Vol. 39 No. 5 2015 年 9 月 1 日発行 頒価 ¥2,000 （税込）送料実費

Journal of the Magnetics Society of Japan

ISSN 2432-0250

Vol.45 No.1
JournalElectronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2021

Spin Electronics

Estimation of Angular Momentum Compensation Temperature in GdFe Film by Magnetic Compton Scattering
発行（公社）日本磁気学会 〠101‒0052 東京都千代田区神田小川町2丁目8番地
三井住友海上小川町ビル5階☎(03)5281-0106
印刷（株）国 際 文 献 社 〠169‒0075 東京都新宿区高田馬場3の8の8☎(03)3362-9741

Tetsuya Ikebuchi, Yuushou Hirata, Shinsaku Funada, Arata Tsukamoto, Haruka Ito, Kosuke Suzuki,…1

Kazushi Hoshi, Naruki Tsuji, Hiroshi Sakurai, Yoichi Shiota, Takahiro Moriyama, and Teruo Ono…1

Magnetic Recording
Low Current Driven Vertical Domain Wall Motion Memory with an Artiﬁcial Ferromagnet

広告◇東英工業株式会社Y. M. Hung, T. Li, R. Hisatomi, Y. Shiota, T. Moriyama, and T. Ono

…6

45

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

1

2021

INDEX

Journal of the Magnetics Society of Japan
Vol. 45, No. 1
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Spin Electronics
Estimation of Angular Momentum Compensation Temperature in GdFe Film by Magnetic Compton
Scattering………………… Tetsuya Ikebuchi, Yuushou Hirata, Shinsaku Funada, Arata Tsukamoto, Haruka Ito,
Kosuke Suzuki, Kazushi Hoshi, Naruki Tsuji, Hiroshi Sakurai, Yoichi Shiota,
Takahiro Moriyama, and Teruo Ono

1

Magnetic Recording
Low Current Driven Vertical Domain Wall Motion Memory with an Artificial Ferromagnet…………………………………… Y. M. Hung, T. Li, R. Hisatomi, Y. Shiota, T. Moriyama, and T. Ono

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
Directors, Treasurer:
K. Ishiyama, H. Takahashi
Directors, Planning:
S. Nakagawa, T. Kondo
Directors, Editorial:
T. Ono, T. Kato
Directors, Public Relations:S. Greaves, S. Sakurada
Directors, International Affairs:
M. Nakano, H. Yanagihara
Specially Appointed Director, Gender Equality:
F. Akagi
Specially Appointed Director, Societies Collaborations: K. Fujisaki
Specially Appointed Director, International Conferences: Y. Miyamoto
Auditors:
R. Nakatani, Y. Takano

6

INDEX
J. Magn. Soc. Jpn., 45, 1-5 (2021)
LetterEstimation of angular momentum compensation temperaturein GdFe film by magnetic Compton scattering
Tetsuya Ikebuchi†, Yuushou Hirata†, Shinsaku Funada, Arata Tsukamoto*,
Haruka Ito**, Kosuke Suzuki**, Kazushi Hoshi**, Naruki Tsuji***, Hiroshi Sakurai**,
Yoichi Shiota, Takahiro Moriyama, and Teruo Ono ****

Institute for Chemical Research, Kyoto University, Gokasho Uji, Kyoto 611-0011, Japan*College of Science and Technology, Nihon University, Narashino-dai Funabashi, Chiba 274-8501, Japan**Department of Electronics and Informatics, Gunma University, Tenjin-cho Kiryu, Gunma 376-8515, Japan***JASRI, Kouto Sayo-cho, Hyogo 679-5198, Japan****Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University,

Toyonaka, Osaka 560-8531, JapanThe angular momentum compensation temperature, 𝑇𝑇A , in transition metal rare earth (TM-RE) ferrimagnetic
materials is a crucial property for utilizing antiferromagnetic spin dynamics, which is much faster than its
ferromagnetic counterpart. However, reports on the estimation of 𝑇𝑇A in ferrimagnets are limited. In this study, wemeasured the temperature dependence of the spin magnetization and orbital magnetization of GdFe amorphous
perpendicular magnetization film by using magnetic Compton scattering. Then, we estimated 𝑇𝑇A experimentally.
Keywords: magnetic Compton scattering, TM-RE ferrimagnets, angular momentum compensation temperature

Antiferromagnets are a promising candidate for thecore elements of future spintronic devices because they
exhibit ultra-fast spin dynamics and a low magnetic
susceptibility to magnetic fields 1)-4). These desirable
properties originate from the antiferromagnetic ordering,in which the magnetic moments are compensated for on
an atomic scale 5). However, generally, antiferromagnets
are difficult to manipulate and probe due to the small net
magnetization and magnetic immunity. Hence, recently,
transition metal and rare earth (TM-RE) ferrimagnetic
materials, in which two inequivalent magnetic
sublattices are antiferromagnetically coupled, have been
attracting attention 6)-11). This is because these materials
have nonzero magnetization, which enables us tomanipulate and probe them. These ferrimagnets exhibit
two compensation temperatures due to the different
Landé g-factors of the TM and RE elements. One is themagnetization compensation temperature, 𝑇𝑇M , at which
the net magnetic moment vanishes. The other is theangular momentum compensation temperature, 𝑇𝑇A , atwhich the net angular momentum vanishes. Ultra-fast
domain wall (DW) motions were demonstrated at 𝑇𝑇A in
TM-RE ferrimagnets in both field-driven and currentdriven cases 12)-17). These results suggest that the
ferrimagnets exhibit antiferromagnetic spin dynamics at
𝑇𝑇A . This is because the time evolution of the state of amagnet is governed by the commutation relation of theangular momentum, not of the magnetic moment.
Therefore, the estimation of 𝑇𝑇A is a crucial step towardutilizing antiferromagnetic spin dynamics, but reports on                     Corresponding author:
Hiroshi Sakurai (e-mail: sakuraih@gunma-u.ac.jp).
Teruo Ono (e-mail: ono@scl.kyoto-u.ac.jp).
† These authors contributed equally to this work.

this have been limited.
Recently, Imai et al. 18) reported an angular momentum
compensation temperature in a ferrimagnet insulator
Ho3Fe5O12, by using the Barnett effect measurement
technique. This measurement is simple, but there is noelement specific information, which is important tounderstanding ferrimagnetic properties. Here, as apioneering new experimental method, we focus onmagnetic Compton scattering. Compton scattering
photons reflect the momentum density distribution of thetarget electron. Experimentally, by irradiating amagnetic substance with circular polarized X-rays, thespin magnetization of magnetically active electrons canbe measured. If the system is composed of independent
particles described by a single wave function, 𝜓𝜓𝜎𝜎 𝑖𝑖 (𝒓𝒓)(𝜎𝜎 = majority spin or minority spin), within the limit of
the impulse approximation, we can write the momentum
density 𝑛𝑛𝜎𝜎 (𝒑𝒑) by summing over all occupied single
electron states of the system 𝜒𝜒𝜎𝜎𝜎𝜎 (𝒑𝒑) as follows 19)-21).
2𝑛𝑛𝜎𝜎 (𝒑𝒑) = ∑𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖 |𝜒𝜒𝜎𝜎𝜎𝜎 (𝒑𝒑)| .

𝜒𝜒𝜎𝜎𝜎𝜎 (𝒑𝒑) = (

1

√2𝜋𝜋ℏ

3

) ∫ 𝜓𝜓𝜎𝜎 𝑖𝑖 (𝒓𝒓) 𝑒𝑒𝑒𝑒𝑒𝑒( −(1)𝑖𝑖𝒑𝒑𝒑𝒑ℏ) 𝑑𝑑 𝒓𝒓.

(2)Here, 𝒑𝒑 (= (𝑝𝑝𝑥𝑥 , 𝑝𝑝𝑦𝑦 , 𝑝𝑝𝑧𝑧 )) is the momentum of an electron

in a solid, and 𝑝𝑝z is the momentum of an electron in thematerial along the X-ray scattering vector, 𝑲𝑲 . The
scattering vector is defined as
𝑲𝑲 = 𝑲𝑲𝟐𝟐 − 𝑲𝑲𝟏𝟏 .

(3)

Here, 𝑲𝑲𝟐𝟐 and 𝑲𝑲𝟏𝟏 denote the wave vectors of incident
and Compton scattering X-rays, respectively. A magnetic

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

1

INDEX

Compton profile, (MCP), 𝐽𝐽𝑚𝑚𝑚𝑚𝑚𝑚 (𝑝𝑝𝑧𝑧 ) , is given by thefollowing equation.
𝐽𝐽𝑚𝑚𝑚𝑚𝑚𝑚 (𝑝𝑝𝑧𝑧 ) = ∬(𝑛𝑛𝑚𝑚𝑚𝑚𝑚𝑚 (𝒑𝒑) − 𝑛𝑛𝑚𝑚𝑚𝑚𝑚𝑚 (𝒑𝒑))d𝑝𝑝𝑥𝑥 d𝑝𝑝𝑦𝑦 .

(4)𝜇𝜇s = ∫ 𝐽𝐽mag (𝑝𝑝z )𝑑𝑑𝑝𝑝z .

(5)Here, 𝑛𝑛𝑚𝑚𝑚𝑚𝑚𝑚 (𝒑𝒑) (𝑛𝑛𝑚𝑚𝑚𝑚𝑚𝑚 (𝒑𝒑)) denotes the momentum densitywith the majority (minority) spin. Then, the spin
magnetic moment, 𝜇𝜇s , is determined from the 𝐽𝐽𝑚𝑚𝑚𝑚𝑚𝑚 (𝑝𝑝𝑧𝑧 )as 19)-20)

Total magnetization 𝑀𝑀t , which is measured by asuperconducting
quantuminterference
magnetometer, is expressed as the following.

device(6)𝑀𝑀t = 𝑀𝑀s + 𝑀𝑀l .

Here, 𝑀𝑀s denotes the spin magnetization, which is
obtained from a magnetic Compton scattering
measurement, and 𝑀𝑀l denotes the orbital magnetization.
Therefore, it is possible to estimate individual 𝑀𝑀t , 𝑀𝑀s ,and 𝑀𝑀l .
In this paper, we focus on a ferrimagnetic GdFe alloy
in which Gd and Fe are antiferromagnetically coupled.
First, the magnetization compensation temperature 𝑇𝑇M
is obtained from the temperature dependence of 𝑀𝑀t . Next,
the magnitudes of the spin magnetizations of Gd and Fe(𝑀𝑀s,Gd and 𝑀𝑀s,Fe ) in the ferrimagnetic GdFe alloy aremeasured using magnetic Compton scattering, and thespin magnetization compensation temperature 𝑇𝑇S , atwhich 𝑀𝑀s,Gd is equal to 𝑀𝑀s,Fe , is determined. Then,assuming that the 𝑀𝑀l,Gd of Gd is zero, the orbital
magnetization 𝑀𝑀l,Fe of Fe is obtained from the difference
between 𝑀𝑀t and 𝑀𝑀s . Then, the g-factor of Gd and Fe isdetermined, and finally, the 𝑇𝑇A of GdFe alloy isestimated.
GdFe films with a thickness of 1 μm were grown by DC
sputtering using Gd and Fe targets on Al film substrates
with a thickness of 6 μm as shown in Fig. 1(a). The GdFe
was covered with a 60-nm-thick SiN cap layer. The

( )
(a)

(b )

composition of the GdFe film was determined to be
Gd22.5Fe77.5 by an electron probe micro analyzer. X-ray
diffraction of the film did not show any peak, suggestingthat the film was amorphous. To increase the intensity of
the MCP signal, 64 films were deposited layer-on-layer.
MCP measurements were performed at the BL08W
beamline at SPring-8, Japan. BL08W provides circularly
polarized high energy X-rays from a wiggler device 21)-22).
The energy of the incident X-rays was 182.6 keV 23). The
sample was set in a vacuum chamber to suppress thescattering of the X-rays by air. MCP was measured inmagnetic field switching mode with a scattering angle of
178 degrees, in which the incident X-rays were parallelto the applied magnetic field. Superconducting magnets
can apply magnetic fields ranging from –0.5 T to 0.5 T
perpendicular to the film plane. MCP measurements
were performed at 289, 250, 225, 200, 175, 150, 100, 50,
and 10 K. The magnetization curves of the 𝑀𝑀t were
measured by a superconducting quantum interference
device (SQUID) magnetometer. The MCP of apolycrystalline Fe plate with a thickness of 0.1 mm wasmeasured at room temperature as a standard
measurement.
Figures 1(b) and 1(c) show the magnetization curves
and temperature dependence of the saturation
magnetization for the remanent state of the Gd22.5Fe77.5
film, respectively. The temperature dependence of thetotal magnetization 𝑀𝑀t can be written as𝑀𝑀t (𝑇𝑇) = |𝑀𝑀t,Fe (𝑇𝑇)| − |𝑀𝑀t,Gd (𝑇𝑇)|.
𝑇𝑇 𝛽𝛽F𝑒𝑒= 𝑀𝑀t,Fe (0) (1 − )𝑇𝑇𝑐𝑐

𝑇𝑇 𝛽𝛽Gd− 𝑀𝑀t,Gd (0) (1 − )
𝑇𝑇𝑐𝑐

. (7)

Here, 𝑀𝑀t,Fe (0) and 𝑀𝑀t,Gd (0) are the totalmagnetization of Fe and Gd at 0 K, respectively. 𝛽𝛽F𝑒𝑒 and𝛽𝛽Gd are the critical exponents of Fe and Gd, respectively,
and 𝑇𝑇𝑐𝑐 is the Curie temperature 14), 24). We assume
𝑀𝑀t,Fe (0) = 1130 emu/cm3 25), 𝛽𝛽F𝑒𝑒 = 0.50 26). Moreover, we
determined 𝑇𝑇c = 520 K by measuring the temperaturedependence of the magnetization 14). It was estimatedthat 𝑀𝑀t,Gd (0) = 1161 ± 30 emu/cm3 and 𝛽𝛽Gd = 0.60 ±0.005, leading to 𝑇𝑇M = 131 K with Eq. (7).
(c)

Fig. 1. (a) Structure of thin film sample used in experiment. For magnetic Compton scattering experiment, films
were stacked in 64 layers to amplify signal intensity. (b) Magnetization curves at 288, 150, and 10 K. (c) Temperaturedependence of saturation magnetization. Temperature at which saturation magnetization becomes zero on this curveis defined as magnetization compensation temperature 𝑇𝑇M , and 𝑇𝑇M = 131 K for this sample.

2

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

INDEX

Figures 2(a)-2(c) show MCP as a function of theelectron momentum (𝑝𝑝z ) in atomic units (au) at 289, 150,
and 10 K. The magnetic field (H = 0.5 T) was applied
perpendicular to the film plane. The measurement points
are indicated by the circles. The measured MCP for GdFe
alloy can be reproduced by a linear combination of MCPs
from 4f orbitals of Gd and those from 3d orbitals of Fe.
This is because the electron orbitals of Gd from 1s to 5p
and those of Fe from 1s to 3p are filled, and they aremagnetically inactive and thus do not contribute to MCP.
Furthermore, the contribution from the Gd 5d orbitals is
negligibly small. Therefore, fitting free atom profiles to ahigh momentum line shape has been exploited toseparate 4f contributions from 3d contributions in 4f rareearth-3d transition metal alloys 27). The purple solid lines
in Figs. 2(a)-2(c) are the best fit with the least square
method based on the above assumption, and the solid
blue lines and the solid red lines indicate the MCPs of Gd
and Fe, respectively. The 4f contribution of Gd obtained
from the literature 28) and the Fe contribution obtained
from the standard measurement were used for the fitting.
Above 𝑇𝑇𝑀𝑀 , we observed that the MCP of Fe was oriented
positive and the MCP of Gd was oriented negative asshown in Figs. 2(a) and 2(b) because 𝑀𝑀t,Fe (𝑇𝑇) > 𝑀𝑀t,Gd (𝑇𝑇).
In contrast, below 𝑇𝑇𝑀𝑀 , we observed that the MCP of Fe
was oriented negative and the MCP of Gd was oriented
positive as shown in Fig. 2(c) because 𝑀𝑀t,Gd (𝑇𝑇) > 𝑀𝑀t,Fe (𝑇𝑇).
𝑇𝑇M was 131 K for this sample.
Figure 2(d) shows the temperature dependences of thespin magnetization of Fe, 𝑀𝑀s,Fe (𝑇𝑇) , and that of Gd,
𝑀𝑀s,Gd (𝑇𝑇) , calculated from the MCPs for Fe and Gd
obtained by the analysis described in a previous
(a)

(b )

(d)

(e )

paragraph. The smaller spin magnetizations at 100 and
150 K indicate that the magnetizations in the GdFe film
were not magnetically saturated because of the small
external magnetic field (≦ 0.5 T). Note that the coercive
field drastically increased around 𝑇𝑇M . Figure 2(e) shows
the temperature dependence of the total spin magnetic
moments, which were calculated from 𝑀𝑀s (𝑇𝑇) =|𝑀𝑀s,Fe (𝑇𝑇)| − |𝑀𝑀s,Gd (𝑇𝑇)| [Eq. (7)]. Here, we assume that the
spin magnetizations also follow Eq. (7). Then, the fitting
indicated that 𝑀𝑀s,Fe (0) is 1104 ± 40 emu/cm3 and 𝑇𝑇S =207 ± 5 K as shown in Fig. 2(e). Here, the measurement
points at 100 K and 150 K are excluded from the fitting.
As we have determined the total magnetization 𝑀𝑀t
and the spin magnetization 𝑀𝑀s , 𝑀𝑀l can be obtained from
Eq. (6). Figure 3 shows the temperature dependences of𝑀𝑀l , 𝑀𝑀t , and 𝑀𝑀s . Since the orbital magnetization of Gd,
𝑀𝑀l,Gd (𝑇𝑇) is zero, the difference between 𝑀𝑀t and 𝑀𝑀s is
considered to correspond to the orbital magnetization ofFe, 𝑀𝑀l,Fe . By assuming that 𝑀𝑀l,Fe has the same
temperature dependence as for 𝑀𝑀s,Fe (𝑇𝑇) , 𝑀𝑀l,Fe (0) is
estimated to be 25 ± 2 emu/cm3. Therefore, the ratio of
the orbital magnetization to the spin magnetization in Fe
is 2.2 ± 0.3 %, which is consistent with a previous study
9).
As the g-factor is given by
𝑔𝑔Fe =2(𝑀𝑀s,Fe (0)+𝑀𝑀l,Fe (0))
𝑀𝑀s,Fe (0),(8)

the g-factor of Fe in the sample is estimated to be 2.04 ±0.01 by using determined values.
(c)Fig. 2. (a) Magnetic Compton profiles (MCP) at 288 K, (b) 150 K, and (c) 10 K. Measurement points are indicated bycircles. Solid purple lines are best fits with least square method. Red diamonds and blue triangles are deduced
contributions from Fe and Gd, respectively. (d) Temperature dependences of spin magnetizations of Fe and Gd. (e)Temperature dependence of spin magnetization of GdFe. Blue dashed line represents fitting result with Eq. (7).
Temperature at which spin magnetization is zero on this line is defined as spin magnetization compensation
temperature 𝑇𝑇S , and 𝑇𝑇S = 207 ± 5 K for this sample.

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

3

INDEX

References1)
2)

Fig. 3. Temperature dependences of orbital
magnetization 𝑀𝑀l (diamonds), spin magnetization 𝑀𝑀S(green line), and total magnetization 𝑀𝑀t (blue line) of
GdFe. 𝑀𝑀t was obtained by magnetization measurements
using SQUID magnetometer, and 𝑀𝑀s was determined bymagnetic Compton scattering measurements.
By applying the relationship between 𝑇𝑇A , 𝑇𝑇M , and 𝑇𝑇C
reported in 25), the following equation is obtained for thepresent system,𝑔𝑔𝛽𝛽

𝑇𝑇A = ( 𝐹𝐹𝐹𝐹 ) 𝐹𝐹𝐹𝐹
𝑔𝑔𝐺𝐺𝐺𝐺

1−𝛽𝛽𝐺𝐺𝐺𝐺𝑔𝑔

𝛽𝛽

𝑇𝑇M + {1 − ( 𝐹𝐹𝐹𝐹 ) 𝐹𝐹𝐹𝐹
𝑔𝑔𝐺𝐺𝐺𝐺

1−𝛽𝛽𝐺𝐺𝐺𝐺} 𝑇𝑇c .

(9)Inserting determined values leads to 𝑇𝑇A = 202 ± 2 K,
which is lower than 𝑇𝑇s = 207 ± 5 K. The small difference
between 𝑇𝑇S and 𝑇𝑇A originate from 𝑀𝑀s,Fe (𝑇𝑇) ≫ 𝑀𝑀l,Fe (𝑇𝑇),𝑀𝑀t,Fe (𝑇𝑇) ~𝑀𝑀s,𝐹𝐹𝐹𝐹 (𝑇𝑇) and 𝑀𝑀s,Gd (𝑇𝑇) = 𝑀𝑀t,Gd (𝑇𝑇) and it isconfirmed that 𝑇𝑇M < 𝑇𝑇A < 𝑇𝑇S in this GdFe system.
In summary, we observed the magnetizationcompensation temperature and the spin magnetizationcompensation temperature in ferrimagnetic GdFe alloy
film with perpendicular magnetic anisotropy using a
SQUID magnetometer and magnetic Compton scattering.
The spin magnetization and orbital magnetization ofeach element constituting the ferrimagnetic GdFe alloy
were independently determined. Furthermore, we
succeeded in estimating the angular momentum
compensation temperature of the ferrimagnetic GdFe
alloy film. Our results show that magnetic Compton
scattering is a unique method for investigating theelement specific spin magnetization and angularmomentum compensation temperature in ferrimagnets.
Acknowledgements This work was supported by JSPS
KAKENHI
Grant
Numbers
JP15H05702
and
JP19J21253, the Collaborative Research Program of theInstitute for Chemical Research, Kyoto University, andthe Cooperative Research Project Program of the
Research Institute of Electrical Communication, Tohoku
University. This experiment was performed with theapproval of the Japan Synchrotron Radiation ResearchInstitute (Proposal Nos. 2019A0921).

4

T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich: Nat.

Nanotechnol., 11, 231 (2016).

V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y.
Tserkovnyak: Rev. Mod. Phys., 90, 015005 (2018).
3) J. Železný, P. Wadley, K. Olejník, A. Hoffmann, and H.
Ohno: Nat. Phys., 14, 220 (2018).
4) M. B. Jungfleisch, W. Zhang, and A. Hoffmann: Phys. Lett.
A, 382, 865 (2018).
5) O. Gomonay, V. Baltz, A. Brataas, and Y. Tserkovnyak: Nat.
Phys., 14, 213 (2018).
6) C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A.
Itoh, A. Kirilyuk, and T. Rasing: Phys. Rev. B, 73, 220402(R)(2006).
7) M. Binder, A. Weber, O. Mosendz, G. Woltersdorf, M.
Izquierdo, J. R. Dahn, T. D. Hatchard, J.–U. Thiele, C. H.
Back, and M. R. Scheinfein: Phys. Rev. B, 74, 134404 (2006).
8) C. D. Stanciu, A. Tsukamoto, A. V. Kimel, F. Hansteen, A.
Kirilyuk, A. Itoh, and T. Rasing: Phys. Rev. Lett., 99,
217204 (2007).
9) A. Kirilyuk, A. V. Kimel, and T. Rasing: Rev. Mod. Phys., 82,
2731 (2010).
10) A. Mekonnen, M. Cormier, A. V. Kimel, A. Kirilyuk, A.
Hrabec, L. Ranno, and T. Rasing: Phys. Rev. Lett., 107,
117202 (2011).
11) A. Kirilyuk, A. V. Kimel, and T. Rasing: Rep. Prog. Phys.,
76, 026501 (2013).
12) K.–J. Kim, S. K. Kim, Y. Hirata, S.–H. Oh, T. Tono, D.–H.
Kim, T. Okuno, W. S. Kim, S. Kim, G. Go, Y. Tserkovnyak,
A. Tsukamoto, T. Moriyama, K.–J. Lee, and T. Ono: Nat.
Mater., 16, 1187 (2017).
13) S. A. Siddiqui, J. Han, J. T. Finley, C. A. Ross, and L. Liu:
Phys. Rev. Lett., 121, 057701 (2018).
14) L. Caretta, M. Mann, F. Büttner, K. Ueda, B. Pfau, C. M.
Günther, P. Hessing, A. Churikova, C. Klose, M. Schneider,
D. Engel, C. Marcus, D. Bono, K. Bagschik, and G. S. D.
Beach: Nat. Nanotech., 13 (2018).
15) K. Aoshima, R. Ebisawa, N. Funabashi, K. Kuga, and K.
Machida: Jpn. J. Appl. Phys., 57, 09TC03 (2018).
16) D.–H. Kim, T. Okuno, S. K. Kim, S.–H. Oh, T. Nishimura,
Y. Hirata, Y. Futakawa, H. Yoshikawa, A. Tsukamoto, Y.
Tserkovnyak, Y. Shiota, T. Moriyama, K.–J. Kim, K.–J. Lee,and T. Ono: Phys. Rev. Lett., 122, 127203 (2019).
17) T. Okuno, S. K. Kim, T. Moriyama, D.–H. Kim, H. Mizuno,
T. Ikebuchi, Y. Hirata, H. Yoshikawa, A. Tsukamoto, K.–J.
Kim, Y. Shiota, K.–J. Lee, and T. Ono: Appl. Phys. Express,
12, 093001 (2019).
18) M. Imai, Y. Ogata, H. Chudo, M. Ono, K. Harii, M. Matsuo,
Y. Ohnuma, S. Maekawa, and E. Saitoh: Appl. Phys. Lett.,
113, 052402 (2018).
19) N. Sakai, M. Ito, H. Kawata, T. Iwazumi, M. Ando, N.
Shiotani, F. Itoh, Y. Sakurai, and S. Nanao: Nucl. Instrum.
Methods A, 303, 488 (1991).
20) N. Sakai: J. Appl. Crst., 29, 81 (1996).
21) Y. Kakutani, Y. Kubo, A. Koizumi, N. Sakai, L. B. Ahuja,
and K. B. Sharma: J. Phys. Soc. Jpn., 72, 72599 (2003).
22) M. Itou, A. Koizumi, and Y. Sakurai: Appl. Phys. Lett., 102,082403 (2013).
23) A. Agui, A. Harako, A. Shibayama, K. Haishi, N. Tsuji, X.
Liu, G. Ma, and H. Sakurai: Journal of Magn. and Magn.
Mater., 484 (2019).
24) Y. Hirata, D.–H. Kim, T. Okuno, T. Nishimura, D.–Y. Kim,
Y. Futakawa, H. Yoshikawa, A. Tsukamoto, K.–J. Kim,
S.–B. Choe, and T. Ono: Phys. Rev. B, 97, 220403(R) (2018).

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

INDEX

25) R. Hasegawa and R. Ray: Phys. Rev. B, 20, 1 (1979).
26) S. Blindell: Magnetism in Condensed Matter (2001).
27) H. Sakurai, M. Ota, X. Liu, A. Morisako, Y. Sakurai, M. Itou,
T. Nagao, and A. Koizumi: J. Appl. Phys., 102, 013902(2007).

28) F. Biggs, L. B. Mendelsohn, and J. B. Mann: Atom. Data
Nucl. Data, 16 (1975).

29) S. Mangin, C. Bellouard, S. Andrieu, F. Montaigne, P.

Ohresser, N. B. Brookes, and B. Barbara: Phys. Rev. B, 70,014401 (2004).

Received Oct. 25, 2020; Accepted Nov. 19, 2020

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

5

INDEX
J. Magn. Soc. Jpn., 45, 6-11 (2021)<Paper>Low Current Driven Vertical Domain Wall Motion Memory
with an Artificial Ferromagnet
Y. M. Hung1, T. Li1, R. Hisatomi1, Y. Shiota1, T. Moriyama1, and T. Ono1,2
1Institute for Chemical Research, Kyoto University,

Gokasho, Uji, Kyoto 611-0011, Japan.

2Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University,

560-8531, Japan.

Toyonaka, Osaka

We propose a new structure of vertical domain wall (DW) motion memory with artificial ferromagnet to achieve
high DW controllability. The artificial ferromagnet is composed of periodically stacked ferromagnetic bilayers withrelatively large and small exchange stiffness constants (Aex), which refer to as strong coupling layers and weak couplinglayers. By optimizing Aex and the magnetic anisotropy of the weak coupling layers, DW width and position can beeasily controlled. Furthermore, micromagnetic analysis shows that low critical current density for DW motion down
to 2 ×1010 A/m2 can be achieved as we increase the Aex of weak coupling layers to larger than 2 pJ/m.
Key words: artificial ferromagnet, vertical domain wall motion memory, exchange stiffness constant, perpendicularmagnetic anisotropy, critical current, micromagnetic analysis
1. Introduction
Domain wall (DW) motion in ferromagnetic
nanowires1) are potential candidates of future memory
technologies such as racetrack memory2)-7), in which
digital bits are stored in a series of DW, and transported
through a nanowire with DW motion driven by electricalcurrent. Since multiple DW can be compactly encoded
into one ferromagnetic wire, racetrack memory promises
ultra-high storage density compared with conventional
magnetic memories3),7). In a ferromagnetic wire-based
memory cell, narrower DW indicates more digital bits
can be stored. Therefore, DW width is a key factor thatmust be concerned. Generally, DW width (Δ) depends on
the properties of ferromagnets, and can be expressed as
Δ = �Aex ⁄ Ku, where Aex is exchange stiffness constantand Ku is uniaxial anisotropy constant8). According toprevious researches, DW width is around 6.7 nm in a 15nm-thick Co film9), while in a 5-nm-thick permalloy
nanowire, DW width can be larger than 200 nm10). The
intrinsic properties of materials determine DW width,and hampers the achievement of high storage density inferromagnetic wires. Besides, in DW motion-based
technology, DW position is another key factor whichneeds to be precisely controlled. Currently, the approach
used to control DW position is to fabricate well-designed
pinning sites in nanowire11)-13). However, this approach
implies complicated nanofabrication is needed, andmakes commercialization of DW motion memory much
more difficult. Furthermore, lowering consumption
power is also important for practical application of
racetrack memory. Even though several approaches had
been proposed to reduce critical current (Jc) for DW
motion down to 1011 A/m3),5),14)-15), to attain low current
driven, precisely controllable, and applicable DW motion
memory with high storage density, there is still a lot ofroom for improvement. In this research, we propose a

6

new structure of vertical DW motion memory with anartificial ferromagnet which is composed of periodicallystacked ferromagnetic bilayers with strong and weakcoupling layers. Based on this structure, we can easily
reduce DW width and precisely control DW position.
Micromagnetic simulations are studied to verify thefeasibility of device and investigate Jc needed to drive
DW motion. It is found that as we increase the Aex of
weak coupling layers to larger than 2 pJ/m, Jc down to
2 × 1010 A/m2 can be achieved.
2. Memory operation scheme
Figure 1(a) shows the vertical DW motion memory
proposed in this research, in which the underlayer is aheavy metal-based conduction wire, e.g., Pt, Ta, and acts
as a word line for data writing. A cylindrical magnetic
wire, referred to as one memory cell, is an artificial
ferromagnet, which is composed of ferromagnetic
multilayers with different magnetic properties. The
lowermost layer of magnetic wire, colored with blue,
named layer1 in Figs. 1(b) and 1(c), is set as a pinninglayer with sufficiently large Ku with perpendicularmagnetic anisotropy (PMA). Above layer1, the evenlayers, colored with green, are PMA ferromagnets with
sufficiently large Aex and Ku, which are referred to as
strong coupling layers. The rest odd layers, colored withyellow and referred to as weak coupling layers, are nonPMA ferromagnets with sufficiently weak Aex. The
character of strong coupling layers is to carry storage bit,while the character of weak coupling layers is to carry
DW. If the Aex of weak coupling layer is sufficiently small,the smallest storage unit of one bit can be limited withina unit of one strong coupling layer (storage), and one
weak coupling layer (DW). Above layer12, a set of tunneloxide and fixed magnetic layer is connected, and actswith layer12 as a magnetic tunneling junction (MTJ)16)-

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

INDEX

Fig. 1 (a) Illustration of vertical DW motion memory with artificial ferromagnets. Left panel: Memory array withperpendicularly arranged word line and bit line. The cylinders inside array are the multi-bit storage memory cells
constructed with artificial ferromagnets. To operate a specific cylinder (cell), we can use the word line and bit line
select transistors in the peripheral circuit to select the desired cell. Right panel: Detailed structure of one memory
cell. (b) Data-writing scheme and (c) Data-reading scheme of the proposed memory. In (b) and (c), the numbers
labeled in the left indicate layer numbers from 1 to 12, and the numbers labeled in the right of magnetic wires,next to strong coupling layers (the green layers), are the bit logic defined by magnetization of layers.
18). With MTJ, the logic bit performed by magnetizationof layer12 can be read.
Data-writing scheme is shown in Fig. 1(b). At initialstate, all layers are magnetized toward -z direction. Here,
we defined -z magnetization as logic ‘0’, and +z
magnetization as logic ‘1’. To write bit1 ‘1’ into magnetic
wire, a current pulse is injected along x-direction into theheavy metal wire (word line). Because of the heavy
metal/ferromagnet interface, a z-direction spin current isthen induced and injected into magnetic wire, which canbe referred to as spin Hall effect19). The injected spincurrent results in spin-orbit torque (SOT) inside
ferromagnetic layers, and thus switches layer1 andlayer2 toward +z direction. This switching process of SOT
had been widely studied in magnetic memories19)-21).
When layer1 and layer2 switched, the weak couplinglayer3 performs like a DW in the artificial ferromagnet
as shown in Fig. 1(b). After writing, write shift process isneeded to move bit1 to other storage layer. In this process,-z-direction current pulses (J) are injected into magnetic
wire and drive DW upward with spin transfer torque(STT)22). As bit1 reached the storage layer (layer8 shownin Fig. 1(b)), the weak coupling layer - layer9, performs
as a new DW. To write bit2 ‘0’ into magnetic wire, anegative current pulse is injected along x-direction into
the heavy metal wire, and switched layer2 downward
again. After the writing of bit2, another DW in layer3 isnucleated, and another write shift process will be
executed to move bit2 to the storage layer. Data reading
scheme is shown in Fig. 1(c). Similar to the write shift
process, -z-direction current pulses are injected to drive
DW, and shift the program bit to layer12 for reading by
MTJ. Here, we assume that bit2 had already be shiftedto layer4, and thus bit1 was shifted to layer10, at initialstate. To read bit1, a current pulse is needed to shift bit1
to layer12, and logic ‘1’ inside layer12 can be read.
Likewise, as more pulses are injected, bit2 can also be
shifted to layer12, and the logic ‘0’ of bit2 can be read.

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

7

INDEX

Fig. 2 (a) The z-axis magnetization of 12 layers with weak coupling layers Aex = 1 pJ/m and 10 pJ/m aftermagnetization relaxation. The insets in upper panel illustrate the magnetization of layers near DW layer. The DW
layers are colored with red, while the inset connected with layer5 in the case of Aex = 1 pJ/m shows themagnetization of three magnetic cells inside layer5. (b) DW widths counted with layers and (c) Jc needed to drive
the program bit from layer5 to layer7, as a function of Aex of weak coupling layers. The inset of (c) illustrates z-axis
magnetization change from layer4 to layer8 as a function of time in the case of weak coupling layers Aex = 2 pJ/m.
A 10 ns, J = Jc = 3 × 1010 A/m2 current pulse is injected from 1 ns (yellow area), and cause the switching of layer5,
layer6, and layer7.
The proposed scheme suggests that DW position canalways be controlled in the weak coupling layers and theprogram bits are carried only by the strong couplinglayers. By using this structure, we can effectively control
DW position and achieve high storage density inmagnetic wire. It should be noticed that the data-reading
scheme of this memory is destructive, in which thestorage bits disappear after the reading process.
Therefore, a write-after-read architecture23), or wellpositioned reading heads (MTJ) is suggested for theactual application. Here, we focus on the feasibility of the
proposed structure by using micromagnetic analysis.
3 Micromagnetic analysis
3.1 Parameters setting
To verify the feasibility of vertical DW motion memory,
micromagnetic simulations were performed in Mumax3
3.10, a GPU-accelerated simulation program24). In our
simulation, 12 layers in a vertical magnetic wire wereconstructed, as introduced in Fig. 1. The magnetic wireof artificial ferromagnet is a cylinder with 20 nmdiameter and the thickness of each layer is 3 nm. The sizeof magnetic cells is defined as a 1 nm × 1 nm × 1 nm
cube. Therefore, 3 cells are included inside one layer

8along z-axis direction. The Aex and Ku of each layer usedin this work are summarized in table 1. Layer1 is with
Ku = 107 J/m3, and Aex =10 pJ/m as a pinning layer. Even
layers from layer2 to layer12 are strong coupling layers,
with Ku = 106 J/m3 and Aex = 10 pJ/m, based on thereference25). Odd layers from layer3 to layer11 are weakcoupling layers without PMA, in which Ku = 0 J/m3, andAex with 0-10 pJ/m are assigned. The Aex between strong
and weak coupling layers is calculated by the harmonicmeans of those of the strong and weak coupling layers24).
Saturation magnetization (Ms) and Gilbert damping
constant (α) are 8×105 A/m and 0.01, respectively25). The
initial magnetization from layer1 to layer4 are set with+z, while layer6 to layer12 are set with -z. DW is assigned
in layer5. After the setting, magnetization relaxation wasthen executed to see if DW could be controlled in weakcoupling layer in steady state.
3.2 Domain wall position and thickness
The magnetization of each layer with weak couplinglayers Aex = 1 pJ/m and 10 pJ/m after magnetization
relaxation are shown in Fig. 2(a). To derive DW width,
we defined DW as the layers with z-axis reduced
magnetization (Mz/Ms) ranged from -0.75 to 0.75, as the

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

INDEX

yellow area labeled in Fig. 2(a). In the case of Aex = 1 pJ/m,
DW is limited only at layer5 after relaxation, whichindicates that it is possible to control DW position within
weak coupling layers. Besides, in the case of Aex = 10
pJ/m, DW width is enlarged to 3 layers from layer4 tolayer6. These results suggest that DW width can becontrolled by assigning different Aex of weak couplinglayers. Since DW width Δ can be expressed as Δ ∝ �Aex8),
it is expected that higher Aex results in the larger DW
width. The correlation of DW width and the Aex of weakcoupling layers is exhibited in Fig. 2(b). If the Aex of weakcoupling layers is optimized to smaller than 3 pJ/m, DW
width can be controlled only inside one layer. The
narrower DW width promises that more storage unit canbe stacked in memory cells under the same aspect ratio,
which indicates higher storage density of one memory
cell can be achieved under the same process limitation.

2(c) shows the Jc as a function of the Aex of weak couplinglayers. It can be noticed that a prominent drop of Jc
occurs when Aex increases from 1 pJ/m to 2 pJ/m. As Aex
increases to larger than 2 pJ/m, Jc can be reduced down
to 2 × 1010 A/m2, and shows almost no Aex dependence
from 2 to 10 pJ/m. The results above suggest that, by
optimizing Aex and Ku of the bilayers in artificial
ferromagnet, for example, with the given parameters inour simulations with Aex of weak coupling layers from 2
to 3 pJ/m, it is promising to obtain narrow DW width,
controllable DW position, and also low current driven
properties simultaneously.

Table 1 Aex and Ku of 12 layers used in this work.
Layer Name
Pinninglayer
Strong coupling
layer
Weak coupling
layer

Layer Number

Aex

Ku

(pJ/m)(J/m3)

1

10

107

2, 4, 6, 8, 10, 12

10

106

3, 5, 7, 9, 11

0-10

0

3.3 Critical current density study
Critical current density Jc needed to drive DW motion
are also studied. In this research, Jc is defined as thelowest current density for driving DW from layer5 tolayer7 under a 10 ns-long current pulse. To verify Jc,
firstly, DW was assigned in layer5, and magnetization
relaxation was executed. After relaxation, Mz/Ms of eachlayer was then measured from 0 ns. At the time t = 1 ns,
a 10 ns current pulse was injected into magnetic wire
along -z-direction, as exhibited in reading scheme shownin Fig. 1(c). When the current pulse injection finished at
t = 11 ns, we examined whether Mz/Ms of layer5 andlayer6 can be switched to larger than 0.75. The lowest
current density that can drive the switching was thenextracted as Jc. The non-adiabaticity of STT22),24) is set aszero, and only the adiabatic torque22) is considered in our
analysis. The Mz/Ms dynamics from layer4 to layer8 as afunction of time in the case of Aex = 2 pJ/m under a 10 ns
current pulse with J = Jc = 3 × 1010 A/m2 is shown in theinset of Fig. 2(c). At the beginning, Mz/Ms of layer5 wasaround 0, and performed as a DW. Layer6 and layer7
were magnetized downward. When the current pulse wasinjected at 1 ns (see the yellow area), layer5, layer6, andlayer7 started to switch upward. At t = 9 ns, the Mz/Ms oflayer5 and layer6 were all larger than 0.75, which meansthat layer5 and layer6 are switched by the current pulse.
At the meanwhile, Mz/Ms of layer7 reached around 0, andbecame a new DW. With a current pulse with J = Jc, DW
can be successfully shifted from layer5 to layer7. Figure

Fig. 3 (a) Illustration of the cells from layer4 to layer6in the simulation of this work. The icons labeled in
the left are the name of cells. The arrows inside thecells are magnetization after relaxation. DW is
assigned in the three cells of layer5. (b) Timedependent dynamics of Mz/Ms and (c) Mx/Ms of thecells from layer4 to layer6 in the case of Aex = 2 pJ/m
under J = Jc = 3 ×1010 A/m2. The gray dash line andthe yellow area labeled in (b)(c) indicates the timecurrent pulse was injected and time interval thatlayer5 and layer6 switched.
3.4 Discussions
To specify the dynamics of DW motion in artificial
ferromagnet-based magnetic wire, we firstly study
switching behaviors of the cells from layer4 to layer6. In
our simulations, the thickness of each layer is 3 nm andthe size of micromagnetic cell is a 1 nm-sized cube.
Therefore, for each layer, 3 cells along z-axis are included,
as labeled with a, b, c of every layers shown in Fig. 3(a).
In this analysis, DW was initially assigned in layer5, andmagnetization relaxation was then executed. Current
pulse was injected at t = 1 ns, like the measurement used
to study Jc. Reduced magnetization along z-axis and x-

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

9

INDEX

axis (Mx/Ms) of the cells from layer4 to layer6 in the caseof weak coupling layers Aex = 2 pJ/m under J = Jc =3 × 1010 A/m2 correlated with time are shown in Figs. 3(b)and 3(c). Here, we should notice that the magnetizationof each cell shown in Fig. 3 is the average magnetizationof the cells in its xy plane. For example, themagnetization of cell 5-b indicates the averagemagnetization of the cells in cell 5-b plane. From Fig. 3(b),when current pulse was injected at t = 1 ns (see the yellowarea), the cells of layer5 and layer6 started to switch
upward. At t = 9 ns, all of the cells in layer5 and layer6
magnetized toward +z, and the switching process
finished. The magnetization precession in the xy plane ofcell 5-a, 5-b, and 5-c can be observed from the Mx/Ms
shown in Fig. 3(c). When current pulse was injected, thecells started to precess. As current induced STT became
large enough to overcome the damping torque22), allmagnetization of the cells switched upward. The
switching can be figured out as a DW depinning
process25). Therefore, we can conclude that, if Aex of weakcoupling layers is sufficiently large (> 2 pJ/m), DW
motion memory based on the artificial ferromagnet canbe attained.

Fig. 4 Magnetization distribution of cells in cell 5-b
plane in the case of (a) Aex = 2 pJ/m and (b) Aex = 0.5
pJ/m after magnetization relaxation and without
current injection. XY coordinate indicates the
position of each cell in cell 5-b plane since the xy
cross-section of our device is a circle with 20 nmdiameter.
The abrupt Jc drop as Aex of weak coupling layers
increase from 1 pJ/m to 2 pJ/m shown in Fig. 2(c) is thephenomenon beyond our comprehension. To understandthe underlying physics, we study magnetization
distribution of cell 5-b plane in the DW layer - layer5, indifferent Aex cases. The magnetization vector maps of thecell 5-b plane after magnetization relaxation in the caseof Aex = 2 pJ/m (Jc = 3 × 1010 A/m2) and Aex = 0.5 pJ/m
(Jc = 1.6 × 1012 A/m2) are shown in Fig. 4. Since the cells
in cell 5-b plane are in the center of layer5 along z-axis,
magnetization of cells in cell 5-b plane always direct
perpendicularly to z-axis, as illustrated in Fig. 3(a).
Hence, the z-axis magnetization can be neglected. In Fig.
4(a), it is exhibited that, at Aex = 2 pJ/m, themagnetization of cells in cell 5-b plane performs as asingle domain structure26). We can infer that STT acts

10

only toward one direction as current pulse is injected.
The STT in this case is quite efficient and small current
injection is enough to drive DW. Therefore, small Jc canbe attained. On the other hand, if Aex of weak couplinglayers is too small, like the Aex = 0.5 pJ/m case shown in
Fig. 4(b), the magnetization of cells in DW layer perform
as a vortex structure27),28). In this case, STT is cancelled
out in DW layer. The switching process could be achieved
only if injected current is sufficiently large to break thesymmetry of magnetization. Therefore, we can conclude
that the abrupt Jc drop from Aex = 1 pJ/m to 2 pJ/m shownin Fig. 2(c) is resulted from the transition ofmagnetization in DW layer from vortex into single
domain structure because of sufficiently large intra-layer
exchange coupling of weak coupling layers. Besides, as
Aex increases from 2 to 10 pJ/m, since single domain
structure in DW layer is already achieved, no apparent
dependence between Jc and Aex can be observed.
4. Conclusion
In summary, we proposed a new structure of vertical
DW motion memory with artificial ferromagnet thatcomposed of periodic bilayers with different exchange
stiffness constants Aex and uniaxial magnetic anisotropy
energy constants Ku in this research. Based on the
structure, we can simply manipulate DW position within
the weak coupling layers and also minimize DW width bytuning Aex and Ku of the individual layer. Furthermore,
micromagnetic analysis suggests that Aex larger than 2
pJ/m in weak coupling layers can effectively reduce
critical current density Jc down to 2 × 1010 A/m2, which
can be explained by the transition of magnetization in
DW layer from vortex into single domain structure
because sufficiently large intra-layer exchange couplingof weak coupling layers are achieved.
The artificial ferromagnet-based structure proposed inour research provides several advantages compared withconventional DW motion memories2)-7). First, to precisely
control DW position, what we should do in this structure
is to fabricate appropriate periodical bilayers with simple
film deposition instead of complicated processes formaking pinning sites11)-13). This suggests high feasibilityof commercialization. Second, since the artificial
ferromagnet is composed of bilayers with different
magnetic properties, the parameters of weak and strong
coupling layers can be adjusted separately, which meansthat we can optimize the layers for program bit and DW
according to their own device requirements. Therefore, it
is simple to narrow the DW width by tuning theparameters in weak coupling layers without affecting theproperties of strong coupling layers. To select appropriatematerials for the artificial ferromagnet, one can choose
the traditional ferromagnet, such as Co, or Ni, as strong
coupling layers. Weak coupling layers can be fabricatedwith the alloys of ferromagnet and non-magnetic metals,
for example, CoPt, or CoCu, and the DW properties canbe tuned by adjusting the atomic percentage of alloys. It

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

INDEXis much simpler to optimize total performance of device
on this structure than on traditional ones. Third, theproposed structure shows prominently low current
driven properties as sufficiently high Aex of weakcoupling layers can be achieved. These evidences indicatethat artificial ferromagnet-based structure is prospective
to achieve low power consumption, precisely controllable,high storage density DW motion memory, andfurthermore, as a promising candidate to speed up thecommercialization of DW motion memory.
Acknowledgements This work was partly supported by
JSPS KAKENHI (Grant numbers JP15H05702,
JP18K19021, JP18H01859, JP17H04924, JP19K21972,
JP20H00332, JP20K15161, and 18J22219), andCollaborative Research Program of the Institute for
Chemical Research, Kyoto University.
References
1) T. Ono, H. Miyajima, K. Shigeto, K. Mibu, N. Hosoito and T.
Shinjo, Science, 284, 468 (1999).

2) S. Parkin, M. Hayashi, and L. Thomas, Science, 320, 190(2008).

Lett., 72, 1116 (1998).

12) H. Tanigawa, K. Kondou, T. Koyama, K. Nakano, S. Kasai,
N. Ohshima1, S. Fukami, N. Ishiwata, and T. Ono, Appl. Phys.

Express, 1, 011301 (2008).

13) T. Koyama, G. Yamada, H. Tanigawa, S. Kasai, N. Ohshima,
S. Fukami, N. Ishiwata, Y. Nakatani, T. Ono, Appl. Phys.

Express, 1, 101303 (2008).

14) D. Ravelosona, S. Mangin, J. A. Katine, Eric E. Fullerton,and B. D. Terris, Appl. Phys. Lett., 90, 072508 (2007).

15) Z. Meng, S. He, L. Huang, J. Qiu, T. Zhou, C. Panagopoulos,
G. Han, and K.-L. Teo, Appl. Phys. Lett., 109, 142403 (2016).

16) N. Nishimura, T. Hirai, A. Koganei, T. Ikeda, K. Okano, Y.
Sekiguchi, and Y. Osada, J. Appl. Phys., 91, 5246 (2002).

17) S. Ikeda, J. Hayakawa, Y. M. Lee, F. Matsukura, Y. Ohno, T.

Hanyu, and H. Ohno, IEEE Trans. Electron. Devices, 54, 991(2007).

18) S. Ikeda, K. Miura, H. Yamamoto, K. Mizunuma, H. D. Gan,
M. Endo, S. Kanai, J. Hayakawa, F. Matsukura, and H. Ohno,Nat. Mater., 9, 721 (2010).

19) L. Lu, O. J. Lee, T. J. Gundmundsen, D. C. Ralph, and A.
Buhrman, Phys. Rev. Lett., 109, 096602 (2012).

20) S. Fukami, T. Anekawa, C. Zhang, and H. Ohno, Nat.

Nanotechol., 11, 621 (2016).

21) T. Moriyama, W. Zhou, T. Seki, K. Takanashi, and T. Ono,

3) S. Parkin, and S.-H. Yang, Nat. Nanotechnol., 10, 195 (2015).

Phys. Rev. Lett., 121, 167202 (2018).

C. Chappert, IEEE Trans. Circuits Syst., 60, 1469 (2013).

(2012).

3, 389 (2018).

Witowski, Y.T.Lii, P.Chu, and S. J. Gillespie, Thin Solid Films,

4) H.-P. Trinh, W. Zhao, J.-O. Klein, Y. Zhang, D. Ravelsona, and

5) D. Bang, P. V. Thach, and H. Awano, J. Sci. Adv. Mater. Dev.,

6) Y. Zhang, X. Zhang, J. Hu, J. Nan, Z. Zheng, Z. Zhang, Y.

Zhang, N. Vernier, D. Ravelosona, and W. Zhao, Sci. Rep., 6,35062 (2016).

7) W. S. Zhao, Y. Zhang, H.-P. Trinh, J.-O. Klein, C. Chappert,
R. Mantovan, A. Lamperti, R. P. Cowburn, T. Trypiniotis, M.
Klaui, J. Heinen, B. Ocker, and D. Ravelosona, Magnetic

domain-wall racetrack memory for high density and fast data
storage (IEEE, 2012).
8) P. Chureemart, R. F. L. Evans, and R. W. Chantrell, Phys.
Rev. B, 83, 184416 (2011).
9) L. Thomas, M. G. Samant, and S. S. P. Parkin, Phys. Rev.
Lett., 84, 1816 (2000).
10) D. Atkinson, D. A. Allwood, C. C. Faulkner, G. Xiong, M. D.
Cooke, and R. P. Cowburn, IEEE T. Magn., 39, 2663 (2003).

11) T. Ono, H. Miyajima, K. Shigeto and T. Shinjo, Appl. Phys.

22) A. Brataas, A. D. Kent, and H. Ohno, Nat. Mater., 11, 372

23) R. E. Jones Jr., P. D. Maniar, R. Moazzami, P. Zurcher, J. Z.
270, 580, (1995).

24) A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F.

Garcia-Sanchez, and B. V. Waeyenberge, AIP Adv., 4, 107133(2014).

25) C. Yoshida, T. Tanaka, T. Ataka, and A. Furuya, IEEE T.

Magn., 55, 3401105 (2019).

26) J. Shibata, G. Tatara, and H. Kohno, J. Phys. D: Appl. Phys.,

44, 384004 (2011).

27) C. L. Dennis, R. P. Borges, L. D. Buda, U. Ebels, J. F. Gregg,
M. Hehn, E. Jouguelet, K. Ounadjela, I. Petej, I. L. Prejbeanu,
and M. J. Thornton, J. Phys.: Condens. Mater., 14, 1175 (2002).

28) T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono,

Science, 289, 930 (2000).

Received Aug. 20, 2020; Accepted Sep. 25, 2020

Journal of the Magnetics Society of Japan Vol.45, No.1, 2021

11

INDEX

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
K. ThamS. YamadaT. Yamamoto

T. Kimura
T. Morita
D. Oyama
T. Shima
K. Yamazaki

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. SatoT. Tanaka

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

Notice for Photocopying
If you wish to photocopy any work of this publication, you have to get permission from the following organization to which licensing of copyright clearance is delegated by the copyright owner.
〈All users except those in USA〉
〈Users in USA〉
Japan Academic Association for Copyright Clearance, Inc.（JAACC）
Copyright Clearance Center, Inc.
6–41 Akasaka 9-chome, Minato-ku, Tokyo 107–0052 Japan
222 Rosewood Drive, Danvers, MA01923 USA
Phone 81–3–3475–5618 FAX 81–3–3475–5619 E-mail: info@jaacc.jp
Phone 1–978–750–8400 FAX 1–978–646–8600

編 集 委 員・論 文 委 員
小 野 輝 男 （理事） 加 藤 剛 志 （理事）
磯上慎二
小瀬木淳一
小山大介
小田洋平
後藤博樹
笹山瑛由
THAM KIMKONG
直江正幸
槙
智仁
室賀
翔
森田
孝
安達信泰
桑波田晃弘
土井達也
薮上
信

伊藤啓太
佐藤
拓
土井正晶
吉村
哲

乾
成里
末綱倫浩
仲村泰明
脇谷尚樹

小 池 邦 博 （幹事） 谷 山 智 康 （幹事） 小 林 宏 一 郎 （幹事）
鎌田清孝
菊池弘昭
木村
崇
窪田崇秀
神田哲典
古門聡士
佐藤
岳
嶋
敏之
白土
優
関口康爾
田倉哲也
中山英俊
長浜太郎
成田正敬
長谷川 崇
PHAM NAMHAI
山崎慶太
山田晋也
山本崇史
稲葉信幸
清野智史
西島健一

大竹
充
田河育也
野崎友大

加藤宏朗
竹澤昌晃
日置恵子

加藤和夫
田島克文
別所和宏

金井
靖
田中哲郎
本多周太

神原陽一
角田匡清
増田啓介

複写をされる方へ
当学会は下記協会に複写複製および転載複製に係る権利委託をしています．当該利用をご希望の方は，学術著作権協会（https://www.jaacc.org/）が提供している複製利用許諾システムもしくは転載許諾システムを通じて申請ください．ただし，本誌掲載記
事の執筆者が転載利用の申請をされる場合には，当学会に直接お問い合わせください．当学会に直接ご申請いただくことで無償で転載利用いただくことが可能です．
権利委託先：一般社団法人学術著作権協会〒107‒0052 東京都港区赤坂9‒6‒41 乃木坂ビル
電話（03）3475‒5618 FAX（03）3475‒5619 E-mail: info@jaacc.jp

本誌掲載記事の無断転載を禁じます．

Journal of the Magnetics Society of Japan
Vol. 45 No. 1 (通巻第 313号) 2021年1月1日発行

Vol. 45 No. 1 Published Jan. 1, 2021
by the Magnetics Society of JapanTokyo YWCA building Rm207, 1–8–11 Kanda surugadai, Chiyoda-ku, Tokyo 101–0062
Tel. +81–3–5281–0106
Fax. +81–3–5281–0107
Printed by JP Corporation Co., Ltd.
Sports Plaza building 401, 2–4–3, Shinkamata Ota-ku, Tokyo 144–0054
Advertising agency: Kagaku Gijutsu-sha

発行：（公社）日本磁気学会

101‒0062 東京都千代田区神田駿河台 1‒8‒11

東京YWCA会館 207 号室

製作：ジェイピーシー 144‒0054 東京都大田区新蒲田 2‒4‒3 スポーツプラザビル401 Tel.（03 ）6715‒7915
広告取扱い：科学技術社

Copyright

111‒0052 東京都台東区柳橋 2‒10‒8Ⓒ 2021 by the Magnetics Society of Japan

武田ビル 4F

Tel.（03 ）5809‒1132