recently, there was an attempt toinvestigate the performance of sputtered non-epitaxial
BixSe1-x TI thin films by Mahendra DC et al., 39) who
found a promisingly large θSH = 8.7−18.6 but very low σ= 7.8 × 103 Ω−1m−1. On the other hand, we havedemonstrated that it is possible to deposit BiSb thinfilms on sapphire substrates by sputtering deposition
with a high crystal quality and high electricalconductivity approaching those of MBE-grown thinfilms. 40) Furthermore, we found that even non-epitaxial
BiSb thin films deposited on Si substrates by MBE or

Journal of the Magnetics Society of Japan Vol.44, No.6, 2020

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sputtering deposition could show a high spin Hall
performance. 41) Further work is needed to demonstrate
BiSb thin films with a high crystal quality andoptimized spin Hall performance on Si substrates with
sputtering deposition for ultralow power SOT-MRAM.

Fig. 8. (a) Switching current and (b) switching energy of
SOT-MRAM using various materials as pure spincurrent source, plotted against their sheet resistance.38)
Acknowledgements The work on MBE-grown BiSb
thin films was conducted in collaboration with Y. Ueda,
N.H. D. Khang, and K. Yao and was supported by aGrant-in-Aid for Challenging Exploratory Researchfrom MEXT (No. 16K14228).
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3, 2020

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Journal of the Magnetics Society of Japan Vol.44, No.6, 2020

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Editorial Committee Members・Paper Committee Members
T. Ono and T. Kato (Chairperson), K. Koike, T. Taniyama and K. Kobayashi (Secretary)
H. GotoT. Hasegawa
S. Isogami
K. KamataH. Kikuchi
T. Kouda
S. Kokado
Y. Kota
T. Kubota
T. MakiS. Muroga
T. Nagahama
H. Nakayama
M. NaoeT. Narita
J. OzekiN. PhamT. Sasayama
T. SatoK. Sekiguchi
Y. Shiratsuchi
T. Takura
S. YamadaT. Yamamoto
K. Yamazaki

T. Kimura
T. Morita
D. Oyama
T. Shima

N. Adachi
N. Inaba
Y. Kamihara
M. Ohtake
T. Tanaka

S. Honda
K. KatoT. Nozaki
I. Tagawa
S. Yoshimura

K. Bessho
S. Inui
A. Kuwahata
T. SatoM. Takezawa

M. DoiK. ItoK. Masuda
S. Seino
M. Tsunoda

T. DoiY. Kanai
Y. Nakamura
T. Suetsuna
N. Wakiya

K. Hioki
H. KatoK. Nishijima
K. Tajima
S. Yabukami

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