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ISSN 2432-0250

Vol.47 No.1
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2023

Magnetic Recording
Comparison of Shingled Heat-Assisted Magnetic Recording and Three-Dimensional Heat-Assisted Magnetic
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
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Recording

T. Kobayashi, Y. Nakatani, and Y. Fujiwara…1

Thin Films, Fine Particles, Multilayers, Superlattices
Synthesis and Analyses of Acicular Spinel Iron Oxide Particles with Core-Shell Structure Containing Manganese
Ferrite and Magnetite

Spintronics

S. Yamada, M. Kishimoto, and H. Yanagihara…15

Current-Induced Helicity Switching of Frustrated Skyrmions on a Square-Grid Obstacle Pattern
X. Zhang, J. Xia, O. A. Tretiakov, H. T. Diep, G. Zhao, J. Yang, Y. Zhou, M. Ezawa, and X. Liu

…20

47

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

1

2023

INDEX

Journal of the Magnetics Society of Japan
Vol. 47, No. 1
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Magnetic Recording
Comparison of Shingled Heat-Assisted Magnetic Recording and Three-Dimensional Heat-Assisted Magnetic
Recording……………………………………………………………………T. Kobayashi, Y. Nakatani, and Y. Fujiwara

1

Thin Films, Fine Particles, Multilayers, Superlattices
Synthesis and Analyses of Acicular Spinel Iron Oxide Particles with Core-Shell Structure Containing
Manganese Ferrite and Magnetite………………………………………………………………… S. Yamada, M. Kishimoto, and H. Yanagihara

15

Spintronics
Current-Induced Helicity Switching of Frustrated Skyrmions on a Square-Grid Obstacle Pattern……… X. Zhang, J. Xia, O. A. Tretiakov, H. T. Diep, G. Zhao, J. Yang, Y. Zhou, M. Ezawa, and X. Liu

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INDEX

Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
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J. Magn. Soc. Jpn., 47, 1-14 (2023)<Paper>C o m p a r is o n o f S h in g le d H e a t - A s s is t e d M a g n e t ic R e c o r d in g
a n d T h r e e - D im e n s io n a l H e a t - A s s is t e d M a g n e t ic R e c o r d in g
T. Kobayashi, Y. Nakatani*, and Y. Fujiwara

Graduate School of Engineering, Mie Univ., 1577 Kurimamachiya-cho, Tsu 514-8507, Japan*Graduate School of Informatics and Engineering, Univ. of Electro-Communications,

1-5-1 Chofugaoka, Chofu 182-8585, Japan

In this work we examine grain arrangement and medium structure, temperature profile during writing, adjacent
track interference, information stability during 10 years of archiving, information stability in a high Curie temperature(HC) layer during writing in a low Curie temperature (LC) layer, and writing sensitivity on 4 Tbpsi shingled heatassisted magnetic recording (HAMR) with a bit aspect ratio of 1.5 and 2 Tbpsi/layer (total density of 4 Tbpsi) threedimensional (3D) HAMR with bit aspect ratios of 1.0 and 2.0. A small bit aspect ratio is preferable in 3D HAMR. The
grain aspect ratios for both HAMR and 3D HAMR may be too large when it comes to manufacturing the recording
layer. The low Curie temperature of the LC layer may be disadvantageous with respect to the writing property. The
readout field is small for both the LC and HC layers in 3D HAMR. The writing sensitivity for HAMR is worse thanthat for 3D HAMR because the statistical factor is affected by the readout grain number and erasure-after-write isaffected by the grain column number. Although both HAMR and 3D HAMR have disadvantages, the poor writing
sensitivity in HAMR is a serious problem.
Key words: 3D HAMR, temperature profile, ATI, 10 years of archiving, LC writing, writing sensitivity, bit aspect ratio
1. Introduction

Heat-assisted magnetic recording (HAMR) has
potential as a next-generation magnetic recording
method with a high recording capacity. HAMR is arecording technique in which the medium is heated toreduce coercivity during the writing period. Threedimensional HAMR (3D HAMR) has been proposed1)
where the medium consists of a high mean Curie
temperature 𝑇𝑇!" (HC) layer with a grain height ℎ!" , alow mean Curie temperature 𝑇𝑇#" (LC) layer with agrain height ℎ#" , and an isolation layer inserted
between the two layers to suppress exchange coupling
between them. With 3D HAMR, once data have been
written in the HC layer (HC writing), other data can be
written in the LC layer (LC writing) by employing lower
temperature heating. Yamane et al. reported a dual
structure, namely 3D HAMR on bit patterned media2).
We have previously discussed the medium layer
structure in 3D HAMR on granular media3), andadjacent track interference in HAMR4). Our research has
led us to believe that the upper LC / lower HC layer
structure is preferable if the problem of heat resistancecan be solved.
It is important to establish whether or not 3D HAMR
has an advantage over conventional HAMR. In thispaper, we compared 4 Tbpsi shingled HAMR with 2
Tbpsi/layer (total density of 4 Tbpsi) 3D LC / HC HAMR,
since 3D HAMR must be combined with shingled
magnetic recording because of the large adjacent track
interference in the LC layer during HC writing.
We must comprehensively consider all the factors
Corresponding author: T. Kobayashi (e-mail: kobayasi@phen.mie-u.ac.jp).

when comparing shingled HAMR and 3D HAMR.
Therefore, we examine
1.1 grain arrangement and medium structure,
1.2 temperature profile during writing,
1.3 adjacent track interference,
1.4 information stability during 10 years of archiving,
1.5 information stability in the HC layer during LC
writing, and
1.6 writing sensitivity
on 4 Tbpsi shingled HAMR ( 3 × 2 = 6 grains/bit) in
section 3.1, 2 Tbpsi/layer 3D HAMR ( 3 × 3 = 9
grains/bit) in 3.2, and 2 Tbpsi/layer 3D HAMR (4 × 2 =8 grains/bit) in 3.3, where one bit has 𝑚𝑚 grains in the
cross-track direction and 𝑛𝑛 grains in the down-track
direction, i.e., there are 𝑚𝑚 × 𝑛𝑛 grains/bit.
2. Calculation Method and Conditions

2.1 Magnetic properties
The temperature dependence of the medium
magnetization 𝑀𝑀$ was calculated by employing mean
field analysis5), and that of the medium anisotropy
constant 𝐾𝐾% was assumed to be proportional to 𝑀𝑀$& 6).
𝑀𝑀$ (𝑇𝑇' , 𝑇𝑇) is a function of the Curie temperature 𝑇𝑇' andtemperature 𝑇𝑇. 𝑀𝑀$ (𝑇𝑇' = 770 K, 𝑇𝑇 = 300 K) = 1000 emu/cm3 was assumed for FePt, which is a potential HAMR
medium material thanks to its large 𝐾𝐾% and relatively
low 𝑇𝑇' . Based on this assumption, the 𝑀𝑀$ value can becalculated for all values of 𝑇𝑇' and 𝑇𝑇.
We have introduced an HAMR medium parameter,
namely, the medium anisotropy constant ratio 𝐾𝐾% /𝐾𝐾(%)* 7) in place of 𝐾𝐾% , since the 𝐾𝐾% value at the storage
temperature is a function of 𝑇𝑇' , which is strongly related
to the writing property. 𝐾𝐾% /𝐾𝐾(%)* is the intrinsic ratio of
the medium 𝐾𝐾% to bulk FePt 𝐾𝐾% , which is independentof 𝑇𝑇' , and is valid for any temperature from zero Kelvin

Journal of the Magnetics Society of Japan Vol.47, No.1, 2023

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to the Curie temperature.
The 𝐾𝐾% (𝑇𝑇' , 𝐾𝐾% /𝐾𝐾(%)* , 𝑇𝑇) value is a function of 𝑇𝑇' , 𝐾𝐾% /𝐾𝐾(%)* , and 𝑇𝑇 . 𝐾𝐾% (𝑇𝑇' = 770 K, 𝐾𝐾% /𝐾𝐾(%)* = 1, 𝑇𝑇 = 300 K) =70 Merg/cm3 was assumed for bulk FePt. Using thisassumption, the 𝐾𝐾% value can be calculated for all
values of 𝑇𝑇' , 𝐾𝐾% /𝐾𝐾(%)* , and 𝑇𝑇. No intrinsic distributionof 𝐾𝐾% was assumed. However, there was a fluctuation in
𝐾𝐾% caused by 𝑇𝑇' variation.
The 𝑇𝑇' value can be adjusted by changing the Cu
composition 𝑧𝑧 for (Fe+.- Pt +.- )./0 Cu0 .

2.2 Temperature profile
The thermal gradient during the writing period can be
adjusted by changing the medium structure for HAMR.
For simplicity, the thermal gradients 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 8, 10,
and 12 K/nm in the cross-track direction and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 0
in the down-track direction were assumed to be constantwhen we examined adjacent track interference. The
𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 8, 10, and 12 K/nm and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 0 wereassumed to be constant when we examined writing
sensitivity.
On the other hand, for 3D HAMR, since there is acorrelation between the thermal gradients in the upperand lower layers, we used a previously publishedtemperature profile8), in which a heat transfer
simulation was carried out using Poynting for Optics
software (Fujitsu Ltd.). The light spot diameter was
about 9.0 nm (FWHM) in the down-track and cross-track
directions. The linear velocity was 10 m/s. The ambientis the maximum working
temperature 𝑇𝑇12(
temperature of the hard disk drive, and was assumed tobe 330 K.
We also focused on the medium surface temperature
𝑇𝑇$%34 at the track center during HC writing, and thelayer temperature difference Δ𝑇𝑇!# between the HC andLC layers at the track edges during LC writing.
2.3 Information stability
We assumed the medium to be granular. One bit has
𝑚𝑚 grains in the cross-track (row 𝑖𝑖 ) direction and 𝑛𝑛
grains in the down-track (column 𝑗𝑗) direction, i.e., there
are 𝑚𝑚 × 𝑛𝑛 grains/bit.
The information stability was estimated using thegrain error probability 𝑃𝑃9),56

𝑃𝑃 = 1 − exp G−𝑓𝑓+ 𝑡𝑡 exp J− !"## K1 +(|𝐻𝐻: | < 𝐻𝐻*;44 )

78

9$

9%"##

&

M NO, (1)taking account of the shape anisotropy 𝑀𝑀$ 𝐻𝐻< /2 using aself-demagnetizing field 𝐻𝐻< , where 𝑓𝑓+ , 𝑡𝑡, 𝐾𝐾%;44 , 𝑉𝑉, 𝑘𝑘, 𝑇𝑇,
and 𝐻𝐻: are, respectively, the attempt frequency10), time,effective anisotropy constant, grain volume, Boltzmann
constant, grain temperature, and writing field. The 𝑓𝑓+
value is a function of the Gilbert damping constant 𝛼𝛼10).
The 𝛼𝛼 value used here was 0.1 without temperaturedependence, since the 𝛼𝛼 value and its temperaturedependence for FePt near the Curie temperature are not
𝐻𝐻< =currently
known.
𝐾𝐾%;44 = 𝐾𝐾% − 𝑀𝑀$ 𝐻𝐻< /2,
2

8𝑀𝑀$ arctan (𝐷𝐷& /(ℎ√2𝐷𝐷& + ℎ& )), 𝑉𝑉 = 𝐷𝐷 × 𝐷𝐷 × ℎ where 𝐷𝐷
and ℎ are the grain size and height, respectively.
However, 𝐻𝐻< does not affect the results, as reported ina previous paper11), since 𝐾𝐾% ≫ 𝑀𝑀$ 𝐻𝐻< /2. Therefore, themagnetostatic field from surrounding grains can also be
ignored. It was assumed that there was no exchange
coupling between grains.
To evaluate the grain error distribution, we calculated
the expected value of the magnetization 𝐸𝐸[𝑀𝑀$ ],𝐸𝐸[𝑀𝑀$ ] = (1 − 𝑃𝑃)𝑀𝑀$ + 𝑃𝑃(−𝑀𝑀$ ) = (1 − 2𝑃𝑃)𝑀𝑀$ . (2)Since there is a temperature distribution in the crosstrack direction during LC writing, the 𝐸𝐸[𝑀𝑀$ ] value wasaveraged over one row of grains as
𝐸𝐸[𝑀𝑀$= ] =∑%"&'(#$%&!" )(#!" ()$!" , ,,- .)/(3)

at a readout temperature of 330 K.
The bit error rate bER was also calculated by
employing 𝑃𝑃. For example, for 4 grains/bit, the bit error
rate 4bER1 for 1 grain error is expressed as
4bER1 =

𝐸𝐸𝐸𝐸. 𝑃𝑃. (1 − 𝑃𝑃& )(1 − 𝑃𝑃> )(1 − 𝑃𝑃? ) + ∙ ∙ ∙+𝐸𝐸𝐸𝐸? (1 − 𝑃𝑃. )(1 − 𝑃𝑃& )(1 − 𝑃𝑃> )𝑃𝑃? ,(4)

the bit error rate 4bER2 for 2 grain errors as
4bER2 =

𝐸𝐸𝐸𝐸.& 𝑃𝑃. 𝑃𝑃& (1 − 𝑃𝑃> )(1 − 𝑃𝑃? ) + ∙ ∙ ∙+𝐸𝐸𝐸𝐸>? (1 − 𝑃𝑃. )(1 − 𝑃𝑃& )𝑃𝑃> 𝑃𝑃? ,(5)

the bit error rate 4bER3 for 3 grain errors as
4bER3 =

𝐸𝐸𝐸𝐸.&> 𝑃𝑃. 𝑃𝑃& 𝑃𝑃> (1 − 𝑃𝑃? ) + ∙ ∙ ∙+𝐸𝐸𝐸𝐸&>? (1 − 𝑃𝑃. )𝑃𝑃& 𝑃𝑃> 𝑃𝑃? ,(6)

and the bit error rate 4bER4 for 4 grain errors as
4bER4 =

where

𝑃𝑃. 𝑃𝑃& 𝑃𝑃> 𝑃𝑃? ,𝐸𝐸𝐸𝐸7 = 1, if

and𝐸𝐸𝐸𝐸7 = 0, if(∑!," (#!" ()$!" , ,,- .)0!"((1×/)(# ()$* , ,,- .)0*(∑!," (#!" ()$!" , ,,- .)0!"((1×/)(# ()$* , ,,- .)0*

(7)

≤ 𝐸𝐸@A , (8)> 𝐸𝐸@A , (9)where 𝑇𝑇'2 and 𝐷𝐷2 are the mean Curie temperatureand the mean grain size, respectively. Errors occur insome grains of a bit. We assumed that if the ratio of&∑=,B 𝑀𝑀$=B (𝑇𝑇'=B , 330 K)𝐷𝐷=B& to (𝑚𝑚 × 𝑛𝑛)𝑀𝑀$ (𝑇𝑇'2 , 330 K)𝐷𝐷2
isgreater than a calculation parameter named error
threshold 𝐸𝐸@A as shown in Eq. (9), the bit will be errorwhere the numerator
free, namely
𝐸𝐸𝐸𝐸7 = 0,∑=,B 𝑀𝑀$=B (𝑇𝑇'=B , 330 K)𝐷𝐷=B& is the surface magnetic charge ofthe grains that are magnetized in the recording direction,&is theand the denominator (𝑚𝑚 × 𝑛𝑛)𝑀𝑀$ (𝑇𝑇'2 , 330 K)𝐷𝐷2
total surface magnetic charge. 𝑀𝑀$=B , 𝑇𝑇'=B , and 𝐷𝐷=B are,respectively, the magnetization, the Curie temperature,and the grain size of the 𝑖𝑖𝑖𝑖-th grain. The total bit error

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rate 4bER is the summation of each bit error rate 4bERk
as follows
4bER =

Σk 4bERk.

(10)

Therefore, the bit error rate is a function of 𝐸𝐸@A . The
calculation bit number was 107. The criterion
determining whether or not information was stable wasassumed to be a bER of 10-3.
We defined the normalized readout field 𝐻𝐻+ as areadout magnetic field normalized by that from thegrains where all the grains possess 𝑇𝑇'2 and 𝐷𝐷2 , and all
the grains are magnetized in the recording direction,
which corresponds to the denominator in Eqs. (8) and (9).
Therefore, 𝐻𝐻+ can roughly be represented by 𝐸𝐸@A as(11)

𝐻𝐻+ = 2𝐸𝐸@A − 1.

For example, assuming all the grains are homogeneous,
𝐸𝐸@A equals one when the magnetization directions of all
the grains are parallel to the recording direction. The 𝐻𝐻+value becomes one. When the magnetization directionsof half the grains are parallel, and those of the other half
are antiparallel to the recording direction, 𝐸𝐸@A equals ahalf. The 𝐻𝐻+ value becomes zero. The minimum
normalized readout field, which must be readable
without error after writing in the adjacent track (ATwriting), after 10 years of archiving, and after LC
writing, can be estimated with 𝐸𝐸@A to have a bER of
10-3.
We also defined the information degradation rate 𝑅𝑅+
during 10 years of archiving as
𝑅𝑅+ =345(#-.- 789)$345(-.--# 789)
345(-.--# 789)

,

(12)

where 0.001 years corresponds to about 9 hours. For
example, the 𝑅𝑅+ values are 99, 9.0, and 0.11 when thebER(0.001 yrs) values are 10-5, 10-4, and 9 × 10-4,
respectively, since the bER(10.0 yrs) value is 10-3. The
𝑅𝑅+ value for no information degradation is less thanabout 0.1.
2.4 Field strength
The flying height was 4.0 nm, which is the distance
between the magnetic head reader and the recording
layer surface.
The magnetic field strength from the medium at thecenter of readout row 𝑚𝑚D (see Fig. 1) grains and at thereader position was calculated using 𝑚𝑚D × 30 grains
with no grain size distribution and no 𝑇𝑇' variation whencalculating the field strength.
2.5 Writing sensitivity
We examined the writing field 𝐻𝐻: dependence of thesignal to noise ratio SNR by employing a micromagnetic
calculation using the Landau-Lifshitz-Gilbert (LLG)
equation where the magnetic properties used herechange with temperature. The temperature dependence
was calculated using mean field analysis. We believethat the use of the LLG equation that includes thetemperature dependence of magnetic properties is asuitable replacement for the Landau-Lifshitz-Bloch(LLB) equation. We also examined the 𝐻𝐻: dependenceof the bER using our model calculation12), with the aimof grasping the physical implications of the writing
property in HAMR.
The 𝛼𝛼 value used here was 0.1 without temperaturedependence. The linear velocity 𝑣𝑣 was 10 m/s. For
simplicity, the thermal gradients 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of
0 were assumed to be uniformly constant. The writing
field was assumed to be spatially uniform, the direction
to be perpendicular to the medium plane, the recording
frequency to be 𝑣𝑣/(2𝐷𝐷E ), and the rise time to be zero,
where 𝐷𝐷E is the bit length. The demagnetizing field
inside the grain was included, but the magnetostatic
field from surrounding grains during writing wasneglected.
In the LLG calculation, the output signal, media noise,and media SNR were calculated using a sensitivity
function13), which is the same as the cross-track width of
the simulation region, a magnetoresistive read headwith a 15 nm shield-shield spacing, and a 4.0 nm headmedium spacing for 2 Tbpsi and 6 grains/bit shingled
HAMR with a 𝐷𝐷E of 14.7 nm4). Since the SNR value isalso affected by the resolution of the read head, wechanged the shield-shield spacing to (𝐷𝐷E /14.7) × 15 nm
for other calculations. The number of the grains for the
down-track direction was fixed at 2304. Simulation was
repeated 32 times for each condition with different grain
size distribution patterns with same averaged size anddeviation, and the averaged SNR value was obtained.
In the model calculation, the resolution of the readhead corresponds to infinity. The calculation bit number
was 106. The bER value in this paper is useful only forcomparisons such as information stability and writing
sensitivity between various media.
3. Calculation Results
3.1 4 Tbpsi shingled HAMR (𝟑𝟑 × 𝟐𝟐 = 6 grains/bit)
3.1.1 Grain arrangement and medium structure
There is a trade-off relationship between adjacent
track interference (ATI) and writing sensitivity, since
ATI means writing in the adjacent track4):(1) Grain number per bit
Reducing the grain number per bit improves ATI,
since the grain temperature can be reduced due to thelarger grain pitch.
Reducing the grain number per bit worsens thewriting sensitivity. The bER increases with decreasing
grain number, since the probability of a simultaneous
error in grains becomes statistically higher.
(2) Grain height (recording layer thickness)
Increasing the grain height ℎ improves ATI, since thethermal stability factor 𝐾𝐾%;44 𝑉𝑉/(𝑘𝑘𝑘𝑘) becomes larger due
to the larger 𝑉𝑉 = 𝐷𝐷 × 𝐷𝐷 × ℎ value.
Increasing the ℎ value worsens the writing
sensitivity for the same reason.

Journal of the Magnetics Society of Japan Vol.47, No.1, 2023

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Table 2 Temperature profile in 4 Tbpsi shingled HAMR
(3 × 2 = 6 grains/bit).

Fig.. 1 Grain arrangement and medium structure in 4
Tbpsi shingled HAMR (3 × 2 = 6 grains/bit).

Table 1 Grain and bit sizes in 4 Tbpsi shingled HAMR
(3 × 2 = 6 grains/bit).

(3) Grain aspect ratio
Furthermore, the simultaneous realization of a small
𝐷𝐷2 value, large grain aspect ratio ℎ/𝐷𝐷2 , and large
anisotropy constant appears to make it too difficult tomanufacture a recording layer.
The design of grain number per bit and grain height isaffected by above factors (1), (2), and (3). We chose agrain arrangement of 𝑚𝑚 × 𝑛𝑛 = 3 × 2 = 6 grains/bit andan ℎ value of 8.5 nm, taking account of factors (1) and(2) (see Figs. 3 and 6), respectively, as shown in Fig. 1.
Factor (3) is currently being experimentally investigatedby many researchers14,15).
The writing temperature of the grains at the edge of
the writing track was assumed to be 𝑇𝑇'2 + 2𝜎𝜎F' , taking
account of the standard deviation 𝜎𝜎F' of the mean Curie
temperature 𝑇𝑇'2 . Based on this assumption, almost all
grains in the writing track are heated to above theirCurie temperatures during the writing period.
The bER value is a function of the readout track width
after AT writing. We therefore calculated the bER andthe 𝐻𝐻+ values for readout rows 𝑚𝑚D of 1 (𝑖𝑖 = 1), 2 (𝑖𝑖 = 1
and 2), and 3 (𝑖𝑖 = 1, 2, and 3).
The grain and bit sizes are summarized in Table 1. The
𝐷𝐷2 value was determined by

4

𝐷𝐷2 = !

:

1×/

− ΔG ,(13)

where 𝑆𝑆 is the bit area for 4 Tbpsi. We assumed theintergrain spacing ΔG to be 1.0 nm regardless of therecording density and the grain number per bit. The
grain size distribution was log-normal with a standard
deviation 𝜎𝜎H /𝐷𝐷2 of 15 % for 𝐷𝐷2 . The bit aspect ratio
was 𝐷𝐷F /𝐷𝐷E = 𝑚𝑚/𝑛𝑛 where 𝐷𝐷F = 𝑚𝑚(𝐷𝐷2 + ΔG ), 𝐷𝐷E =𝑛𝑛(𝐷𝐷2 + ΔG ), and 𝐷𝐷2 + ΔG are the track width, bit length,
and grain pitch, respectively.
The large ℎ/𝐷𝐷2 value of 2.0 may make it too difficult
to manufacture the recording layer15).
3.1.2 Temperature profile
We used a 𝐾𝐾% /𝐾𝐾(%)* value of 0.8 as shown in Table 2.
When the 𝑇𝑇' value is low, the anisotropy field obtainedby the experiment does not decrease steeply toward 𝑇𝑇'
compared to that predicted by the theory16). Since thismay be disadvantageous in terms of jitter to the writing
property, a 𝑇𝑇'2 value of 750 K was used. The 𝑇𝑇'
distribution was normal with a standard deviation
𝜎𝜎F' /𝑇𝑇'2 of 2 % for 𝑇𝑇'2 . The 𝑇𝑇' variation means that thewriting time is advanced or delayed. For example, theadvanced and delayed times correspond to 𝜎𝜎F' /(𝑣𝑣 ∙𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕) for grains with 𝑇𝑇' = 𝑇𝑇'2 + 𝜎𝜎F' and 𝑇𝑇' = 𝑇𝑇'2 −𝜎𝜎F' , respectively17). Therefore, the 𝜎𝜎F' is equivalent tothe standard deviation 𝜎𝜎I of the grain position as 𝜎𝜎I =𝜎𝜎F' /(𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕). For example, 𝜎𝜎I /𝐷𝐷2 is about 30 % whenthe 𝜎𝜎F' /𝑇𝑇'2 and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 values are 2 % and 12 K/nm,
respectively. Therefore, the value of 2 % includes
𝜎𝜎F' /𝑇𝑇'2 and 𝜎𝜎I /𝐷𝐷2 .

3.1.3 Adjacent track interference
Figure 2 shows the minimum normalized readout field
𝐻𝐻+ for various numbers of readout rows 𝑚𝑚D (see Fig. 1)
after AT writing. Time 𝑡𝑡 and the writing field 𝐻𝐻: wereassumed to be 1 ns and −10 kOe, respectively.
There is no 𝐻𝐻+ greater than 0 that satisfies a bER of
10-3 for 𝑚𝑚D of 3. Therefore, the 3rd row (𝑖𝑖 = 3) grains isused as a guard band. The 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 value of more thanabout 12 K/nm is necessary to improve ATI. The
temperature at the 1st row (𝑖𝑖 = 1) is obviously lower
than that at the 2nd row (𝑖𝑖 = 2). However, when 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕equals 12 K/nm, Fig. 2 shows the 𝐻𝐻+ value for an 𝑚𝑚D of

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2 (𝑖𝑖 = 1 and 2) to be greater than that for an 𝑚𝑚D of 1 (𝑖𝑖= 1) for a statistical reason.
For an 𝑚𝑚D of 2 (𝑚𝑚D × 𝑛𝑛 = 2 × 2 = 4 grains), Fig. 3
shows the bER value as a function of 𝐸𝐸@A before andafter AT writing for various grain heights ℎ. The second
horizontal axis is the 𝐻𝐻+ value estimated using Eq. (11).

Fig. 2 Minimum normalized readout field 𝐻𝐻+ for various
numbers of readout rows 𝑚𝑚D (see Fig. 1) after adjacent
track (AT) writing in 4 Tbpsi shingled HAMR (3 × 2 = 6
grains/bit).

The bER value increases as the ℎ value decreases, since
the 𝐾𝐾%;44 𝑉𝑉/(𝑘𝑘𝑘𝑘) value becomes smaller due to thesmaller 𝑉𝑉 = 𝐷𝐷 × 𝐷𝐷 × ℎ value4). There is almost no
increase in the bER after AT writing for an ℎ of 10.5 nm.
On the other hand, a considerable increase can be seenin the bER for an ℎ of 6.5 nm.
The ATI results are summarized in Table 3 for a𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of 12 K/nm. The resultant readout grain number
𝑚𝑚D × 𝑛𝑛 and readout track width 𝐷𝐷DF are 2 × 2 and 9.4
nm, respectively. The 𝐻𝐻+ value, that must be readable
without error after AT writing, and the peak 𝑧𝑧
component 𝐻𝐻0J;1* of the readout field for an 𝑚𝑚D of 2 are
0.20 and 1197 Oe, respectively. We roughly evaluatedthe readout property using the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1*
product. The 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product is 2.3 knmOe.
3.1.4 10 years of archiving
We examined the information stability for 10 years ofarchiving with no 𝐻𝐻: . The storage temperature was 350
K. We took a certain temperature margin into account.
Figure 4 (a) shows that since 2 grains in 6 grains/bit areused as a guard band, the bER value after 10 years of(a)Fig. 3 Bit error rate as a function of error threshold 𝐸𝐸@A
and normalized readout field 𝐻𝐻+ before and after AT
writing for various grain heights ℎ in 4 Tbpsi shingled
HAMR (2 × 2 = 4 grains).
Table 3 Adjacent track interference in 4 Tbpsi shingled
HAMR (3 × 2 = 6 grains/bit).

(b)
Fig. 4 (a) Bit error rate as a function of error threshold
𝐸𝐸@A and normalized readout field 𝐻𝐻+ after 10 years ofarchiving and (b) time dependence of bit error rateduring 10 years of archiving in 4 Tbpsi shingled HAMR
(2 × 2 = 4 grains).
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Table 4 10 years of archiving in 4 Tbpsi shingled HAMR
(3 × 2 = 6 grains/bit).

archiving for 𝑚𝑚D × 𝑛𝑛 = 2 × 2 = 4 grains is higher thanthat for 𝑚𝑚 × 𝑛𝑛 = 3 × 2 = 6 grains for a statistical reason.
Table 4 shows that the 𝐻𝐻+ value for 𝑚𝑚D of 2 that must
be readable without error after 10 years of archiving is0.26, and the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product is 3.0 knmOe.
Since the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product is 2.3 knmOe for
ATI as shown in Table 3, the limiting factor is ATI.
Since the 𝐾𝐾%;44 𝑉𝑉/(𝑘𝑘𝑇𝑇) value of 152 is sufficiently large,
the 𝑅𝑅+ value is less than 0.1 as shown in Table 4.
Therefore, no information degradation can be seen
during 10 years as shown in Fig. 4 (b).
3.1.5 Writing sensitivity
For an 𝑚𝑚D of 2 (𝑚𝑚D × 𝑛𝑛 = 2 × 2 = 4 grains), Fig. 5
shows the writing field 𝐻𝐻: dependence of (a) SNR
calculated using the LLG equation and (b) bER using ourmodel for various 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 values. Our model calculation
can almost entirely explain the results of the LLG
simulation. Therefore, the physical implications of thewriting property can be grasped by employing our model.
A relatively large 𝐻𝐻: is needed to increase the SNRor to reduce the bER, which means that the writing
sensitivity is worse. Furthermore, the influence oferasure-after-write (EAW) is strongly evident in therelatively large 𝐻𝐻: region. EAW consists of grain
magnetization reversal in the opposite direction to therecording direction. This is caused by the change in thewriting field direction at the end of the writing time.
EAW thus occurs after writing. A 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 value of morethan about 12 K/nm is needed to suppress EAW17).
The 𝐻𝐻: dependence of the bER for various grainheights ℎ is shown in Fig. 6. The bER value increases
as the ℎ value increases, which means that the writing
sensitivity worsens as the ℎ value increases, since the𝐾𝐾%;44 𝑉𝑉/(𝑘𝑘𝑘𝑘) value becomes larger due to the larger 𝑉𝑉 =𝐷𝐷 × 𝐷𝐷 × ℎ value4). As regards ℎ , there is a trade-off
relationship between ATI as shown in Fig. 3 and writing
sensitivity as shown in Fig. 6, since ATI means writingin the adjacent track.
Figure 7 shows the 𝐻𝐻: dependence of the bER for 1
bit (“010” data using 2 × 2 = 4 grains) and 2 bits of data(“0110” data using 2 × 4 = 8 grains). The bER value for

6

(a)

(b)
Fig. 5 Writing field 𝐻𝐻: dependence of (a) signal to noise
ratio and (b) bit error rate for various thermal gradients𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 in 4 Tbpsi shingled HAMR (2 × 2 = 4 grains).

Fig. 6 Writing field 𝐻𝐻: dependence of bit error rate forvarious grain heights ℎ in 4 Tbpsi shingled HAMR
(2 × 2 = 4 grains).

2 bits of data is considerably smaller than that for 1 bitof data. Since the readout resolution corresponds toinfinity, the bER value is not affected by the resolutionof the read head. The reasons for the difference in bER
are the statistical factor affected by the grain number
and EAW affected by the grain column number17).

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Table 5. The (ℎ#" + ℎ!" )/𝐷𝐷2 value of 2.1 is relatively
large as well as the ℎ/𝐷𝐷2 value of 2.0 for HAMR as
shown in Table 1.
3.2.2 Temperature profile
Figures 9 (a) and (b) show the temperature profiles
calculated by employing a heat transfer simulation forthe cross-track direction during HC and LC writing,respectively.

Fig. 7 Writing field 𝐻𝐻: dependence of bit error rate for1 bit (“010” data using 2 × 2 = 4 grains) and 2 bits ofdata (“0110” data using 2 × 4 = 8 grains) in 4 Tbpsi
shingled HAMR.
3.2 2 Tbpsi/layer 3D HAMR (𝟑𝟑 × 𝟑𝟑 = 9 grains/bit)
3.2.1 Grain arrangement and medium structure
Figure 8 shows the grain arrangement and medium
structure in 2 Tbpsi/layer 3D HAMR (3 × 3 = 9
grains/bit). The grain heights were revised for the LC
and HC layers3), taking account of ATI and 10 years ofarchiving. The grain and bit sizes are summarized in

Fig.. 8 Grain arrangement and medium structure in 2
Tbpsi/layer 3D HAMR (3 × 3 = 9 grains/bit).

Table 5 Grain and bit sizes in 2 Tbpsi/layer 3D HAMR
(3 × 3 = 9 grains/bit).

(a)

(b)
Fig. 9 Temperature profile for cross-track direction
during (a) HC and (b) LC writing in 2 Tbpsi/layer 3D
HAMR (3 × 3 = 9 grains/bit).
Table 6 Temperature profile in 2 Tbpsi/layer 3D HAMR
(3 × 3 = 9 grains/bit).

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The solid lines indicate the temperatures at the layerboundaries, and the dotted lines indicate those at thelayer centers. The temperature profile results are
summarized in Table 6.
(a) HC writing
The temperature at the track edge and the HC layer
center is 𝑇𝑇!" + 2𝜎𝜎F!" = 780 K at which 𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 is 8.8
K/nm. The 𝑇𝑇$%34 value of 959 K is relatively high, since
HC is the lower layer. This is disadvantageous in termsof the heat resistance of the writing head and/or thesurface lubricant.
(b) LC writing
The temperature at the track edge and the LC layer
center is 𝑇𝑇#" + 2𝜎𝜎F#" = 676 K at which 𝜕𝜕𝑇𝑇# /𝜕𝜕𝜕𝜕 is 11.8
K/nm. The negative Δ𝑇𝑇!# value of −42 K means thatthe temperature in the HC layer is lower than that in the
LC layer, and this is advantageous in terms of
information stability in the HC layer during LC writing.
We have previously reported the thermal gradient in
3D HAMR8):(1) The thermal gradient for the upper layer isintrinsically larger than that for the lower layer due to aheat flow in the in-plane direction in the deep part of thelayer.
(2) The thermal gradient for the HC layer is intrinsicallylarger than that for the LC layer due to their respective
Curie temperatures.
Although 𝑇𝑇!" > 𝑇𝑇#" , the 𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 value of 8.8 K/nm issmaller than the 𝜕𝜕𝑇𝑇# /𝜕𝜕𝜕𝜕 value of 11.8 K/nm as shown in
Table 6, since HC is the lower layer.
The low 𝑇𝑇#" value of 650 K may be disadvantageous
as regards the HAMR writing property, since thetemperature dependence of the anisotropy field issomewhat smaller than that predicted by the theory16).
3.2.3 Adjacent track interference
The 𝐻𝐻+ value for various 𝑚𝑚D values after AT writingis shown in Fig. 10. There is no 𝐻𝐻+ greater than 0 thatsatisfies a bER of 10-3 for an 𝑚𝑚D of 3 as well as the resultfor HAMR as shown in Fig. 2. Therefore, the 3rd row (𝑖𝑖= 3) grains is used as a guard band.

Fig. 10 Minimum normalized readout field 𝐻𝐻+ forvarious numbers of readout rows 𝑚𝑚D after AT writing in
2 Tbpsi/layer 3D HAMR (3 × 3 = 9 grains/bit).

8

Fig. 11 Bit error rate as a function of error threshold 𝐸𝐸@A
and normalized readout field 𝐻𝐻+ before and after AT
writing in 2 Tbpsi/layer 3D HAMR (2 × 3 = 6 grains).

Table 7 Adjacent track interference in 2 Tbpsi/layer 3D
HAMR (3 × 3 = 9 grains/bit).

For an 𝑚𝑚D of 2 (𝑚𝑚D × 𝑛𝑛 = 2 × 3 = 6 grains), the bER
value as a function of 𝐸𝐸@A before and after AT writing for
the LC and HC layers is shown in Fig. 11. The bER value
for 3D HAMR is smaller than that for HAMR as shownin Fig. 3 for a statistical reason affected by the grain
number.
The ATI results are summarized in Table 7. The
𝑚𝑚D × 𝑛𝑛 and 𝐷𝐷DF values are 2 × 3 and 11.0 nm,
respectively. For the HC layer, although the 𝐻𝐻+ value of0.30 is relatively large, the 𝐻𝐻0J;1* value of 401 Oe issmall due to the lower layer. The 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1*
product of 1.3 knmOe is small when compared with thatof 2.3 knmOe for HAMR as shown in Table 3.
3.2.4 10 years of archiving
For an 𝑚𝑚D of 2 (𝑚𝑚D × 𝑛𝑛 = 2 × 3 = 6 grains), the bER
value as a function of 𝐸𝐸@A after 10 years of archiving for
the LC and HC layers is shown in Fig. 12 (a). The bER
value for the LC layer is larger than that for the HC layer,since the ℎ#" and/or 𝑇𝑇#" values are small. Table 8shows that the 𝐻𝐻+ value of 0.13 for the LC layer is small,and therefore, the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product of 1.6
knmOe is also small. Since the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1*
product is 3.2 knmOe for ATI as shown in Table 7, thelimiting factor for the LC layer is 10 years of archiving.

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(a)
(a)

(b)
Fig. 12 (a) Bit error rate as a function of error threshold
𝐸𝐸@A and normalized readout field 𝐻𝐻+ after 10 years ofarchiving and (b) time dependence of bit error rateduring 10 years of archiving in 2 Tbpsi/layer 3D HAMR
(2 × 3 = 6 grains).
Table 8 10 years of archiving in 2 Tbpsi/layer 3D HAMR
(3 × 3 = 9 grains/bit).

Since the 𝐾𝐾%;44 𝑉𝑉/(𝑘𝑘𝑘𝑘) value of 87 for the LC layer israther small, the 𝑅𝑅+ value is 21 as shown in Table 8.
Therefore, some information degradation can be seen
during the 10 years as shown in Fig. 12 (b).
3.2.5 LC writing
For an 𝑚𝑚D of 2 (𝑚𝑚D × 𝑛𝑛 = 2 × 3 = 6 grains), Fig. 13(a) shows the number of bits plotted against the expectedvalue of magnetization 𝐸𝐸[𝑀𝑀$= ] averaged over one-row
grains for the HC layer before and after LC writing.

(b)
Fig. 13 (a) Number of bits plotted against expected valueof magnetization 𝐸𝐸[𝑀𝑀$= ] and (b) bit error rate for the HC
layer as a function of error threshold 𝐸𝐸@A andnormalized readout field 𝐻𝐻+ before and after LC writingin 2 Tbpsi/layer 3D HAMR (2 × 3 = 6 grains).

Table 9 LC writing in 2 Tbpsi/layer 3D HAMR (3 × 3 =9 grains/bit).

Time 𝑡𝑡 and the writing field 𝐻𝐻: were assumed to be 1
ns and −10 kOe, respectively. It also shows the grain
error distribution. The negative 𝐸𝐸[𝑀𝑀$= ] represents morethan half of 3 grain errors, since the number of one-row
grains 𝑛𝑛 is three. The peaks in the figure represent thegrain error for the grains with the mean Curie
temperature. The grain error for the 2nd (𝑖𝑖 = 2) row islarger than that for the 1st ( 𝑖𝑖 = 1) row, since thetemperature for the 2nd (𝑖𝑖 = 2) row is higher. There isno significant information degradation even in the 2nd (𝑖𝑖= 2) row grains.
The bER value as a function of 𝐸𝐸@A for the HC layer

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Fig. 14 Writing field 𝐻𝐻: dependence of bit error rate in
2 Tbpsi/layer 3D HAMR (2 × 3 = 6 grains).

before and after LC writing is shown in Fig. 13 (b). Thereis little information degradation for the HC layer during
LC writing.
The 𝐻𝐻+ values of 0.30, 0.38, and 0.32 for the HC layer
are large for ATI, 10 years of archiving, and LC writing
as shown in Tables 7, 8, and 9, respectively. However,the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* products of 1.3, 1.7, and 1.4
knmOe for the HC layer are small as also shown in
Tables 7, 8, and 9, respectively, since the 𝐻𝐻0J;1* value of
401 Oe is small as shown in Table 7 due to the lower HC
layer. The limiting factor for the HC layer is thus the
𝐻𝐻0J;1* value.

3.2.6 Writing sensitivity
The bER value for 3D HAMR as shown in Fig. 14 isconsiderably smaller than that for HAMR as shown in
Fig. 5. This means that the writing sensitivity for 3D
HAMR is better than that for HAMR. Since the 𝑉𝑉
values are 149, 124, and 137 nm3 for HAMR, the LC, andHC layers as shown in Tables 1 and 5, respectively, thereasons for the difference in bER are the statisticalfactor affected by the grain numbers 𝑚𝑚D × 𝑛𝑛 of 4 and 6,
and EAW affected by the grain column numbers 𝑛𝑛 of 2
and 3 for HAMR and 3D HAMR, respectively. EAW,
which appeared in the relatively large 𝐻𝐻: region, israther large for the HC layer, since the 𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 value israther small.

3.3 2 Tbpsi/layer 3D HAMR (𝟒𝟒 × 𝟐𝟐 = 8 grains/bit)
3.3.1 Grain arrangement and medium structure
Before comparing HAMR and 3D HAMR, we examined
the bit aspect ratio on 3D HAMR.
Figure 15 shows the grain arrangement and medium
structure in 2 Tbpsi/layer 3D HAMR ( 4 × 2 = 8
grains/bit). The grain and bit sizes are summarized inTable 10.
3.3.2 Temperature profile
Figures 16 (a) and (b) show the temperature profiles
for the cross-track direction during HC and LC writing,respectively. The temperature profile results are
summarized in Table 11.

10

Fig.. 15 Grain arrangement and medium structure in 2
Tbpsi/layer 3D HAMR (4 × 2 = 8 grains/bit).

Table 10 Grain and bit sizes in 2 Tbpsi/layer 3D HAMR
(4 × 2 = 8 grains/bit).

(a) HC writing
The 𝑇𝑇$%34 value of 1009 K in Fig. 16 (a) for 3D HAMR
with 4 × 2 = 8 grains/bit is higher than that of 959 K in
Fig. 9 (a) for 3D HAMR with 3 × 3 = 9 grains/bit. Since
the temperatures 𝑇𝑇!" + 2𝜎𝜎F!" = 780 K at the track edge
are the same, the 𝑇𝑇$%34 value increases as the 𝐷𝐷F value
increases as shown in Figs. 9 (a) and 16 (a). Increasing
the bit aspect ratio is disadvantageous in terms of theheat resistance of the writing head and/or the surface
lubricant.
(b) LC writing
The |Δ𝑇𝑇!# | value of 29 K in Fig. 16 (b) is smaller thanthat of 42 K in Fig. 9 (b). The temperature difference
between the LC and HC layers becomes smaller as the
cross-track position is far from the track center as shownin Fig. 16 (b). Therefore, the |Δ𝑇𝑇!# | value decreases as
the 𝐷𝐷F value increases as shown in Figs. 9 (b) and 16 (b).
Increasing the bit aspect ratio is also disadvantageous interms of the information stability in the HC layer during
LC writing.
Furthermore, since the |Δ𝑇𝑇!# | value is small, thedifference between the 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 values of the LC and HC
layers is relatively small.

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Fig. 16 Temperature profile for cross-track direction
during (a) HC and (b) LC writing in 2 Tbpsi/layer 3D
HAMR (4 × 2 = 8 grains/bit).
Table 11 Temperature profile in 2 Tbpsi/layer 3D HAMR
(4 × 2 = 8 grains/bit).

3.3.3 Adjacent track interference
The 𝐻𝐻+ values for various 𝑚𝑚D values after AT
writing are shown in Fig. 17. A comparison with theresult in Fig. 10 shows that ATI can be improved byincreasing the bit aspect ratio. However, the 4th row (𝑖𝑖= 4) grains is still used as a guard band. The readout
grain numbers 𝑚𝑚D × 𝑛𝑛 = 2 × 3 = 6 grains and 3 × 2 = 6
grains are still the same for 3D HAMR with 3 × 3 = 9
grains/bit and 4 × 2 = 8 grains/bit, respectively.

Fig. 17 Minimum normalized readout field 𝐻𝐻+ forvarious numbers of readout rows 𝑚𝑚D after AT writing in
2 Tbpsi/layer 3D HAMR (4 × 2 = 8 grains/bit).

Fig. 18 Bit error rate as a function of error threshold 𝐸𝐸@A
and normalized readout field 𝐻𝐻+ before and after AT
writing in 2 Tbpsi/layer 3D HAMR (3 × 2 = 6 grains).

Table 12 Adjacent track interference in 2 Tbpsi/layer 3D
HAMR (4 × 2 = 8 grains/bit).

For an 𝑚𝑚D of 3 (𝑚𝑚D × 𝑛𝑛 = 3 × 2 = 6 grains), the bER
value as a function of 𝐸𝐸@A before and after AT writing for
the LC and HC layers is shown in Fig. 18. There isalmost no information degradation of the HC layer
during AT writing.
The ATI results are summarized in Table 12. The
𝑚𝑚D × 𝑛𝑛 and 𝐷𝐷DF values are 3 × 2 and 18.1 nm,
respectively. For the HC layer, although the 𝐻𝐻0J;1*
value of 377 Oe is small, the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product

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INDEXof 2.6 knmOe is large when compared with that of 2.3
knmOe for HAMR as shown in Table 3, since the 𝐷𝐷DF
value of 18.1 nm is large.
3.3.4 10 years of archiving
When 3D HAMR with 3 × 3 = 9 grains/bit and with
4 × 2 = 8 grains/bit are compared, the results for 10
years of archiving, as shown in Figs. 12 and 19, arealmost the same, since the 𝑉𝑉 values of 124 and 129 nm3
are almost the same for the LC layer as shown in Tables

5 and 10, and the 𝐾𝐾%;44 𝑉𝑉/(𝑘𝑘𝑘𝑘) values of 137 and 172 are
sufficiently large for the HC layer as shown in Tables 8
and 13, respectively. Although the 𝐻𝐻+ value of 0.17 forthe LC layer is small, the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product of
3.4 knmOe is large as shown in Table 13, because the
𝐷𝐷DF value is large. Since the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* productis 6.1 knmOe for ATI as shown in Table 12, the limiting
factor for the LC layer is 10 years of archiving. The
𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product of 3.4 knmOe for the LC layer
is larger than that of 2.3 knmOe for HAMR as shown in
Table 3.
For the HC layer, the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* products for
ATI and 10 years of archiving are almost the same asshown in Tables 12 and 13. The 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1*
product of 2.6 knmOe for the HC layer is larger than thatof 2.3 knmOe for HAMR as shown in Table 3.
3.3.5 LC writing
For an 𝑚𝑚D of 3 (𝑚𝑚D × 𝑛𝑛 = 3 × 2 = 6 grains), Fig. 20(a) shows the number of bits plotted against the expectedvalue of magnetization 𝐸𝐸[𝑀𝑀$= ] averaged over one-row
grains for the HC layer before and after LC writing.

(a)

(a)

(b)
Fig. 19 (a) Bit error rate as a function of error threshold
𝐸𝐸@A and normalized readout field 𝐻𝐻+ after 10 years ofarchiving and (b) time dependence of bit error rateduring 10 years of archiving in 2 Tbpsi/layer 3D HAMR
(3 × 2 = 6 grains).

Table 13 10 years of archiving in 2 Tbpsi/layer 3D HAMR
(4 × 2 = 8 grains/bit).

(b)
Fig. 20 (a) Number of bits plotted against expected valueof magnetization 𝐸𝐸[𝑀𝑀$= ] and (b) bit error rate for the HC
layer as a function of error threshold 𝐸𝐸@A andnormalized readout field 𝐻𝐻+ before and after LC writingin 2 Tbpsi/layer 3D HAMR (3 × 2 = 6 grains).
12

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Table 14 LC writing in 2 Tbpsi/layer 3D HAMR (4 × 2 =8 grains/bit).

Significant information degradation can be seen in the
2nd (𝑖𝑖 = 2) and 3rd (𝑖𝑖 = 3) row grains when comparedwith the result shown in Fig. 13 (a), since the HC grain
temperature during LC writing shown in Fig. 16 (b) ishigher than that shown in Fig. 9 (b). Although thetemperatures for the 1st and 2nd row grains in Fig. 9 (b)are 634 and 655 K, those for the 1st and 2nd (3rd) row
grains in Fig. 16 (b) are 647 and 690 K, respectively.
Temperature has a strong impact, since the 𝑇𝑇 value isrelated to the 𝐾𝐾%;44 (𝑇𝑇) value and the denominator 𝑇𝑇 in
the 𝐾𝐾%;44 (𝑇𝑇)𝑉𝑉/(𝑘𝑘𝑘𝑘), and 𝐾𝐾%;44 (𝑇𝑇)𝑉𝑉/(𝑘𝑘𝑘𝑘) is a variable in
the exponential function shown in Eq. (1). Accordingly,
Fig. 20 (b) and Table 14 show that there is no 𝐸𝐸@A
greater than 0.5, namely, no 𝐻𝐻+ greater than 0 thatsatisfies a bER of 10-3 for the HC layer after LC writing.
A large bit aspect ratio is advantageous in terms of
ATI and the 𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* product. However, theinformation degradation in the HC layer during LC
writing is large. Therefore, we believe that a small bit
aspect ratio is preferable in 3D HAMR.

the 𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 values of 8.8 and 11.3 K/nm as shown in
Tables 6 and 11, respectively, as well as by the 𝑛𝑛 valuesof 3 and 2. EAW can be suppressed by increasing the𝜕𝜕𝑇𝑇! /𝜕𝜕𝜕𝜕 value.

3.4 Comparison of shingled HAMR and 3D HAMR
We think the medium for comparison with 4 Tbpsi
shingled HAMR is 2 Tbpsi/layer 3D HAMR with 3 × 3 =9 grains/bit. The comparison results are summarized inTable 15.
(1) Grain aspect ratio
The (ℎ#" + ℎ!" )/𝐷𝐷2 values for both HAMR and 3D
HAMR may be too large to allow us to manufacture therecording layer.
(2) Mean Curie temperature
The low 𝑇𝑇#" value of 650 K may be disadvantageous
as regards the writing property, since the temperaturedependence of the anisotropy field is somewhat smaller
than that predicted by the theory.
Table 15 Comparison of 4 Tbpsi shingled HAMR (3 × 2= 6 grains/bit) and 2 Tbpsi/layer 3D HAMR (3 × 3 = 9
grains/bit).

3.3.6 Writing sensitivity
The 𝐻𝐻: dependence of the bER for the LC and HC
layers is shown in Fig. 21. The writing sensitivity is also
better than that for HAMR as shown in Fig. 5.
The reason for the difference between the bERs of the
LC layers in Figs. 14 and 21 is that EAW is affected by
the 𝑛𝑛 values of 3 and 2, respectively. EAW can besuppressed by increasing the 𝑛𝑛 value. On the other
hand, the reasons for the difference between the bERs of
the HC layers are the 𝑉𝑉 values of 137 and 172 nm3 asshown in Tables 5 and 10, and that EAW is affected by

Fig. 21 Writing field 𝐻𝐻: dependence of bit error rate in
2 Tbpsi/layer 3D HAMR (3 × 2 = 6 grains).

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INDEX(3) Readout property
In HAMR, the 𝐻𝐻+ values are 0.20 and 0.26 for ATI
and 10 years of archiving, respectively. Therefore, thelimiting factor is ATI, since the grain pitch is small.
For the upper LC layer in 3D HAMR, the 𝐻𝐻+ values
are 0.26 and 0.13 for ATI and 10 years of archiving,
respectively. Therefore, the limiting factor is 10 years ofarchiving, since the ℎ#" and/or 𝑇𝑇#" values are small.
For the lower HC layer in 3D HAMR, the 𝐻𝐻+ values of
0.30, 0.38, and 0.32 are large for ATI, 10 years ofarchiving, and LC writing, respectively. However, the
𝐷𝐷DF × 𝐻𝐻+ × 𝐻𝐻0J;1* products are small, since the 𝐻𝐻0J;1*
value of 401 Oe from the lower HC layer is small due tothe limitation of thinning the upper LC layer related tothe information stability in the LC layer. Therefore, thelimiting factor is the 𝐻𝐻0J;1* value.
(4) Writing sensitivity
The bER for HAMR is higher than that for 3D HAMR.
The reasons for the difference in bER are the statisticalfactor affected by the 𝑚𝑚D × 𝑛𝑛 value and EAW affected by
the 𝑛𝑛 value. This means that the writing sensitivity for
HAMR is worse than that for 3D HAMR.
4. Conclusions

We compared 4 Tbpsi shingled HAMR and 2
Tbpsi/layer 3D HAMR.
Prior to the comparison, we examined the bit aspectratio on 3D HAMR. A large bit aspect ratio isadvantageous in terms of ATI and the readout property.
However, there is considerable information degradationin the HC layer during LC writing. Therefore, we
consider a small bit aspect ratio to be preferable in 3D
HAMR.
For the upper LC layer in 3D HAMR, the minimum
normalized readout field is small for 10 years ofarchiving, since the LC grain height and/or LC Curie
temperature are small.
The peak 𝑧𝑧 component of the readout field from thelower HC layer is small due to the limitation of thinningthe upper LC layer related to the information stability inthe LC layer.

14

The writing sensitivity for HAMR is worse than thatfor 3D HAMR because of a statistical factor affected by
the readout grain number and erasure-after-write
affected by the grain column number.
Although both HAMR and 3D HAMR havedisadvantages, we think that the poor writing sensitivity
in HAMR is a serious problem.
Acknowledgement We acknowledge the support of theAdvanced Storage Research Consortium (ASRC), Japan.
References
1) Western Digital (private communication, December, 2018).
2) H. Yamane, S. J. Greaves, and Y. Tanaka: IEEE Trans.
Magn., 57, 3200706-1-6 (2021).
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Jpn., 45, 16 (2021).
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39, 8 (2015).
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Jpn., 44, 122 (2020).
9) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 44, 34 (2020).
10) E. D. Boerner and H. N. Bertram: IEEE Trans. Magn., 34,
1678 (1998).
11) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 46, 10 (2022).
12) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 42, 127 (2018).
13) Y. Kanai, Y. Jinbo, T. Tsukamoto, S. J. Greaves, K. Yoshida,and H. Muraoka: IEEE. Trans. Magn., 46, 715 (2010).
14) I. Suzuki, J. Wang, Y. K. Takahashi, and K. Hono: J. Magn.
Magn. Mat., 500, 166418 (2020).
15) C. Xu, B. Zhou, T. Du, B. S. D. Ch. S. Varaprasad, D. E.
Laughlin, and J. -G. Zhu: APL Mat., 10, 051105 (2022).
16) T. Kobayashi, Y. Isowaki, and Y. Fujiwara: J. Magn. Soc.
Jpn., 40, 28 (2016).
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Jpn., 43, 70 (2019).
R eceiv ed A u g . 2 2 , 2 0 2 2 ; A ccep ted O ct. 1 0 , 2 0 2 2

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 15-19 (2023)<Paper>Synthesis and Analyses of Acicular Spinel Iron Oxide Particles with Core-Shell Structure
Containing Manganese Ferrite and Magnetite
Sota Yamada*, Mikio Kishimoto*, and Hideto Yanagihara*,***Department of Applied Physics, Univ. of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8573, Japan** Tsukuba Research Center for Energy Materials Science (TREMS), Univ. of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8573, Japan

Acicular spinel iron oxide particles with a core-shell structure containing manganese ferrite (MnFe2O4) andmagnetite (Fe3O4) were synthesized by uniformly crystallizing MnFe2O4 on the surface of the magnetite particles in an
alkaline dispersion. Crystallizing 50 wt% of MnFe2O4 on Fe3O4 led to an increase in the apparent lattice constant from
0.839 nm to 0.841 nm. Transmission electron microscopy (TEM) observations of the particle shape and lattice images
showed that MnFe2O4 was uniformly crystallized on the surface of the magnetite particles and their acicular shape wasmaintained. The coercive force and saturation magnetization were almost constant at 29.5 kA/m and 80-81 Am2/kg,
respectively, when the crystallized MnFe2O4 content ranged from 0 to 30 wt%. When the MnFe2O4 content was increased
to 50 wt%, the coercive force and saturation magnetization slightly decreased to approximately 28.0 kA/m and 74.1
Am2/kg, respectively, reflecting the lower magnetization of MnFe2O4 compared to that of Fe3O4.
Key words: magnetic nanoparticles, core-shell structure, spinel ferrite
1. In troduction

There are many reports on particles synthesized with acore-shell structure that find applications in a variety offields, such as electronics, biomedical, optics, andcatalysis1)-5). Among them, particles containing cobalt
ferrite (CoFe2O4) are of particular interest from a practicalstandpoint due to the high magnetic anisotropy of
CoFe2O46)-11). To synthesize particles with a core-shellstructure containing CoFe2O4, precipitation methods havebeen reported to be effective for controlling the magnetic
anisotropy12),13).
Several studies have investigated to improve therecording density of particulate magnetic recording tapes
by increasing the coercive force through the addition of
Co ions to spinel iron oxide particles14). Initially, this wasachieved by the substitution of Co ions in maghemite(γ-Fe2O3) particles15). However, the magnetic anisotropy
resulting from this method was cubic, whereas a uniaxial
magnetic anisotropy is essential for recording tapes. To
overcome this problem, particles with a core-shellstructure were synthesized. In these particles, the CoFe2O4
layer was epitaxially crystallized on the surface of theseed γ-Fe2O3 particles with the same spinel structure16). In
this method, γ-Fe2O3 was reduced to magnetite (Fe3O4) inan alkaline dispersion.
The lattice constants of CoFe2O4 and Fe3O4 are close invalue, at 0.838 and 0.839 nm, respectively. Therefore, we
explored the possibility of epitaxially crystallizing anotherspinel oxide with a significantly different lattice constantfrom that of Fe3O4. Manganese ferrite (MnFe2O4) is
known to possess the lattice constant of 0.851 nm, which
is significantly different from that of Fe3O4. In this study,
we tried to epitaxially or uniformly crystallize MnFe2O4
Corresponding author: Hideto Yanagihara
yanagihara.hideto.fm@u.tsukuba.ac.jp).

(e-mail:on the surface of acicular Fe3O4 particles, and examinedthe changes in the lattice constant, particle shape, andmagnetic properties of the resulting acicular iron oxide
particles with a core-shell structure containing MnFe2O4
and Fe3O4.
2. Experimental procedures

2.1 Sample preparation
Commercially available acicular γ-Fe2O3 particles(Titan Kogyo, Ltd. AV-60) were used as the raw material.
The Fe3+ ions in the γ-Fe2O3 particles were partiallyreduced to Fe2+ ions under a H2 atmosphere at 300 ℃ for
2 h. Acicular iron oxide particles with a composition close
to that of Fe3O4 were obtained, which were used as seedparticles in this study.
MnFe2O4 was crystallized on the Fe3O4 particles asfollows: One gram of Fe3O4 particles was dispersed in 100
mL of water using an ultrasonic disperser. Manganesechloride and ferrous chloride were dissolved in a 1:2
molar ratio in the above dispersion, following which threetimes the equivalent of sodium hydroxide required to form
Mn(OH)2 and Fe(OH)2 was added under continuous
stirring. The dispersion containing the Fe3O4 particle,
Mn(OH)2, and Fe(OH)2 was treated hydrothermally in an
autoclave at 110 ℃ for 24 h, where Fe2+ was oxidized toFe3+, and MnFe2O4 was crystallized in the dispersion.
Using the above method, four samples containing
different contents of MnFe2O4 were synthesized. In thisreport, the composition of the samples is defined as
MnFe2O4(x wt%): Fe3O4(100- x wt%) (x =10, 20, 30, and50). The expressed compositions of the samples are theamounts prepared upon the synthesis.
MnFe2O4 particles were prepared without the Fe3O4
seed particles using the above method in order to compare
the particle shape with that of the core-shell-structured
manganese ferrite particles (CSMPs) and magnetite
particles.

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2.2 Measurement
Transmission electron microscopy (TEM: JEN2010F,
JEOL) was used to observe the shapes of the Fe3O4
particles, MnFe2O4 particles, and CSMPs, and lattice
images were acquired to examine the crystal structure of
the product formed on the CSMPs and magnetite particles.
X-ray diffraction (XRD; MiniFlex600, Rigaku) using
CuKα radiation was conducted in the 2θ range of 20 60 for structural analyses. The lattice constants (a) of the
CSMPs and magnetite particles were calculated from the dvalues of the 311 peak for each particle; this peak is thestrongest peak in the spinel structure. This allowed theexamination of the variation in the lattice due to the
crystallization of MnFe2O4 on the surface of the Fe3O4
particles.
The particle size distribution was obtained bymeasuring the length and width of approximately one
hundred particles on the corresponding TEM image. The
data were used to examine the particle shape variation due
to the crystallization of MnFe2O4 on the Fe3O4 particles.
The coercive force and saturation magnetization were
measured using a vibrating sample magnetometer(TM-VSM2106-HGC, Tamakawa) under a maximum
magnetic field of 1353 kA/m.

of iron oxides with a spinel structure. We note that theobserved 311 peaks could be the combined 311 reflectionsof both MnFe2O4 and Fe3O4. The apparent lattice

MnFe2O4(x wt%)/Fe3O4(100-x wt%)

Fig. 2 Relationship between the crystallized MnFe2O4
content (ranging from 10 to 50 wt%) on the surface of
Fe3O4 particles and the lattice constant.

3. Results and discussion

3.1 Structural analyses
The XRD patterns measured in the 2θ range of 20 60 for the MnFe2O4 particles, Fe3O4 particles, andCSMPs (containing different content of MnFe2O4 in therange of 10 to 50 wt% with respect to Fe3O4) are shown in
Figure 1. These patterns show typical peaks representative(a)Fig. 1 XRD patterns measured in the 2θ range of 20 to60 ˚ for MnFe2O4 particles, Fe3O4 particles, andcrystallized MnFe2O4 (10 to 50 wt%) on the surface of
Fe3O4 particles.

16

(b)

Fig. 3 TEM images of (a) Fe3O4 particles used as
the seed particles and (b) crystallized 30 wt%
MnFe2O4 on the surface of Fe3O4 particles.

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INDEX(a)Fig. 4 TEM image of MnFe2O4 particles synthesized
without Fe3O4 seed particles.

(b)

(a)

Fig. 6 Particle size distribution crystallized 30 wt%
MnFe2O4 on Fe3O4 particles. The particle size
distribution was obtained by measuring the (a) lengthand (b) width of approximately one hundred particles
on the corresponding TEM image.

(b)

Fig. 5 Particle size distribution of Fe3O4 seed particles.
The particle size distribution was obtained bymeasuring the (a) length and (b) width ofapproximately one hundred particles on thecorresponding TEM image.
constants (a) of MnFe2O4 calculated from the d values of
the 311 peak seems 0.846 nm, slightly lower than thevalue of 0.851 nm reported for bulk MnFe2O4.
Figure 2 shows the relationship between the MnFe2O4
content and apparent lattice constant of the respective

CSMPs. The apparent lattice constant of the CSMPs
increased with increasing amount of MnFe2O4 from 0.839
nm in the Fe3O4 particles to 0.841 nm in the sample with
50 wt% MnFe2O4, reflecting the larger lattice constant of
the crystallized MnFe2O4 compared to that of the Fe3O4
particles. Although the experimental error in the apparent
lattice constant could be in the order of ~0.0005 nm, theapparent lattice constant appears to increase withincreasing MnFe2O4 content, for which reproducibility
was verified by several measurements.
3.2 Particle shapes and lattice images
The TEM images of the Fe3O4 particles used as seedparticles and CSMPs crystallized with 30 wt% MnFe2O4
on the Fe3O4 particles are shown in Figures 3(a) and (b),respectively. Compared with the Fe3O4 particles, theCSMPs are clearly thicker because of the crystallization of
MnFe2O4, while their acicular shapes were maintained.
Figure 4 shows the TEM image of the MnFe2O4 particles
synthesized without the seed Fe3O4 particles. The
MnFe2O4 particles are hexagonal in shapes with adiameter of approximately 50 nm, which is distinctly
different from those of CSMPs. These results show that
the CSMPs have a core-shell structure in which MnFe2O4

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Fig. 7 Lattice image of crystallized 30 wt% MnFe2O4
on seed Fe3O4 seed particles.
is uniformly crystallized on the surface of the Fe3O4
particles.
3.3 Particle size distribution
The particle size distributions measured along thelength and width of the Fe3O4 particles are shown in
Figures 5(a) and (b), respectively. The median length andwidth are approximately 200 nm and 30 nm, respectively.
Figures 6(a) and (b) show the particle size distribution
measured along the length and width, respectively, of the
CSMPs crystallized with 30 wt% MnFe2O4 on the Fe3O4
particles. The particle size distribution of the MCFPs is
broader compared to that of the Fe3O4 particles due to the
crystallization of MnFe2O4. The median length and widthof the CSMPs are approximately 300 nm and 40-50 nm,
respectively.
The lattice image of the CSMPs crystallized with 30
wt% MnFe2O4 on the Fe3O4 particles (as shown in Figure3(b)) is shown in Figure 7. The lattice image is clear witha lattice spacing of 0.243 nm, which corresponds to that of
the 222 peak in the spinel structure. The lattice constantcalculated from the lattice spacing is 0.843 nm, whichfalls between the lattice constants for the Fe3O4 particles(0.839 nm) and MnFe2O4 particles (0.846 nm).
3.4 Magnetic properties
Figures 8 (a) and (b) show the relationship between thecoercive force and saturation magnetization and theamount of MnFe2O4 in the CSMPs, respectively. The
coercive force is approximately 29.5 kA/m, the same asthat of the Fe3O4 particles with 10 to 30 wt% MnFe2O4 in
the CSMPs, as shown in Figure 8 (a). When the amount of
MnFe2O4 is increased to 50 wt%, the coercive force
slightly decreases to approximately 28.0 kA/m. A similar
dependency on the amount of MnFe2O4 is observed for thesaturation magnetization, which remains 80-81 Am2/kg in
the range of 0 to 30 wt% MnFe2O4 in the CSMPs anddecreases to 74.1 Am2/kg for 50 wt% MnFe2O4, as shownin Figure 8 (b).
The coercive force in acicular particles depends on the
shape magnetic anisotropy, which in turn is a function of
the acicular ratio (ratio of the length and width of the18

MnFe2O4(x wt%)/Fe3O4(100-x wt%)

MnFe2O4(x wt%)/Fe3O4(100-x wt%)
Fig. 8 Relationship between the (a) coercive force and(b) saturation magnetization, and crystallized MnFe2O4
content on Fe3O4 seed particles.
particles) and the saturation magnetization. The
almost-constant coercive force (Figure 8 (a)) is anindication that both, the acicular ratio and saturation
magnetization, also do not change significantly with theuse of 0 to 30 wt% MnFe2O4 in the CSMPs. The average
acicular ratios calculated from the particle size distribution
shown in Figures 5 and 6 are approximately 7 and 6 forthe Fe3O4 particles and CSMPs with 30 wt% MnFe2O4,
respectively. The almost- constant acicular ratio andsaturation magnetization with 0 to 30 wt% MnFe2O4 in the
CSMPs corresponds to the almost-constant coercive force
in the same range of MnFe2O4 in the CSMPs. The
significant decrease in the coercive force andmagnetization at 50 wt% MnFe2O4 is attributed to thelarge amount of MnFe2O4, whose magnetization issignificantly lower than that of the Fe3O4 particles.
The results obtained from TEM and the magnetic
properties indicate that MnFe2O4 is uniformly crystallizedon the surface of Fe3O4 particles, preserving the acicularshape of the particles.
4. Conclusion
MnFe2O4 was uniformly crystallized on the surface ofacicular Fe3O4 particles in an alkaline dispersion. TEM
observations of the particle shape and the lattice images
confirmed the uniform crystallization of MnFe2O4 on the

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Fe3O4 particles. The lattice constant increased with the
crystallization of MnFe2O4, reflecting the considerable
difference between the lattice constants of MnFe2O4 andFe3O4 particles. The coercive force and saturation
magnetization were almost constant for 0 to 30 wt%
MnFe2O4 and decreased at 50 wt% MnFe2O4, reflecting
the smaller magnetization of MnFe2O4 compared to that of
the Fe3O4 particles.
Acknowledgments This work was supported by theJapan Society for the Promotion of Science (JSPS)
KAKENHI (Grant Number 20K21072). The TEM
observations were performed using an equipment
registered in the Open Facility System, University ofTsukuba.
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Zamorskyi, A. Tovstolytkin and A. Belous: Nanoscale Res.
Lett., 13, 1 (2018).
13) J. de A. Gomes, M. H. Sousa, F. A. Tourinho, R. Aquino, G.
J. da Silva, J. Depeyrot, E. Dubois, and R. Perzynski: J.
Phys. Chem. C, 112, 6220 (2008).
14) A. A. van der Giessen: Rev. Phys. Appl., 9, 869 (1974).
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16) M. Kishimoto, M. Amemiya, and F. Hayama: IEEE. Trans.
Magn., 21, 2626 (1985).
Received Apr. 19, 2022; Accepted Oct. 2, 2022

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 20-17 (2023)<Paper>Current-Induced Helicity Switching of Frustrated Skyrmions on a SquareGrid Obstacle Pattern
X. Zhang1, J. Xia1, O. A. Tretiakov2, H. T. Diep3, G. Zhao4, J. Yang5, Y. Zhou6, M. Ezawa7, and X. Liu1
1Department of Electrical and Computer Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan
2School of Physics, The University of New South Wales, Sydney 2052, Australia

3Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France
4College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610068, China

5State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China

6School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, China
7Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-8656, Japan

Topological spin textures on artificial pinning landscape may show unique static and dynamic properties. Here,we computationally show that the helicity of frustrated skyrmions on an artificial square-grid obstacle pattern can beswitched by a spin current pulse. The obstacle pattern is formed by defect lines with enhanced perpendicular magnetic
anisotropy, which could protect the skyrmion from being annihilated at the sample edge. It is found that the skyrmion
driven by a moderate current shows a circular motion guided by the boundary of the obstacle pattern, while it showsan almost straight motion toward the sample edge in the absence of the obstacle pattern. By applying a short pulse
current to drive the skyrmion in a sample with the obstacle pattern, we find that the helicity of the skyrmion could beswitched between Bloch-type configurations favored by the dipole-dipole interaction. Besides, we demonstrate the possibility of switching the helicity of an array of skyrmions on the square-grid obstacle pattern using the same method.
Our results could be useful for the helicity control of topological spin textures, and may provide guidelines for building
future helicity-based spintronic functions.
Key words: magnetic skyrmion, frustrated spin system, helicity, obstacle, pinning, spintronics, micromagnetics
1. Introduction
Skyrmions were predicted theoretically to exist in magnetic materials more than three decades ago 1, 2), which
are now in the vanguard of next-generation spintronic
technologies 3-22). They can be found in different types ofmagnetic materials 3-22), including chiral magnets andfrustrated magnets. In chiral magnets, skyrmions arestabilized by the asymmetric exchange interaction 23-25),
which is also called the Dzyaloshinskii-Moriya interaction 26, 27). In frustrated magnets, skyrmions are stabilized by the exchange frustration induced by the competing exchange interactions 28-59). The salient features ofmagnetic skyrmions include nanoscale size, low energy
consumption, and most importantly, multiple degrees of
freedom that can be controlled by external stimuli.
Therefore, it is expected that skyrmions can be used asversatile building blocks in different information processing applications 3-22).
Most recently, it was suggested that frustrated skyrmions could be utilized as qubits in quantum computing
55, 60), where the manipulation of information is achieved
through the precise control of the helicity degree of freedom. However, a frustrated skyrmion usually shows both
center-of-mass and helicity dynamics when it is driven by
an applied current 29, 30, 36, 42, 45, 57). Namely, the helicity
Corresponding author: Y. Zhou (e-mail: zhouyan@cuhk.
edu.cn), M. Ezawa (e-mail: ezawa@ap.t.u-tokyo.ac.jp), X.
Liu (e-mail: liu@cs.shinshu-u.ac.jp).

20

dynamics is coupled to the center-of-mass dynamics.
Such a feature may limit the applications of frustrated
skyrmions in helicity-based quantum computing and relevant devices. Hence, it is vital to find an effective way tocontrol and manipulate the helicity degree of freedom offrustrated skyrmions. We note that the helicity state of ananoscale skyrmion can be experimentally observed byusing the Lorentz transmission electron microscopy(TEM) 61).
Possible solutions to avoid the translational motion of
a frustrated skyrmion include the pinning of the skyrmion by an artificial defect and the geometric confinement of the skyrmion. For example, a ferromagnetic
skyrmion in a nanodisk with the diameter close to theskyrmion diameter may show limited translational motion due to the confinement effect provided by the skyrmion-edge repulsion 62). However, skyrmions could be destroyed by touching the edge. Recently, it has been shownthat a more effective strategy to confine, protect, and control skyrmions in magnetic thin films is to construct defect lines with different magnetic properties 63-74), which
can be realized in engineered multilayer nanostructures75) or by using focused irradiation 76). However, the helicity dynamics of a frustrated skyrmion confined by defectlines have not yet been explored. It is important to study
such a problem, which is highly relevant to the realization of the skyrmion helicity-based applications.
In this work, we report the current-induced dynamics
of isolated frustrated skyrmions on a square-grid obstacle pattern, which is made of orthogonal defect lines with

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Fig. 1 The total energy of a frustrated skyrmion in thesystems with or without the DDI. (a) The total energy ofa frustrated skyrmion as a function of the helicity number η in the system with the DDI. The energies are given
in units of J1 = 1. (b) The total energy of a frustrated skyrmion as a function of the helicity number η in the system
without the DDI. (c) Schematic illustration showing thespin configurations of skyrmions with the helicity numbers of η = 0, π/2, π, 3π/2. The out-of-plane spin component
mz is color coded: blue is into the plane, red is out of theplane, white is in-plane. The total energy is calculated byassuming a fixed helicity number η.
enhanced perpendicular magnetic anisotropy (PMA). We
show that the helicity states of a single isolated frustrated skyrmion as well as an array of isolated frustrated
skyrmions can be switched between Bloch-type configurations by a short current pulse. Our results could be abasis for future storage and computing device applications based on the manipulation of the helicity degree of
freedom of topological spin textures.
2. Simulation and system
We focus on the dynamics of isolated skyrmions in a
two-dimensional (2D) frustrated magnetic spin system,
where the skyrmions are stabilized by a delicate competition among ferromagnetic nearest-neighbor (NN), antiferromagnetic next-NN (NNN), and antiferromagnetic
next-NNN (NNNN) exchange interactions. The system isa J1-J2-J3 classical Heisenberg model on a simple squarelattice 30, 33, 36, 49). The Hamiltonian ℋ is given asℋ = −J1 � mi ⋅mj − J2 � mi ⋅mj
<i,j>

−J3

<<i,j>>

�<<<i,j>>>mi ⋅mj − Ku �(mzi )2

1− MS � BD ⋅mi ,
2
i

i

(1)

where mi represents the normalized spin at the site i,|mi | = 1. ⟨i, j⟩, ⟨⟨i, j⟩⟩, and ⟨⟨⟨i, j⟩⟩⟩ run over all the NN, NNN,and NNNN sites, respectively. J1, J2, and J3 are theFig. 2 Typical current-induced motion of a frustrated
skyrmion in the system with the DDI. (a) A typical trajectory of a frustrated skyrmion in the system with the
DDI, which shows the skyrmion moves almost straight
toward the left edge of the sample. A relaxed skyrmion
with η = π/2 is placed at the sample center as the initialstate at t = 0 ps. The sample size is 51 × 51 spins. The
skyrmion is driven by a current density of j = 70 MA/cm2.
The insets show the zoomed-in view of the skyrmion at t
= 0 ps and t = 50 ps. Note that the insets only focus on theskyrmion texture instead of the whole sample. The arrow
indicates the motion direction of the skyrmion. (b) The
helicity of the skyrmion as a function of time during t = 0− 50 ps. The skyrmion helicity slightly varies with time
due to the current-induced deformation of the skyrmion
during its motion toward the left sample edge. The skyrmion is annihilated by touching the left sample edge at t
= 66 ps, where the skyrmion position and helicity cannot
be tracked due to the significant deformation and annihilation.
constants for the NN, NNN, and NNNN Heisenberg exchange interactions, respectively. Ku is the easy-axis
magnetic anisotropy constant, and the z-axis direction isdefined as the easy axis. BD is the demagnetizing field resulting from the magnetic dipole-dipole interaction (DDI).
MS denotes the saturation magnetization. We note that
we do not consider the interface-induced DzyaloshinskiiMoriya interaction in this work as it could be suppressed
for an ultrathin monolayer 77).
The spin dynamics is governed by the Landau-LifshitzGilbert equation augmented with the damping-like spinorbit torque 78-81),
𝜕𝜕𝜕𝜕t m = −γ0 m × heff + α(m × 𝜕𝜕𝜕𝜕t m) + τd ,(2)

where t is the time, γ0 is the absolute gyromagnetic ratio,
and α is the Gilbert damping parameter. heff =− δℋ ⁄(δmµ0 MS ) is the effective field with µ0 and ε being
the vacuum permeability constant and average energy
density, respectively. The saturation magnetization MS =580 kA/m. The damping-like spin-orbit torque is expressed as τd = u (m × p × m), where the coefficient u=|(γ0ℏ/µ0e)|(jθSH/2aMS). ℏ is the reduced Planck constant, e
is the electron charge, a is the sample thickness, j is thecurrent density, and θSH is the spin Hall angle. The spinpolarization direction p = +ŷ. For the sake of simplicity,
we assume that θSH = 1 so that the driving force is simply

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Fig. 3 Current-induced motion of a frustrated skyrmion
in a sample with the obstacle pattern. (a) The trajectoryof a frustrated skyrmion in a sample with the squareshaped obstacle pattern, which is formed by edge spinswith enhanced PMA (i.e., Ko/Ku = 10 with Ko being the
PMA of the obstacle defect line). A relaxed skyrmion with
η = π/2 is placed at the sample center as the initial state
at t = 0 ps. The skyrmion moves in an almost circular path
guided by the obstacle pattern, which is driven by a current density of j = 40 MA/cm2. The sample size is 21 × 21
spins. The width of the obstacle line is 3 spins. (b) The
helicity of the skyrmion as a function of time during t = 0− 200 ps. The skyrmion helicity changes between Blochtype and Néel-type configurations during the motion of
the skyrmion along the inner edge of the obstacle pattern.
(c) Selected top-view snapshots showing the spin configurations of the skyrmion at t = 0, 43, 55, and 75 ps. The
obstacle pattern with enhanced PMA is indicated by theorange area.
determined by j, i.e., u ∼ j. In this work, we do not consider the effect of the field-like spin-orbit torque considering the helicity dynamics of a frustrated skyrmion isdriven by the damping-like torque 30, 36). The simulation
is done by using the Object Oriented MicroMagnetic
Framework (OOMMF) 82) upgraded with our extension
modules for the J1-J2-J3 classical Heisenberg model 30). In
all simulations, the mesh size is a3 with a = 0.4 nm being
the lattice constant. Other default parameters are 30, 36, 45,
51, 52): J1 = 30 meV, J2 = −0.8 (in units of J1 = 1), J3 = −0.6
(in units of J1 = 1), Ku = 0.02 (in units of J1/a3 = 1), α = 0.3,
and γ0 = 2.211 × 105 m/(As).
3. Results and discussion
The helicity is an important degree of freedom of frustrated skyrmions, which can be used to perform helicitybased storage and computing. As shown in Fig. 1, we firstreview the total energy of a frustrated skyrmion as function of its helicity in the systems with or without the DDI.
In the simulation, we first place a single isolated skyrmion with the skyrmion number of Q = −1 at the centerof a sample with 21 × 21 spins with open boundary

22

Fig. 4 Current-induced motion of a frustrated skyrmion
in a sample without the obstacle pattern. Selected topview snapshots showing the spin configurations of thefrustrated skyrmion at t = 0, 10, 20, 30, 35, 38, 40, 42, and45 ps in a sample without the obstacle pattern. A relaxedskyrmion with η = π/2 is placed at the sample center as
the initial state at t = 0 ps. The sample size is 21×21
spins. The skyrmion is driven by a current density of j =40 MA/cm2. The skyrmion moves toward the sample edge
and annihilates when touching the sample edge.

conditions in the x and y directions. The skyrmion number is defined as Q = 1/4π ∫ m∙ (∂x m×∂y m)dxdy . As theskyrmion can be parametrized as m(r) = m(θ, ϕ) = (sinθcos
ϕ, sinθsin ϕ, cosθ), where ϕ = Qvφ+η with φ being the azimuthal angle (0 ≤ φ < 2π). Hence, the skyrmion consideredin our work has a vorticity of Qv = ∮ Cd ϕ/2π = +1. η ∈ [0,2π) denotes the skyrmion helicity defined mod 2π. It canbe seen that the total energy of a frustrated skyrmion depends on its helicity number η, where the Bloch-type configurations are favored by the DDI. Namely, the total energy of a frustrated skyrmion is independent of η only inthe system without the DDI [see Fig. 1(b)]. Such a property is important for the dynamics of the frustrated skyrmion as the center-of-mass dynamics of frustrated skyrmions is coupled to the helicity dynamics 30). Namely, theskyrmion will move in a straight path with its helicity
being fixed at the energetically favored Bloch-type configurations (i.e., η = π/2, 3π/2) in the system with the DDI
36).
Therefore, in order to switch the helicity of a frustrated
skyrmion in the system with the DDI, one will need toapply a driving current larger than a critical value to induce the helicity switching when the skyrmion can overcome the energy barrier between two different Bloch-type
configurations 36). However, the critical value of the driving current density could be high, although the DDI-

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induced energy barrier may be reduced by reducing thevalue of the saturation magnetization. Note that theskyrmion stability may also be dependent on the saturation magnetization. Meanwhile, the position of the skyrmion may not be controlled due to the center-of-mass motion coupled to the helicity dynamics 36). For example, inFig. 2 we show the current-induced dynamics of a frustrated skyrmion at a moderate driving current density inthe system with the DDI, where the skyrmion with
Bloch-type helicity moves in an almost straight path

toward the left edge of the sample. The trajectory andtime-dependent helicity number of the skyrmion are
given in Figs. 2(a) and 2(b), respectively. The skyrmion
will be annihilated when it touches the edge of the sample. Hence, we propose an effective way to protect thefrustrated skyrmion from being annihilated at the sample edge, and at the same time, to realize the currentinduced switching of the skyrmion helicity in the systemwith the DDI.

Fig. 5 Helicity switching of a frustrated skyrmion in a sample with the obstacle pattern induced by a short current
pulse. (a) The helicity of the skyrmion as a function of time during t = 0 − 300 ps. A relaxed skyrmion with η = π/2 isplaced at the sample center as the initial state at t = 0 ps. The skyrmion is driven by a current density of j = 40 MA/cm2
for 50 ps, followed by a relaxation of 250 ps. The sample size is 21 × 21 spins. The width of the obstacle line is 3 spins.
The obstacle has an enhanced PMA (i.e., Ko/Ku = 10). The skyrmion helicity switches from η = π/2 to η = 3π/2 after theapplication of the current pulse. (b) The in-plane spin components mx,y as functions of time during t = 0 − 300 ps. (c)The out-of-plane spin components mz as a function of time during t = 0 − 300 ps. Note that mx, my, and mz are thenormalized in-plane and out-of-plane spin components for the whole sample. (d) Selected top-view snapshots showing
the spin configurations of the skyrmion at t = 0, 30, 40, 50, and 300 ps. The obstacle pattern with enhanced PMA isindicated by the orange area.

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Fig. 6 Helicity switching of an array of nine frustrated skyrmions in a sample with the square-grid obstacle pattern
induced by a short current pulse. Selected top-view snapshots showing the spin configurations of the frustrated skyrmions at t = 0, 50, and 300 ps. Nine relaxed skyrmions with η = π/2 are placed in the sample as the initial state at t = 0
ps. The system is driven by a current density of j = 40 MA/cm2 for 50 ps, followed by a relaxation of 250 ps. The sample
size is 65 × 65 spins. The width of the obstacle line is 5 spins. The obstacle has an enhanced PMA (i.e., Ko/Ku = 10). The
helicity of all skyrmions switch from η = π/2 to η = 3π/2 after the application of the current pulse. The obstacle patternwith enhanced PMA is indicated by the orange area.
As shown in Fig. 3, we first study the dynamics of asingle isolated frustrated skyrmion driven by a moderatecurrent of j = 40 MA/cm2. The system is a sample of 21 ×
21 spins, where an obstacle pattern is formed by defectlines at the four edges. We assume that the obstacle pattern has an enhanced PMA, i.e., Ko/Ku = 10, which could
be realized by locally modifying the PMA in principle.
Note that we assumed a large value of Ko/Ku in order tomake sure that the skyrmion cannot penetrate the obstacle. In real experiments, it is unnecessary to realize alarge value of Ko/Ku. The width of the defect line is set to
3 spins. As the PMA of the obstacle area is larger thanthat in the interior of the sample, the skyrmion-obstacleinteraction provides a repulsive force, which avoids theskyrmion penetrating the boundary of the obstacle. Sucha feature also protects the skyrmion from be touching theedge of the sample, which may result in a better dynamic
stability in the sample. It can be seen that the skyrmion
moves in a circular path driven by the current and guided
by the inner boundary of the obstacle pattern [see Fig.
3(a)]. We note that the skyrmion dynamics is affected by
the obstacle pattern as soon as the current is applied, because the obstacle is initially very close to the skyrmion.
Namely, the skyrmion is tightly confined by the obstacle
pattern. When the obstacle is initially far from the skyrmion, the skyrmion should, in principle, first move to theleft with a fixed helicity [see Fig. 2(a)] and then performthe circular motion with varying helicity when it is close
to and guided by the obstacle.
As the helicity dynamics is coupled to the center-ofmass dynamics of the skyrmion 30), the helicity of theskyrmion also varies with time during the circular24

motion of the skyrmion, as shown in Fig. 3(b). In Fig. 3(c),we also show some selected top-view snapshots of thespin configurations of the sample, which show that theskyrmion helicity varies between Bloch-type and Néeltype configurations although the Bloch-type ones are favored by the DDI. As long as the driving current is applied, the skyrmion will move in the circular path with avarying helicity. However, it should be noted that theskyrmion driven by the same current of j = 40 MA/cm2
will move toward the left edge and get annihilated fromthe edge in the sample without the obstacle pattern, as
shown in Fig. 4. Namely, the circular motion and helicity
switching of the skyrmion are a result of the skyrmionobstacle interaction. We also note that the helicity
switching is mainly controlled by the driving current, thedipole-dipole interaction, and the skyrmion-obstacle interaction. The frustrated skyrmion is stabilized by the exchange frustration instead of the asymmetric exchangeinteraction (i.e., the Dzyaloshinskii-Moriya interaction).
The exchange frustration is realized by a delicate competition between different exchange interactions, therefore,
the NNN and NNNN exchange interactions may affectthe stability of the skyrmion. However, they may not affect the switching of the skyrmion helicity.
Based on the current-induced dynamic behaviors of afrustrated skyrmion in a sample with the obstacle pattern, we show in Fig. 5 that it is possible to switch thehelicity of a frustrated skyrmion between the Bloch-type
configurations favored by the DDI, i.e., η = π/2 → 3π/2.
To switch the skyrmion helicity, we apply a short current
pulse to drive the dynamics of a single isolated frustrated

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INDEXskyrmion in a sample with the obstacle pattern. The geometry and other system settings are the same as thatused in the simulation in Fig. 3. The current density is j
= 40 MA/cm2 and the pulse length is τ = 50 ps. The pulse
length is determined based on the result given in Fig.
3(b). After the application of a single current pulse, thesystem is relaxed for 250 ps. Namely, the total simulation
time is 300 ps. It can be seen in Fig. 5(a) that the helicityof the skyrmion varies from η = π/2 to η =∼ 3π/2 during theapplication of the current pulse (i.e., t = 0 – 50 ps). Whenthe current is off, the helicity of the skyrmion approaches
η = 3π/2 during the relaxation and finally remains as η =3π/2 at t = 300 ps. Namely, the helicity of the skyrmion isswitched from the Bloch-type configuration η = π/2 to theother Bloch-type configuration η = 3π/2 after the application of a 50-ps-long current pulse.
In Figs. 5(b) and 5(c), we show the time-dependent inplane and out-of-plane spin components of the system
during the helicity switching and relaxation of the system. It shows that the system responds to the driving current instantly during t = 0 − 50 ps and then relatively
slowly relaxes to the energetically favored state during t= 50 − 300 ps. In Fig. 5(d), we show several selected topview snapshots of the spin configurations of the sample.
It can be seen that the skyrmion shows opposite Blochtype helicities at the initial and final states. Namely, theskyrmion helicity is changed from the initial value η = π/2
to η = 3π/2 at the final state.
In Fig. 6, we further demonstrate that it is possible toswitch the helicity of an array of frustrated skyrmions
between the Bloch-type configurations on a square-gridobstacle pattern. The system is a sample of 65 × 65 spins,
where an obstacle pattern is formed by orthogonal defectlines. The width of the defect line is set to 5 spins. Hence,the distance between two nearest-neighboring parallel
defect lines is 15 spins. The geometry and other systemsettings are the same as that used in the simulation in
Fig. 3. It should be noted that the width of the defect line
will not affect the results as we assumed a strong anisotropy for the defect line in this work for the sake of simplicity, i.e., the skyrmion cannot penetrate the defect-line
obstacle.
We put nine relaxed skyrmions with η = π/2 in the sample as the initial state at t = 0 ps. To switch the skyrmion
helicity, we apply a short current pulse to drive the system. The current pulse profile is the same as that used inFig. 5, i.e., the current density is j = 40 MA/cm2 and thepulse length is τ = 50 ps. After the application of a single
current pulse, the system is relaxed for 250 ps. As shownin Fig. 6, the helicity numbers of the nine skyrmions are
switched from η = π/2 to η = 3π/2 in a uniform mannerinduced by the current pulse. We note that the nine skyrmions are far enough from each other, and the applied
spin current is uniform in the whole sample. As a result,each skyrmion can be treated as an isolated skyrmion,and the dipole-dipole interaction will not lead to different
dynamics for different skyrmions. Namely, the dynamics
of each skyrmion is similar to the helicity switching

Fig. 7 A phase diagram showing the helicity switchingof a frustrated skyrmion induced by a short current pulse
in a sample with the obstacle pattern. A relaxed skyrmion with η = π/2 is placed at the sample center as theinitial state at t = 0 ps. The skyrmion is driven by a current pulse, followed by a relaxation until t = 500 ps. The
sample size is 21 × 21 spins. The width of the obstacleline is 3 spins. The obstacle has an enhanced PMA (i.e.,
Ko/Ku = 10). The number in the phase diagram indicatesthe relaxed skyrmion helicity (in units of π) after the application of the current pulse.
dynamics of a single skyrmion given in Fig. 5. Therefore,
in principle, it is possible to switch the helicity of an arrayof many skyrmions in a large-scale sample with thesquare-grid obstacle pattern. Such an array of manyskyrmions may be useful for building skyrmion-based
multistate memory devices.
We also point out that the current-induced switchingprocess of the skyrmion helicity on the obstacle patterndepends on the applied current density and pulse length.
As shown in Fig. 7, for higher current density, the minimum required pulse length to switch the helicity could be
reduced. Namely, for lower current density, the minimum required pulse length to switch the helicity may be
increased. However, when the current density is smaller
than 30 MA/cm2, the skyrmion helicity cannot beswitched, indicating there is a critical current density beyond which the helicity switching can be achieved.
4. Conclusion
In conclusion, we have investigated the current-induced dynamics of a frustrated skyrmion in a sample
with or without the obstacle pattern. The obstacle pattern with enhanced PMA could provide the skyrmion
from being annihilated at the sample edge due to theskyrmion-obstacle repulsion, and more importantly,
could lead to the circular motion of the frustrated

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INDEXskyrmion with time-varying helicity driven by a moderate current density. Namely, the repulsive interaction between the skyrmion and the defect-line obstacle plays animportant role in the helicity dynamics of the skyrmion.
In the system without the obstacle pattern, the frustrated skyrmion will move with a fixed Bloch-type helicity due to the DDI and may be annihilated at the sample
edge. We have also studied the current-induced helicity
switching of a single frustrated skyrmion in a sample
with the obstacle pattern, where we find that the helicityof the skyrmion can be switched from a Bloch-type configuration to the other Bloch-type configuration driven bya short current pulse. In addition, we show that the current-induced switching of the skyrmion helicity can be realized for an array of frustrated skyrmions on a squaregrid obstacle pattern. Our results suggest that the helicity degree of freedom of topological spin textures may beeffectively controlled on nanostructures with well-designed obstacle patterns. Our results also show the possibility that the helicity of skyrmions may be used in
spintronic functions.
Acknowledgements X.Z. was a JSPS International Research Fellow supported by JSPS KAKENHI (Grant No.
JP20F20363). J.X. was a JSPS International Research
Fellow supported by JSPS KAKENHI (Grant No.
JP22F22061). O.A.T. acknowledges support from theAustralian Research Council (Grant No. DP200101027),
Russian Science Foundation (Grant No. 21-42-00035),
NCMAS grant, and the Cooperative Research Project
Program at the Research Institute of Electrical Communication, Tohoku University. G.Z. acknowledges support
from the National Natural Science Foundation of China(Grants No. 51771127, No. 52171188, and No.
52111530143). J.Y. acknowledges support from the National Natural Science Foundation of China (Grant No.
51731001). Y.Z. acknowledges support from the Guangdong Special Support Project (Grant No. 2019BT02X030),
Shenzhen Fundamental Research Fund (Grant No.
JCYJ20210324120213037), Shenzhen Peacock Group
Plan (Grant No. KQTD20180413181702403), Pearl River
Recruitment Program of Talents (Grant No.
2017GC010293), and National Natural Science Foundation of China (Grants No. 11974298, No. 12004320, andNo. 61961136006). M.E. acknowledges support from theGrants-in-Aid for Scientific Research from JSPS
KAKENHI (Grants No. JP18H03676 and No.
JP17K05490) and support from CREST, JST (Grants No.
JPMJCR20T2 and No. JPMJCR16F1). X.L. acknowledges support by the Grants-in-Aid for Scientific Research from JSPS KAKENHI (Grants No. JP20F20363,
No. JP21H01364, No. JP21K18872, and No.
JP22F22061).
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Received Oct. 05, 2022; Revised Oct. 31, 2022; Accepted Nov. 10,
2022

Journal of the Magnetics Society of Japan Vol.47, No.1, 2023

27

INDEX

Editorial Committee Members・Paper Committee Members
T. Kato and S. Yabukami (Chairperson), K. Koike, K. Kobayashi and Pham NamHai (Secretary)
T. Hasegawa
K. Hioki
S, Inui
K. ItoK. KamataH. Kikuchi
S. Kokado
Y. Kota
T. Kouda
A. Kuwahata
S. Muroga
Y. Nakamura
H. Nakayama
T. Narita
K. Nishijima
D. Oyama
T. SatoT. Suetsuna
T. Takura
K. ThamN. Wakiya
T. Yamamoto
K. Yamazaki

Y. Kamihara
K. Masuda
T. Nozaki
T. Tanaka

N. Adachi
T. GotoH. KuraE. Shikoh
M. Toko

M. GotoT. Kojima
M. Sekino
K. Tajima
S. Yoshimura

H. AokiS. Honda
T. MakiK. Suzuki
S. YakataK. Bessho
S. Isogami
M. NaoeI. TagawaS. Yamada

M. DoiM. Iwai
M. OhtakeY. Takamura
A. YaoT. DoiN.Kikuchi
S. Seino
M. Takezawa
M. Yoshida

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編 集 委 員・論 文 委 員
加 藤 剛 志 （理事） 薮 上
伊藤啓太
乾
成里
小田洋平
佐藤
拓
成田正敬
西島健一
脇谷尚樹

信 （理事） 小 池 邦 博 （幹事） 小 林 宏 一 郎 （幹事） Pham NamHai（幹事）
小山大介
鎌田清孝
神原陽一
菊池弘昭
桑波田晃弘
神田哲典
末綱倫浩
田倉哲也
田中哲郎
Kim Kong Tham
仲村泰明
野崎友大
長谷川崇
日置敬子
増田啓介
室賀
翔
山崎慶太

青木英恵
後藤太一
土井正晶
山田晋也

磯上慎二
鈴木和也
都甲
大
吉村
哲

安達信泰
仕幸英治
土井達也
吉田征弘

岩井守生
清野智史
直江正幸

大竹
充
関野正樹
別所和宏

菊池伸明
高村陽太
本多周太

藏
裕彰
田河育也
槙
智仁

小嶋隆幸
竹澤昌晃
八尾
惇

古門聡士
中山英俊
山本崇史

後藤
穣
田島克文
家形
諭

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