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ISSN 2432-0250

Vol.43 No.4
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2019

Magnetic Recording
Impact of Curie Temperature Variation on Bit Error Rate in Heat-Assisted Magnetic Recording
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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

T. Kobayashi, Y. Nakatani, and Y. Fujiwara…70

K. Ito, M. Hayashida, M. Mizuguchi, T. Suemasu, H. Yanagihara, and K. Takanashi…79

Thin Films, Fine Particles, Multilayers, Superlattices
Fabrication of L10-FeNi Films by Denitriding FeNiN Films

Biomagnetism / Medical Applications
Suppression of Heat Generation in Magnetic Stimulation Coil Applied for Treating Dysphagia

広告◇計測エンジニアリングシステム株式会社

H. Mori, H. Kagaya, S. Izumi, K. Yashima, and T. Takagi◇東英工業株式会社

…84

43

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

4

2019

INDEX

Journal of the Magnetics Society of Japan
Vol. 43, No. 4
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Magnetic Recording
Impact of Curie Temperature Variation on Bit Error Rate in Heat-Assisted Magnetic Recording……………………………………………………………… T. Kobayashi, Y. Nakatani, and Y. Fujiwara

70

Thin Films, Fine Particles, Multilayers, Superlattices
Fabrication of L10-FeNi Films by Denitriding FeNiN Films……………… K. Ito, M. Hayashida, M. Mizuguchi, T. Suemasu, H. Yanagihara, and K. Takanashi

79

Biomagnetism / Medical Applications
Suppression of Heat Generation in Magnetic Stimulation Coil Applied for Treating Dysphagia……………………………………………… H. Mori, H. Kagaya, S. Izumi, K. Yashima, and T. Takagi

Board of Directors of The Magnetics Society of Japan
President:

K. Nakagawa

Vice Presidents:

S. Sugimoto, S. Matsunuma

Directors, General Affairs:

K. Niiduma, H. Saito

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
Auditors:

R. Nakatani, Y. Takano

84

INDEX
J. Magn. Soc. Jpn., 43, 70-78 (2019)<Paper>Impact o f Curie Te mperature V ariatio n o n Bit Error Ratein He at-Assis ted M agne tic Reco rding
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*!

The Curie temperature T c variation problem in heat-assisted magnetic recording is discussed. We describe thephysical implication of the T c variation problem, and provide ways of improving the writing property by employing
our simplified model calculation. The bit error rates for mean Curie temperatures of 600 and 700 K are examined.
The T c variation increases both write-error (WE) and erasure-after-write (EAW). The main related calculation! grain column number in one bit and the thermal gradient for the down-track direction.
parameters are the! column number is effective in reducing WE and EAW caused by the T variation. Furthermore,
Increasing the graincincreasing the thermal gradient is necessary since EAW is high. Although a higher writing field of 12 to 14 kOe isnecessary, a bit error rate less than 10-3 can be achieved for recording densities of 4 or 2 Tbpsi under the conditions
used in this study even though the standard deviation of the Curie temperature is 4 %.

!

Key wor ds : heat-assisted magnetic recording, field sensitivity, Curie temperature, variation
2. Calcula tion Metho d

1. I ntro duction

Heat-assisted magnetic recording (HAMR) is a
2.1 Calcula tion condi tions
promising candidate as a next generation magnetic
The areas S of one bit are 161 and 323 nm2 forrecording method that can operate beyond the trilemma
recording densities of 4 and 2 Tbpsi, respectively. The
limit1).
medium was assumed to be bit patterned media (BPM).
The writing field switching timings for an ordinary
We have already proposed a new HAMR model!
granular medium and this BPM model are shown incalculation2)~4). We have also shown in our improved
Figs. 1 (a) and (b), respectively. H w and " min = DBP / v
model calculation that the signal-to-noise ratio derived
by the conventionally used micromagnetic calculation
are the writing field and the time available for writing
can be explained using the temperature dependences ofeach bit, respectively, where DBP and v are the bit
the grain magnetization reversal probability and thepitch and the linear velocity, respectively. There is a
! timing! "t in an ordinary
attempt period, whose inverse is the attemptfluctuation of switching5)
frequency . A feature of our model calculation is that it
granular medium as shown in Fig. 1 (a). However, we!
assume "t = 0, and !
is easy to grasp the physical implication of the HAMR
when the time t = 0, the writing
writing process and the calculation time is short.
grain temperature T becomes the mean Curie!
Since HAMR is a writing method in which thetemperature T cm as shown in Fig. 1 (b) for our
medium is heated to reduce coercivity at the time of
The problem of!discussion of the intrinsic phenomenon.
!
"t is a future subject. The H w direction is upward
writing, the coercivity of the medium can be reduced by!
any amount. However, micromagnetic simulation has
between t = 0 and " min , and downward when t < 0shown that a relatively high writing field is necessary6).
and !t > " min .
The actual HAMR system is very complicated, andIt was assumed that the spatially uniform writing!
!
various problems are intertwined. Therefore, we havefield moves to the down-track
direction successively,!
!
!
separated problems in a simplified model using our
the direction was perpendicular to the medium plane,
model calculation. We have divided the topic of ! and the rise time was zero. Neither the demagnetizing
increasing writing field sensitivity into four problems
nor the magnetostatic fields were considered during
using the bit error rate calculated with our model for
writing since they are negligibly small.
HAMR, and we have discussed the calculation
The grain arrangements for an ordinary granularparameters related to the problems7). The four
medium and this BPM model are also shown in Figs. 1(c) and (d), respectively, for an m " n = 4 "1 grain
problems are write-error, erasure-after-write6), astatistical problem7), and the damping constant3).
arrangement where m and n are the grain numbers
It has been reported that variation in the Curie
in one bit for the cross-track and down-track directions,temperature T c is a serious problem in HAMR8). In
respectively. T cij and Dij are the Curie temperature!
this study, we discuss a fifth problem, namely the T c
and the grain size, respectively. There is also a!
!
fluctuation of position "x < (Dm + ") / 2 in an ordinary
variation problem, and we provide some ways of
improving the writing property employing our model
granular medium as shown in Fig. 1 (c) where Dm and!
! the mean!
" arecalculation.
grain size and the non-magnetic

!

!
70

Journal of the Magnetics! Society of Japan Vol.43, No.4, 2019!

INDEX!

!

spacing, respectively. However, we assume "x = 0 as
shown in Fig. 1 (d) in this BPM model, and the problemof "x is also a future subject. The thermal gradient"T /"y for the cross-track direction!was assumed to be
0 K/nm since complex situations disturb our intrinsic
discussion. Although the problem of "T /"y is also afuture subject, "T /"y # 0 will affect the results.
The mean grain size Dm was determined by

D!
m =

!

!

!

S
"#
mn
!

!

(1)

where " = 1 nm was assumed. The track and bit
pitches were DTP = m(Dm + ") and DBP = n(Dm + ") ,! respectively, and then S = DTP " DBP .
! The calculation conditions are summarized in Table 1,
and the calculation parameters were the recording! the grain number per! bit mn , the mean Curie
density,!
temperature T cm , the standard deviations of the Curie
temperature " Tc /T cm , the Gilbert damping constant " ,the anisotropy constant ratio K u / K bulk , the linear!
velocity v , and the thermal gradient "T /"x . "T /"x!
was assumed to be constant regardless of the position,!
and !the heat distribution moves to the down-track!
deviation of the!direction successively. The standard!
!
grain size " D / Dm and the grain height h were 10 %and 8 nm, respectively, and so the grain volume Vm for
Dm was Dm " Dm " h .
The medium was characterized by (1) T cm , (2) " ,! (3) K / K , which is the!intrinsic ratio of the
and
u
bulk
! FePt K 9).
medium anisotropy constant K u to bulku!
(1) If T cm is low, a larger K u / K bulk is necessary10).
!
!600 and 700 K. The
Therefore, we chose T cm values of!standard deviations of the Curie temperature " /TTccm!
were assumed to be !
0, 2, and 4 %.
! (2) The " value !of FePt just below the Curie
temperature! T c is unknown. Therefore, we calculated!
the bit error rate using " = 0.1 and 0.01.
(3) The K u / K bulk value must be larger than the value!
required for 10 years of archiving.
!
Figure2 shows the minimum K u / K bulk value for 10!
years of archiving as a function of the mean grain size
!D . The inserted scales indicate the grain number perm
bit mn corresponding to Dm for recording densities of!
4 and 2 Tbpsi. The minimum
K u (300 K) value wasroughly estimated using

K u (300 K)V!
m
> 60
!
kT

!

(2)

where k and T = 300 K are the Boltzmann constantand temperature, respectively. And then, the minimum
K u / K bulk value was obtained using the relationship!
between K u (300 K) and T c for various K u / K bulk!
!
values7).
It is also confirmed from Fig. 2 that if T cm is low, alargerK u / K bulk is necessary10). Experimentally!
! FeNiPt11) andobtained results, !namely those for
12)
FePtRu films, are at most between K u / K bulk = 0.4!

!
!

and 0.67).

Fig. 1 (a), (b) Writing field switching timing, and (c),(d) grain arrangement for (a), (c) an ordinary granularmedium and (b), (d) this BPM model.
Table 1 Calculation conditions.

Fig. 2 Minimum anisotropy constant ratio K u / K bulk
necessary for 10 years of archiving as a function ofmean grain size.

!
2.2 Bi t error ra te calculation
The magnetization direction of the grains wascalculated using the magnetization reversal probability
for every attempt time in our model calculation2)~5),7).
The initial magnetization direction, namely upward
or downward, is randomly decided. The switchingprobability
P" for each attempt where themagnetization M s and the writing field H w change!

! Vol.43, No.4, 2019
Journal of the Magnetics Society of Japan!

71

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from antiparallel to parallel is expressed as

P" = exp("K # ") .

t ini2 " t ini1 = # APm =(3)

On the other hand,

P+ = exp("K # + )!

is the probability for each attempt where M s and H wchange from parallel to antiparallel. In these equations,!

!

2
K u (T )V $Hw 'K " #(T , H w ) =&1#) ( H k (T!) " H w ) ,!
kT % H k (T ) (K " #(T , H w ) = 0

!

!
!
!
!

(6)

!

where K u , V , k , T , and H k = 2K u / M s are theanisotropy constant, the grain volume, the Boltzmann
constant, the writing grain temperature, and the!
anisotropy field, respectively.
! ! !
! The
!
temperature dependence of M s was determinedby employing a mean field analysis13), and that of K u
was assumed to be proportional to M s2 11). The Curie
temperature T c was adjusted by the Cu simple! . M (T , T ) is a function
dilution of (Fe 0.5 Pt 0.5 )1" z Cuzscof T c and T , and M s (T c = 770 K, T = 300!K) = 1000
! (Cu composition z = 0).
emu/cm3 was assumed for FePt!
K u (T c , K u / K bulk , T ) is a function of T c , the anisotropy!
constant
ratio K u /!
K bulk , and T . K u (T c = 770!K,!
K u / K bulk =!1, T = 300 K) = 70 Merg/cm3 was assumed!
!
for FePt (z = 0). We used M s (T c , T ) andK u (T c , K u / K bulk , T ) for T cm! = 600 and 700 K in this! !
paper. !
On the other hand, the attempt time t k , whose!
interval is the mean of the! attempt period " AP , isdetermined in !the following5). The inverse of theattempt period is the attempt frequency f 0 = 1 /" AP .
!
Since there was a very good linear relationshipbetween!
f 0 and T , we used!

f 0 (T ) =

2a"
1+"2

V K u / K bulk !
(T c # T )
V0
0.4

(7)

where a = 4.67 and 5.0 (nsK)-1 for T cm = 600 and 700
K, respectively, and V0 = 193 nm3. The f 0 value! becomes zero at T = T c as shown in Eq. (7).
t ini1 at T = T th = T c " 1 K ,! We defined the initial time
which is close to T c , using !

!
!
! T c " T th
(8)t ini1 =!
v(#T /#x) !
!
since " AP = 1 / f 0 diverges to infinity at T = T c . The
next initial time t ini 2 was calculated using the mean
attempt period " APm from t ini1 to t ini 2 expressed by

!
!

tini2

$ # (t)dt . (9)tini1

1
t k+1 " t k

!

tk+1

$ # (t)dt .
tk" M ij (T c , 300 K)Dij2
i ,jmn # M s (T cm , 300 K)Dm2> 0.5,

72

!

(10)

(11)

the bit is error free. The number of calculation bits is105. The criterion determining whether or not recording
is possible was assumed to be a bit error rate (bER) of
10-3. Increasing the writing field sensitivity means
lowering the writing field at which the bER value is 10-3.
The bER in this study is useful only as a comparison.
The calculation procedure is described below. First,
the medium was characterized by T cm , " , andK u / K bulk . The grain temperature fell with time fromT c according to the linear velocity v and the thermal
gradient "T /"x for the down-track direction. The!
attempt times were calculated.!The magnetic
propertyand then P± were calculated by undertaking a mean!
field analysis for every attempt time. The!
magnetization direction was determined by the Monte
Carlo method for every attempt time. Then the bER! obtained.
was
3. Calcula tion Re sults
We have divided the topic of increasing the writing
field sensitivity into four problems for heat-assisted
magnetic recording, and we have discussed thecalculation parameters related to the problems7) as
follows.
(1) Write-error problem
Reducing the anisotropy constant ratio K u / K bulk
and/or the linear velocity v is effective in reducing
write-error (WE), namely, in increasing the writing
field sensitivity.
!
(2) Erasure-after-write problem!
Erasure-after-write (EAW) must be sufficiently low ina low writing field region. Increasing K u / K bulk , thethermal gradient "T /"x for the down-track direction,
and/or the grain column number in one bit n iseffective in reducing EAW.
!
(3) Statistical problem!
Increasing the grain number per bit mn under a!
constant mean grain size is effective in increasing the

!
!

AP

Errors occur in some grains of a bit. We assume that
if the surface magnetic charge of the grains where themagnetization turns in the recording direction" M ij (T c , 300 K)Dij2 is more than 50 % of the total
surface magnetic charge in one bit, the bit is error free.
Namely, if

!
!

AP

We assumed that the first attempt time t1 is randomly
decided between t ini1 and t ini 2 . And the attempt time
t k+1 (k " 1) is determined with the following recurrence
formula:!
!
t k+1 " t k = # APm =

!

(5)

2
K (T )V #Hw &!
K " + (T , H w ) = u%1+( ,kT $ H k (T ) '!

!

( H k (T ) < H w ) ,

and

!

!

!

(4)

1
t ini2 " t ini1!
Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

INDEX

writing field sensitivity for a statistical reason.
However, increasing mn under a constant recording
density is ineffective when there is no Curie
temperature variation. Nevertheless, there is astatistical effect since the recording time window!
decreases and the attempt period increases.
(4) Damping constant problem
When the Gilbert damping constant " is small,writing is difficult and a high writing field is necessary
since the attempt period is long. Reducing v iseffective in increasing the writing field sensitivity since!
WE is dominant for a small " .
In this study, we discuss a fifth problem, namely:!
(5) Curie temperature variation problem
The main related parameters are n and "T /"x .

!

!

3.1 " = 0 .1, Tcm = 700 K , and "T/"x = 15
K/nm
!
!
!
First, we deal with the damping constant " = 0.1,
Curie temperature T cm = 700 K, and the! the mean!
thermal !gradient "T /"x = 15 K/nm. As shown in aprevious paper7), when " = 0.1, T cm = 700 K, and the!
standard deviation of the Curie temperature " Tc /T cm!
= 0 %, a 4 Tbpsi recording ( 4 " 1 grain arrangement)!
can be achieved as shown in Fig. 3, which shows the bit!
!
error rate (bER) dependence
on writing field H w . An
anisotropy constant ratio K u / K bulk of!about 0.35 is the!
best condition7) under a linear velocity v of 10 m/s anda thermal gradient "T /"x of 15 K/nm even though the! of archiving is
minimum K u / K bulk value for 10 years!
0.19 as shown in Fig. 2. If there is a Curie temperature!
T c variation, the signal-to-noise ratio will be degraded8),!
and then the bER will increase as shown in Fig. 3. The!
decrease and increase in bER as H w increases arecaused by a reduction in the write-error (WE) and anincrease in erasure-after-write (EAW)6), respectively.
Therefore, the T c variation increases both WE and!
EAW.
!
This is explained using Fig. 4, which shows the timedependence of the grain magnetization reversal!
probabilities
P" for grains with T c of T cm + " Tc , T cm ,and T cm " # Tc . The filled circles indicate the attempt!
times t k when t1 = t ini1 and t 2 = t ini2 . In this paper,
figures of P" with time are shown in the same format.
!
! time t = 0 is the! onset! of the !
Thewriting time,! which corresponds to the 1st column grain temperature! becoming! T . The attempt!
frequency f 0 is low justcm!
below T c as shown in Eq. (7), and then the attempt!
!
period " AP = 1 / f 0 is long just after t = 0 for a grainwith T c = T cm . The temperature decreases with time,! the mean attempt period! "andAPm , which is the! interval between the attempt times, decreases! accordingly. The time t = " ! is the end of the writing !
min! time, which corresponds to the time available for
writing each bit and " min!= DBP / v as shown in Fig. 1.

!

!

Fig. 3 Dependence of bit error rate on writing field forvarious standard deviations of Curie temperature" Tc /T cm(" = 0.1, T cm = 700 K, 4 " 1 grainarrangement).

!

!

!

Fig. 4 Time dependence of grain magnetization
reversal probabilities P" and temperature for grains
with Curie temperatures of T cm + " Tc , T cm , andT cm " # Tc .
WE means !
that the magnetization does not switch to!
the recording direction,!and WE occurs
during writing( 0 " t " # min ). If there is a T c variation, WE increases
from grains with a higher T c , for example,
T c = T cm + " Tc in Fig. 4. We introduce a new parameter,
namely a Curie temperature variation window " Tc :

!
# Tc
.
" Tc =
v($T /$x)

!

(12)

!

The writing time is advanced for higher T c grains, forexample, by " Tc for a grain with T c = T cm + " Tc . Even
at a time before zero, the grain temperature is lower
than T c , and then the grain is magnetized in the!
downward direction, namely opposite
to the recording!
!
direction. At time zero, the direction of the writing fieldchanges. The P" value for a grain with T c = T cm + " Tc
at t = 0 designated by the open circle in Fig. 4 is low.
Therefore,
theprobability
with
which
the
magnetization reverses to the recording direction is low.
!
Then,!WE increases.
On the other hand, EAW is grain magnetization
reversal in the opposite direction to the recording!
Journal of the Magnetics Society of Japan Vol.43, No.4, 201973

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direction caused by changing the H w direction at theend of the writing time " min , and EAW occurs after
writing ( t > " min ). If there is a T c variation, EAW
increases from grains with a lower T c , for example,! writing time is delayed!forT c = T cm " # Tc in Fig. 4. The!
lower T c grains, for example, by " Tc for a grain with!
! at "
T c = T cm " # Tc . The P" value
min is important for! with T = T " # at
EAW. The P" value for a grain
c
cm
Tc
!
" min designated by the open circle in Fig. 4 is high.
! Therefore, the!
probability
with
which
the
! reverses to! the direction opposite to !
magnetizationthat! increases.
of !
recording is high. Then, EAW!
!
!

2 " 2 grain arrangement does not change. On the other
hand, the writing time for the 2nd column of the 2 " 2grain arrangement is delayed by a time corresponding
to a grain pitch Dm + " as shown in Fig. 6 (b). The
H w direction is the recording direction even at a time!
that corresponds to the grain temperature withT c = T cm2 + " Tc becoming T c . Therefore, WE for the 2nd! the 2 " 2 grain arrangement decreases.
column of
!

!

(a)

Fig. 5 Dependence of bit error rate on writing field for
4 " 1 , 2 " 2 , and 3" 3 grain arrangements ( " = 0.1,
T cm = 700 K, " Tc /T cm = 4 %).
Figure 5 shows the bER dependence on H w for!
!
4 " 1 , 2 " 2 , and 3" 3 grain arrangements where!
is 4 %. A comparison of the bER for" Tc /Tcm
m " n = 4 "1 and that for a 2 " 2 grain arrangement! , the K / K
where the grain numbers per bit mn
u
bulk
!
!
values, and the mean grain sizes Dm are the same for

!
!

!

!
!
!

!

!
!

!

avoiding these problems, reveals that the bER for the!
latter is lower than that for the former in all calculated!
H w ranges. In other words, both! WE and EAW!
decrease. This is also explainedusing Fig. 6 in which
the time dependences of P" for (a) the 1st and (b) the
2nd columns of a 2 " 2 grain arrangement are shown.
The P" values in Fig. 4 and Fig. 6 (a) are identical.
However, the " min value in Fig. 6 is twice that in Fig. 4.
The P" value at! " min in Fig. 6 (a) is sufficiently low!
even for a grain with T c = T cm1 " # Tc . Accordingly, EAW
for the 1st column of the 2 " 2 grain arrangement!
decreases.
On the other hand, the P" values in Fig. 4
and Fig. !
6 (b) are also identical except for time, and!thewriting time! in Fig. 6 (b) is delayed by a time!
corresponding to the grain pitch Dm + " . Consequently,
the P" values at " min in !
Fig. 4 and Fig. 6 (b) are thesame, and EAW for the 2nd column of the 2 " 2 grain!
arrangement does not change. Comprehensively!
increasing the grain column
number n is effective in!
reducing EAW.
!
!
Increasing n is also effective in reducing WE. The
H w switching timings at t =!0 in Fig. 4 and Fig. 6 (a)are identical. Hence, WE for the 1st column of the!
74

Next, we make a comparison between bER for the!
2 " 2 grain arrangement
and that for the 3" 3 grain!
arrangement in Fig. 5. It was assumed that " Tc does
not increase even if Dm is reduced. When the 2 " 2grain arrangement (the grain number per bit mn = 4),!
Dm = 5.4 nm, and K u / K bulk = 0.35 is necessary for a! the 3" 3 grain
low bER. On the other hand, when!
!
arrangement ( mn = 9), Dm = 3.2 nm, and then!
K u / K bulk = 0.52 is necessary for 10 years of archiving.
Reducing! Dm , and then increasing n is effective in!
reducing both WE and EAW as shown in Fig. 5. This is!
! Fig. 7, which shows the time
also explained using
dependences of P" for (a) the 1st, (b) the 2nd, and (c)!
the!3rd columns of the 3" 3 grain arrangement. The
rate at which P" decreases with time becomes slow
according to Eq. (5), in which K u ,V , and

!

!

!

(b)
Fig. 6 Time dependence of grain magnetization
reversal probabilities P" and temperature for (a) 1stand (b) 2nd columns of a 2 " 2 grain arrangement.

!

!

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019 !

!

INDEX!
!

H k = 2K u / M s , namely K u / K bulk and Dm havedifferent values. Furthermore, the recording time
window6) " RW becomes short where " RW is the timefor P" = 1, namely H k < H w according to Eq. (5). And! " = 1 / f for !3" 3 is somewhat !
the attempt periodAP0longer than that for the 2 " 2 grain arrangement!
accordingto Eq. (7) since !
Dm " K u / K bulk for 3" 3 issomewhat !smaller than that for the 2 " 2 grain!
! Although various
arrangement.
factors are involved,!
!
the EAW reduction is roughly explained by the fact that!
! in Fig. 7 (b) is smaller than that
the P" value at " min!
in Fig. 6 (b). The WE reduction is explained as follows.

!

The H w direction is the recording direction when thetemperature of the 2nd and the 3rd column grains
becomes T c as shown in Figs. 7 (b) and (c),respectively.
3.2 " = 0 .1, Tcm = 700 K , and "T/"x = 20!
K/nm
A bER less than 10-3 cannot be achieved as shown in
Fig. 5 since EAW is high. Therefore, we calculate the!
! the thermal gradient"T /"x = 20 K/nm
bER usinginstead of 15 K/nm for the suppression of EAW. The
bER calculation results are shown in Fig. 8. A bER lessthan 10-3 can be achieved for the 3" 3 grain!
arrangement and "T /"x = 20 K/nm as shown in Fig. 8
(b).

!

!
!

(a)

(a)

(b)
Fig. 8 Dependence of bit error rate on writing field forthermal gradients "T /"x = 15 and 20 K/nm ( " = 0.1,
T cm = 700 K, (a) 2 " 2 and (b) 3" 3 grainarrangements).

(b)

!

!

(c)
Fig. 7 Time dependence of grain magnetization
reversal probabilities P" for (a) 1st, (b) 2nd, and (c) 3rd
columns of the 3" 3 grain arrangement.

!

!

!

Figure 9 shows the time dependence of P" for the!
!
respective columns. When "T /"x increases, the Curie
temperature variation window " Tc will be reduced
according to Eq. (12). " Tc is the time during which! to H opposite
grain with T c = T cm1 + " Tc is exposedw!
to the recording direction as shown Fig. 9 (a). Therefore,
the reduction of " Tc! is advantageous for the
suppression of !
WE caused by the T c variation. On the! hand, as "T /"x increases,! the writing fieldothersensitivity becomes somewhat worse7) since the rate at!
which P" decreases
with time becomes steep, and the! reduced when P is highattempt number is somewhat"!

!

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019!

75

INDEX

as shown in Fig. 9. Comprehensively increasing "T /"xis not effective in reducing WE as shown in Fig. 8.
As shown in a previous paper7) and as seen bycomparing Fig. 7 and Fig. 9, increasing "T /"x is!
!
effective in reducing EAW since the P" values at " minbecome low. The resultant bER is shown in Fig. 8, anda bER less than 10-3 can be achieved. However, a higher!
writing field is necessary if there is a T c variation.

!

!

!

!

3.3 " = 0.1 and Tcm = 600 K
Next, we discuss a mean Curie temperature T cm =600 K rather than T cm = 700 K.
Figure 10 (a) shows the bER dependence on H w for!
a 2 " 2 grainarrangement. Although the minimum! 10 years ofanisotropy constant ratio K u / K bulk for!
archiving is 0.27 as shown in Fig. 2, K u / K bulk = 0.35 is! less than 10-3
necessary for a low bER. However, a bER
cannot be achieved even for "T /"x = 20 K/nm.
The results for a!3" 3 grain arrangement are shownin Fig. 10 (b). A large !
K u / K bulk value of 0.75 isnecessary for 10 years of archiving. A bER less than!
10-3 can be achieved for "T /"x = 20 K/nm.

!

!

!

(a)
(a)

(b)

(b)
Fig. 10 Dependence of bit error rate on writing field
for thermal gradients "T /"x = 15 and 20 K/nm ( " =0.1, T cm = 600 K, (a) 2 " 2 and (b) 3" 3 grainarrangements).

!
!
We summarize the writing field H w required for thedamping constant " = 0.1 in Table 2. A recording
density of 4 Tbpsi is available for a linear velocity v =

!

!

(c)
Fig. 9 Time dependence of grain magnetization
reversal probabilities P" for (a) 1st, (b) 2nd, and (c) 3rd
columns of the 3" 3 grain arrangement ( "T /"x = 20K/nm).

!

!

!

!

10 m/s under the conditions used in this study. When!
the mean Curie temperatures
T cm = 700 K, 2 " 2 (the!
mean grain size Dm = 5.4 nm) and 3" 3 (Dm = 3.2!
nm) are necessary for the standard deviations of theCurie temperature " Tc /T cm = 0 % and 4 %,!
!
respectively. Although
the minimum anisotropy!
! of archiving areconstant!ratios K u / K bulk for 10 years
0.19 and 0.52, the K u / K bulk values necessary for bER! and 0.52 for " /T = 0 % and 4 %,< 10-3 are 0.35
Tc
cm

!
76

!

! 2019Journal of the Magnetics Society of Japan Vol.43, No.4,

INDEX

respectively. Furthermore, a larger thermal gradient"T /"x of 20 K/nm is necessary for " Tc /T cm = 4 %. Insummary, H w > 8 and 12 kOe are necessary for" Tc /T cm = 0 % and 4 %, respectively.
When T cm = 600 K, a K u / K bulk of 0.75, which islarger than that of 0.52 for! T cm = 700 K, is necessary
for! " Tc /T cm = 4 % due to a low T cm (see Fig. 2).

!
!

!

!
Table 2 Writing !field H w required for damping!
constant " = 0.1.

!

(a)

!

!

!

!

3.4 " = 0.01
In this section, we discuss a damping constant " =0.01 instead of " = 0.1. In previous papers5,7), we have
! shown that if " is small, WE is dominant and writing
is difficult since the attempt period is long and there is!
almost no opportunity for writing. Since WE is!
dominant, we used a slow linear velocity v of 5 m/s.
!
Figures 11 (a) and (b) show the bER dependence on !
H w for 3" 3 and 4 " 4 grain arrangements,
respectively, where T cm = 700 K. A larger "T /"x of!
20 K/nm is necessary in both cases. With the 4 " 4grain arrangement, a higher H w is necessary since a!
!
larger K u / K bulk is required for 10 years of archiving.
!
!
The results for T cm = 600 K are shown in Fig. 12!
where the same tendency can be seen.
!
We also summarize the writing field H w required! for the damping constant " = 0.01 in Table 3. A
! density of only 2 Tbpsi is available even for arecordinglinear velocity v = 5 m/s under the conditions used inthis study since writing is !difficult. The grain!
arrangement and the anisotropy constant ratio
K u / K!
bulk are 3" 3 (the mean grain size Dm = 5.0nm) and about 0.3, respectively, regardless of the mean
Curie temperature T cm and the standard deviation of
the Curie temperature " Tc /T cm . A larger thermal!
!
gradient "T /"x of 20 K/nm is necessaryfor " Tc /T cm= 4 %. In summary, H w > 12 and 14 kOe are needed! = 0 % and 4 %, respectively.
for " Tc /T cm!
" problem it may be effective to
To solve the small!
use an exchange-coupled composite !medium with a! and a large K / K
large " layerubulk layer.

!

!
!

!

!
!

(b)
Fig. 11 Dependence of bit error rate on writing field
for thermal gradients "T /"x = 15 and 20 K/nm ( " =0.01, T cm = 700 K, (a) 3" 3 and (b) 4 " 4 grainarrangements).

!

!
!

!

(a)

(b)
Fig. 12 Dependence of bit error rate on writing fieldfor "T /"x = 15 and 20 K/nm ( " = 0.01, T cm = 600 K,(a) 3" 3 and (b) 4 " 4 grain arrangements).

!

!

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019!
77

INDEX

Table 3 Writing field
constant " = 0.01.

H w required for damping!

!

When " = 0.01, WE is dominant and writing isdifficult. Therefore, it is necessary to lower v . A
recording density of 2 Tbpsi was available for v = 5
m/s and " Tc /T cm = 4 % under the conditions used in!
this study.
Acknowledge ment!
!

We acknowledge the support of!
the Advanced Storage Research Consortium (ASRC),
Japan.

References

4. Conclusion!

We used our simplified model calculation to discuss
the Curie temperature T c variation problem inheat-assisted magnetic recording. The T c variation
increased both write-error (WE) and erasure-after-write(EAW). Increasing the grain column number in one bit!
was effective in reducing
WE and EAW caused by the!
the thermal
T c variation. Furthermore, increasing
gradient for the down-track direction was necessary
since EAW was high. A higher writing field of 12 to 14
kOe was necessary when the standard deviation of theCurie temperature " Tc /T cm = 4 %.
When the damping constant " was 0.1, a recording
density of 4 Tbpsi was available for a linear velocity v= 10 m/s under the conditions used in this study eventhough "!Tc /T cm = 4 %. When the mean Curie!
temperature T cm = 600 K, a larger anisotropy constant!
ratio of 0.75 than that of 0.52 for T cm = 700 K wasnecessary due to a low T cm .

1) S. H. Charap, P. -L. Lu, and Y. He: IEEE Trans. Magn., 33 ,
978 (1997).
2) T. Kobayashi, F. Inukai, K. Enomoto, and Y. Fujiwara: J.
Magn. Soc. Jpn., 41, 1 (2017).
3) T. Kobayashi, Y. Nakatani, F. Inukai, K. Enomoto, and Y.
Fujiwara: J. Magn. Soc. Jpn., 41 , 52 (2017).
4) T. Kobayashi, Y. Nakatani, K. Enomoto, and Y. Fujiwara: J.
Magn. Soc. Jpn., 42, 15 (2018).
5) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 42 , 127 (2018).
6) J. -G. Zhu and H. Li: IEEE. Trans. Magn., 49 , 765 (2013).
7) T. Kobayashi, Y. Nakatani, and Y. Fujiwara: J. Magn. Soc.
Jpn., 42 , 110 (2018).
8) H. Li and J. -G. Zhu: J. Appl. Phys., 11 5, 17B744 (2014).
9) T. Kobayashi, Y. Isowaki, and Y. Fujiwara: J. Magn. Soc.
Jpn., 39 , 8 (2015).
10) T. Kobayashi, Y. Isowaki, and Y. Fujiwara: J. Magn. Soc.
Jpn., 40 , 28 (2016).
11) J. -U. Thiele, K. R. Coffey, M. F. Toney, J. A. Hedstrom,and A. J. Kellock: J. Appl. Phys., 91, 6595 (2002).
12) T. Ono, H. Nakata, T. Moriya, N. Kikuchi, S. Okamoto, O.
Kitakami, and T. Shimatsu: Appl. Phys. Express, 9, 123002(2016).
13) M. Mansuripur, and M. F. Ruane: IEEE Trans. Magn.,
MAG-22 , 33 (1986).
Rece ived D ec. 2, 2 018; A cc epted Apr. 16, 2 019

!

!
!
!

78

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

INDEX
J. Magn. Soc. Jpn., 43, 79-83 (2019)<Paper>Fabrication of L10-FeNi films by denitriding FeNiN films
Keita Ito*,**, Masahiro Hayashida*, Masaki Mizuguchi*,**, Takashi Suemasu***, Hideto Yanagihara***,and Koki Takanashi*,***Institute for Materials Research, Tohoku Univ., 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan**Center for Spintronics Research Network, Tohoku Univ., 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan***Institute of Applied Physics, Univ. of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

L10-FeNi films textured with the a-axis perpendicular to the film plane were successfully fabricated by denitriding
FeNiN films. 20-nm-thick FeNiN films with two variants were epitaxially grown on SrTiO3(001), MgAl2O4(001), andMgO(001) substrates by molecular beam epitaxy. Denitriding was performed by annealing at 300 °C for 4 h underan H2 gas atmosphere. The epitaxial relationships were L10-FeNi[001](100) || substrate[100](001) andL10-FeNi[010](100) || substrate[100](001). The uniaxial magnetic anisotropy energy (Ku) of the L10-FeNi film wasestimated to be 4.4 × 106 erg/cm3 at room temperature by magnetic torque measurement. This Ku value corresponds
to a degree of long range order of 0.4.
Keywords: L10-FeNi, FeNiN, denitriding, molecular beam epitaxy, uniaxial magnetic anisotropy energy
1. Introduction
According to an increasing demand of a permanent
magnet for a motor of next-generation electric vehicles,
ferromagnetic materials possessing large uniaxial
magnetic anisotropy energy (Ku) and composed of earth
abundant elements are required. We have focused on
the L10-ordered FeNi alloy as a rare-earth- and noble
metal-free high Ku ferromagnetic material.1) L10-FeNi
possesses face centered tetragonal structure withalternate stacking of Fe and Ni monatomic layers along
the c-axis as shown in Fig. 1(a). Lattice constants are a= 3.582 Å and c = 3.607 Å; the c/a ratio is 1.007.2)
Saturation magnetization (MS) is 1270 emu/cm3 3) andthe Curie temperature is higher than 550 °C.4,5) The Ku
value was reported to be 1.3 × 107 erg/cm3 in a bulk
sample, 3,6) and 7.0 × 106 erg/cm3 in a film prepared bymolecular beam epitaxy (MBE).7) We consider thatthese features of L10-FeNi are suitable for application
to a permanent magnet. However, the order-disordertransition temperature of L10-FeNi is very low(320 °C),3,8) and it is difficult to form the L10 structure
by a conventional annealing for FeNi alloys. Atomic
diffusion of Fe and Ni is quite slow below 320 °C, andwe need an astronomical long duration to obtain
L10-ordered FeNi structure by simple annealing. The
formation of bulk L10-FeNi was realized by several
methods, promoting the atomic diffusion of Fe and Ni.
For example, introduction of defects in FeNi alloys byneutron irradiation3,6) or electron bombardment8)
followed by annealing with an external magnetic field,
severe plastic deformation technique for FeNi powder, 9)
and annealing of rapidly quenched amorphous
FeNiSiBPCu alloy.10) On the other hand, L10-FeNi films
were prepared by alternate monatomic layer deposition
using MBE1,7) or sputtering followed by annealing,1,11,12).
Although a lot of studies on the formation of L10-FeNi
were made, the degree of long-range order S or thevolume fraction of L10-FeNi phase was not enough.
Recently, however, the synthesis of polycrystalline
L10-FeNi powder with large S (0.71) has been achieved
by nitrogen topotactic extraction from FeNiN powder. 13)
Figure 1(b) shows the crystal structure of FeNiN.
FeNiN possesses a similar crystal stricture to that of
L10-FeNi, and thermodynamically stable orderedstructure of FeN and Ni layers.14) Actually, thepolycrystalline FeNiN powder with large S was formed
by a simple nitridation method for A1-FeNi (Fe and Ni
are randomly located) powder using NH3 gas.13) The
L10-FeNi powder was formed by denitriding FeNiN byannealing under H2 gas atmosphere. However, theevaluation of its Ku value has never been performed
because of polycrystalline powder. In this study, we
have tried to grow epitaxial FeNiN films on
SrTiO3(STO)(001), MgAl2O4(MAO)(001), and MgO(001)substrates by molecular beam epitaxy (MBE), andfabricated L10-FeNi films with two variants bydenitriding FeNiN films.

Fig. 1

Crystal structure of (a) L10-FeNi and (b)FeNiN.
2. Experiment
20 nm-thick FeNiN films were grown on STO(001),
MAO(001), and MgO(001) substrates by MBE in an

Journal of the Magnetics Society of Japan Vol.43, No.4, 201979

INDEXultra-high vacuum chamber supplying Fe, Ni, andradio-frequency (RF) N2 plasma, simultaneously.15) The
lattice mismatches in the c plane between FeNiN andthe substrates are 2.5 (STO), 0.98 (MAO), and 4.9 %(MgO). Supply rates of Fe and Ni were controlled to get
the equiatomic composition of Fe and Ni. The growthtemperature, N2 gas flow rate, and RF input power were
fixed to be 300 °C, 1.0 sccm, and 240 W, respectively.
Then, denitriding was performed by furnace annealing
at 300 °C for 4 h under H2 gas flow rate of 1 L/min atambient pressure. Structure of the samples wascharacterized by out-of-plane (ω-2θ) and in-plane(φ-2θχ) x-ray diffraction (XRD) using Cu-Kα radiation.
The thickness of the L10-FeNi layer was estimated by
x-ray reflectometry (XRR). Magnetization curves were
measured by vibrating sample magnetometer at room
temperature (RT). Magnetic field was applied toin-plane or out-of-plane direction of the films. The Ku
value was estimated by a magnetic torque (L)measurement with a 45°-torque method.16) Torquecurves were measured at RT under the applied field in
the range of 2 to 19 kOe by rotating the electromagnet
clockwise and counterclockwise around the (010)-planeof the substrates.
3. Results and discussion
Figure 2(a) shows the ω-2θ XRD patterns of the
FeNiN films. Only the diffraction peak of FeNiN 200 isobserved, and the a-axes of FeNiN films areperpendicular to the film plane for all the substrates.
Figures 2(b) and 2(c) show the φ-2θχ XRD patterns of(a)

MgO 002 - 2

Q // substrate[100]

1
40

45

50

2 or 2 [deg]Fig. 2
samples.

80

55

40

(c)

Epitaxial relationship between FeNiN layerand substrate.
the same samples. The scattering vector (Q) was set tothe [100] direction of the substrates. In Fig. 2(b), thepeaks of FeNiN 020 and 002 are obtained. This meansthat the FeNiN films are epitaxially grown with two
variants: the epitaxial relationships are
FeNiN[001](100) || STO, MAO, MgO[100](001) andFeNiN[010](100) || STO, MAO, MgO[100](001),
as shown schematically in Fig. 3. There are the twovariants with the in-plane c-axis of FeNiN intersecting
at 90°. In Fig. 2(c), the super lattice peak of FeNiN 001
is clearly observed for all the samples. This is
attributed to the long-range order of N atoms in the
FeNiN films.15)
Figures 4(a) and 4(b) show the XRR patterns of thesample grown on the STO(001) substrate before andafter the denitriding process, respectively. The red andblue curves correspond to the experiments and thecalculations based on the models shown in theright-hand figures, respectively. After denitriding, theFeN iN 001

50
Intensity [counts]

10

FeNiN 002

FeNiN 020

100

STO 200

 - 2

MAO 400(b)

MgO 200

Intensity [counts]

10

1000

STO(001)
MAO(001)
MgO(001)

FeNiN 200

100

STO 002

MAO 004

1000

Fig. 3

30
20
10
0
23

24

25

2  [deg](a) ω-2θ and (b)(c) φ-2θχ XRD patterns ofFig. 4

XRR patterns of FeNiN/STO(001) (a) beforeand (b) after denitriding.

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

INDEX

L10-FeNi[010](100) || STO, MAO, MgO[100](001).

L10-FeNi 200

10Fig. 7(a) and 7(b) display the magnetization curves of
the L10-FeNi films in the in-plane ([100] of thesubstrates)andout-of-planemagnetic
fields,respectively. MS of the samples are approximately 1100
emu/cm3 for all the samples. For comparison an
epitaxilally grown A1-FeNi film was prepared on
STO(001) and the magnetization curves were measured
as shown by black ones in Figs. 7(a) and 7(b). In Fig.
7(a), the L10-FeNi films formed by denitriding show

L10-FeNi 002 and 020

1000

Q // substrate[100]STO 200(b) - 2

MAO 400

10000

MgO 200

Intensity [counts]

L10-FeNi[001](100) || STO, MAO, MgO[100](001) andSTO(001)
MAO(001)
MgO(001)

100

100

1500

3

10

1
40

45

50

55

2 or 2 [deg]Fig. 5dashed lines indicate the peak position of L10-FeNi 002
and 200 expected from the lattice constants of bulk
L10-FeNi. The diffraction around 2θ = 52° in Fig. 5(a)corresponds to L10-FeNi 200, and that around 2θχ = 51°
in Fig. 5(b) is associated with L10-FeNi 002 and 020.
The peak shift from the dashed lines indicates thetensile strain induced in the films by the larger lattice
constants of substrates than that of L10-FeNi. Therefore,
we can say that the epitaxial relationship between the
L10-FeNi films and the substrates is maintained after
the denitriding process as shown in Fig. 6:

Magnetization [emu/cm ]Bulk
STO 002

MAO 004(a)
 - 2

MgO 002

1000

L10-FeNi 002
L10-FeNi 200

calculated curve assuming the existence of the surface
oxidation layer agrees well to the experiment. The total
film thickness becomes thinner after denitriding. This
is attributed to the shrink of the unit-cell volume
associated with the change from FeNiN to L10-FeNi.
Figures 5(a) and 5(b) show the ω-2θ and φ-2θχ XRD
patterns of the denitrided samples, respectively. The(a) ω-2θ and (b) φ-2θχ XRD patterns ofdenitrided samples.

(a)

1000

STO(001)
MAO(001)
MgO(001)
A1-FeNi

500
0
-500

H // substrate[100]T = RT

-1000
-1500
-3000

-2000

-1000

0

1000

2000

3000

External magnetic field [Oe]3

Magnetization [emu/cm ]

1500
1000
500

(b)
STO(001)
MAO(001)
MgO(001)
A1-FeNi0-500

H // substrate[001]T = RT-1000-1500-30000 -20000 -10000

010000 20000 30000

External magnetic field [Oe]Fig. 7
Fig. 6

Epitaxial relationship between L10-FeNi

layer and substrate.

Magnetization curves of L10-FeNi films whenmagnetic field was applied to (a) in-plane and (b)out-of-plane directions of films.

Journal of the Magnetics Society of Japan Vol.43, No.4, 201981

INDEX

larger coercive fields and smaller remanent
magnetizations than those of the A1-FeNi film. This is
attributed to the presence of the a-axis (magnetic hardaxis) of L10-FeNi along to the in-plane direction of thedenitrided samples, as shown in Fig. 6. Furthermore, inFig. 7(b), the saturation fields of denitrided L10-FeNi
films are larger than that of the A1-FeNi film. This is
explained by the a-axis (magnetic hard axis) orientationof L10-FeNi perpendicular to the film plane in the
denitrided samples. These results strongly suggest theformation of a-axis textured L10-FeNi films which havetwo variants with different c-axis directions from eachother, showing uniaxial magnetic anisotropy for each.
There is no significant difference in structure andmagnetic properties of the denitrided samples grown on
the three different substrates.
Figure 8 shows the torque curves of the L10-FeNi film
on STO(001). The inset shows the geometry of the film
sample and the magnetic field. θ is the angle relative tothe surface normal: θ = 90° and θ = 0° show that themagnetic field was applied in parallel to the in-planeand out-of-plane of the L10-FeNi film, respectively. The
saw-tooth-like curves show that the magnetization is
not saturated at 19 kOe. These curves exhibit two-holdsymmetry because of Ku in the L10-FeNi film. Figure 9shows the L - (L/H)2 plots using the averaging absolutevalues at θ = 45°, 135°, 225°, and 315°. The MS and20
15

L [dyne·cm]

5
0
-5
-10

2 kOe
5 kOe
10 kOe-15

Fig. 8090

15 kOe19 kOe
180

270

360

 [deg]Magnetic torque curves of L10-FeNi film on

STO(001).
0.7

data
fit

0.6
0.5
0.4

6

0.3

2

2

-4

-2

(L/H) [10 dyne ·cm ·Oe ]

0.8

0.2
0.1
0.0

0

2

4

6
6

Fig. 9
STO(001).

82

EA = 1/2·(Ku + 2πMS2)·sin2θ + 1/2·2πMS2·sin2θ

(1)

L = dEA/dθ = (Ku/2 + 2πMS2)·sin2θ

(2)Here, it is noted that positive Ku means the easymagnetization axis in the in-plane direction. Using theequation Kueff = Ku/2 + 2πMS2, the Ku value is calculated
to be 4.4 × 106 erg/cm3 for L10-FeNi/STO(001). From therelationship between Ku and S reported for L10-FeNi
films prepared by MBE,7) Ku of 4.4 × 106 erg/cm3
corresponds to S of 0.4. This value is smaller than thatof the L10-FeNi powder reported in ref. 13 (S = 0.71). In
our case, denitriding was performed at 300 °C, which ishigher than that in ref. 13 (250 °C). We chose higher
temperature to promote denitriding. However, this hightemperature might have caused the deterioration of theL10 structure and the reduction of S and Ku, when the Natoms were extracted from the FeNiN lattice. Further
optimization of the denitriding conditions and theelucidation of the denitriding mechanism are requiredin order to obtain much larger S and Ku values.
4. Summary

10

-20

effective uniaxial magnetic anisotropy energy (Kueff)values were obtained from the intersections of thefitting lines with the vertical and horizontal axes,
respectively. By considering the two variants of thesample, magnetic anisotropy energy (EA) and L areexpressed by equations (1) and (2), respectively.

8

10

12

-2

L [10 dyne·cm ]L - (L/H)2 plots for L10-FeNi film on

We have succeeded in growing a-axis textured FeNiN
films with the two variants on STO(001), MAO(001),
and MgO(001) substrates by MBE, and forming
L10-FeNi films by denitriding them. The Ku of the
L10-FeNi film is estimated to be 4.4 × 106 erg/cm3 at RT,
and the S is expected to be approximately 0.4. In
ordered to get higher S and Ku, as a next step, theoptimization of the growth conditions and denitriding
conditions of the FeNiN films are required.
Acknowledgements This work was supported in partby the Elements Strategy Initiative Center for Magnetic
Materials (ESICMM) under the outsourcing project ofMinistry of Education, Culture, Sports, Science andTechnology, Japan. The XRD measurements werecarried out at the Cooperative Research andDevelopment Center for Advanced Materials, IMR,
Tohoku University. The magnetic torque curvemeasurements were performed with the help of T.
Sekido, the University of Tsukuba. We thank S. Gotoand H. Kura, DENSO CORPORATION, for fruitful
discussion about the denitriding process.
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Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

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Ohkochi, M. Kotsugi, T. Kojima, M. Mizuguchi, and K.
Takanashi: Phil. Mag. Lett., 94, 639 (2014).
10) A. Makino, P. Sharma, K. Sato, A. Takeuchi Y. Zhang, andK. Takenaka: Sci. Rep., 5, 16627 (2015).
11) T. Y. Tashiro, M. Mizuguchi, T. Kojima, T. Koganezawa, M.
Kotsugi, T. Ohtsuki, K. Sato, T. Konno, and K. Takanashi: J.
Alloys Compd., 750, 164 (2018).
12) A. Frisk, B. Lindgren, S. D. Pappas, E. Johansson, and G.
Andersson: J. Phys.: Condens. Matter., 28, 406002 (2016).
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Y. Shimada, M. Mizuguchi, K. Takanashi, and E. Kita: Sci.
Rep., 7, 13216 (2017).
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15) F. Takata, K. Ito, and T. Suemasu: Jpn. J. Appl. Phys., 57,
058004 (2018).
16) H. Miyajima, K. Sato, and T. Mizoguchi: J. Appl. Phys., 47,
4669 (1976).
Received Jan. 18, 2019; Accepted Apr. 16, 2019

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J. Magn. Soc. Jpn., 43, 84-90 (2019)<Paper>

Suppression of Heat Generation in Magnetic Stimulation CoilApplied for Treating Dysphagia
H. Mori*,**, H. Kagaya***, S. Izumi****, K. Yashima*, and T. Takagi******IFG Corporation,

1-14-9 Oritate, Aoba-ku, Sendai 982-0261, Japan
6-6 Aramaki aza aoba, Aoba-ku, Sendai 980-8579, Japan**Graduate School of Engineering, Tohoku Univ.,***Department of Rehabilitation Medicine I, School of Medicine, Fujita Health Univ.

1-98 Dengakugakubo, Kutsukake-cho, Toyoake, Aichi, 470-1192 Japan
2-1 Seiryo-machi, Aoba-ku, Sendai, 980-8575 Japan*****Institute of Fluid Science, Tohoku Univ., 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan****Graduate School of Biomedical Engineering, Tohoku Univ.,

The authors are developing magnetic stimulation coils for use in the treatment of dysphagia. The prototype coilmanufactured in our previous research can induce large contraction of the suprahyoid muscles, which should betrained for normal swallowing. In this study, the heat generation in the coil during magnetic stimulation isinvestigated and suppressed. A numerical analysis showed that the main cause of the generated heat is the eddy
current in the coil conductor induced by magnetic flux from the tip of the magnetic core. The analysis also showedthat a parallel coil with a cross connection has an ideal current distribution in the coil conductor and thus best
suppresses heat generation during magnetic stimulation. The heat-suppressing coil has parallel divided coilconductors and an appropriate connection between the conductors to level the current in each conductor. Moreover,measurements of the temperature rise in prototype coils during magnetic stimulation confirm that heat generation
can be greatly suppressed by dividing the conductor and using an appropriate connection between the divided
conductors.
Key words: magnetic stimulation, dysphagia, suprahyoid muscles, eddy current, parallel coil

1. Introduction
Dysphagia, or difficulty swallowing, is mainly caused
by cerebrovascular disorders and aging. In Japan, asuper-aging society, the number of people withdysphagia is rapidly increasing. When food enters thetrachea or bronchi due to inappropriate swallowing
motion, it can cause aspiration pneumonia1,2).
Pneumonia is the 3rd leading cause of death in Japan.
More than 70% of pneumonia cases in elderly people are
related to aspiration3). Recovery from dysphagia is thus
important for protecting the elderly.
Neuromuscular electrical stimulation (NMES), a
stimulation method that uses electrodes that are stacked
directly on the epidermis above swallowing-related
muscles such as the suprahyoid muscles, has recently
been used for the treatment of dysphagia. Several
studies have shown that treatment with NMES
promotes swallowing recovery4,5). NMES is frequently
recommended by therapists in the United States 6).
However, when NMES is applied to the suprahyoidmuscles using an intensity that does not cause pain or
discomfort, the induced contraction of muscles is smaller
than that in usual swallowing7,8). This occurs because
the current intensity required to stimulate the motor
point of the suprahyoid muscles deep below the
epidermis is also sufficient to stimulate nociceptors justunder the epidermis. In addition, it is difficult to adhere
electrodes to the lower jaw epidermis of the elderly
because of slack skin, leading to insufficient electrical

84

contact. Moreover, for men, beards make electrodecontact more difficult.
To overcome these problems, a method that uses
magnetic stimulation has been proposed9,10). Magnetic
stimulation excites motor nerves via a current inducedby rapid changes of the magnetic flux of a coil; thiscurrent induces contraction of the target muscle.
Magnetic
stimulation
onlyslightly
stimulates
nociceptors, so there is little pain or discomfort during
stimulation11). Moreover, contact with skin is
unnecessary for stimulation, so beards and slack skin do
not cause problems. In our previous studies, numericalanalysis showed that a coil with a U-shaped magnetic
core (U-core coil hereafter) is the most suitable coil for
stimulating the motor point of the suprahyoid muscles12).
The figure-8 coil developed by Ueno is widely known for
local magnetic stimulation 13). A U-core coil consists of a
figure-8 coil and a magnetic core. It focuses a strong
magnetic flux to stimulate the motor point of thesuprahyoid muscles but not the lower alveolar nerve. A
clinical test on healthy humans confirmed that magnetic
stimulation with a U-core coil can induce contraction of
the suprahyoid muscles. Figure 1 shows the placementof a coil for stimulating the motor point of thesuprahyoid muscles. Contraction of the suprahyoidmuscles upon stimulation can be monitored by imaging
the movement of the hyoid bone connected to the muscle
using X-ray fluoroscopy. Figure 2 shows X-ray
fluoroscopy images of the region near the lower jaw
before and during stimulation. Upon stimulation, theJournal of the Magnetics Society of Japan Vol.43, No.4, 2019

INDEX       Fig. 1 Placement of coil for stimulating the motor pointof the suprahyoid muscles.

(a)



(a)

(b)
Fig. 2 Measurement of hyoid bone movement using
X-ray fluoroscopy. The shaded region indicated by theblack triangle is the hyoid bone. (a) Before and (b)during stimulation.
hyoid bone significantly moved in the anterior andsuperior directions, indicating that the suprahyoidmuscles greatly contracted. It has been shown that acontraction comparable to that in swallowing by ahealthy person can be obtained using magnetic
stimulation, significantly exceeding that induced by
NMES, without great pain or discomfort14).

(b)
Fig. 3 (a) External view of magnetic stimulation coilwithout a coil case. (b) Temperature distribution after
the generation of 600 magnetic pulses measured bythermography.
Continuous stimulation using a U-core coil generates
heat around the tip of the magnetic core, which
increases the temperature of the surface in contact withthe patient's skin. In particular, for the small
stimulation coil used for patients with a small jaw,
because the heat capacity is small (i.e., it is easy to heat),the surface temperature rises to an unsafe value. Fig. 3
shows a thermographic image of the surface of a small
coil after 600 continuously generated magnetic pulses. It
can be seen that the coil is overheated from the tip sideof the magnetic core; the temperature of the coil reaches
about 75 °C. Although the coil is covered with a resin
cover for insulation, there is a danger of burning thepatient via the heat transmitted through the resin cover.
The cover itself may also to be damaged by the heat.
In this study, to reduce the temperature of the coilsurface during magnetic stimulation, the current
density distribution inside the coil during magnetic
stimulation is obtained using numerical analysis toclarify the mechanism of heat generation. Based on thisinformation, a method for suppressing heat generation isdeveloped. A temperature test using prototype coils isused to validate the proposed heat suppression method.

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INDEX

2. Numerical Analysis
2.1 Model and conditions

The software ANSYS Electromagnetics Suite 19.1 wasused for numerical analysis and Eddy Current Solver
was used for AC steady state analysis. For numericalanalysis, various coil models were prepared. Figure 4 (a)shows a conventional coil model with the same shapeand size as those of a prototype U-core coil. The U-corecoil is composed of a U-shaped magnetic core made of asilicon steel sheet and a pair of coils. As shown in Fig. 5(a), the coils are manufactured by winding an insulated
copper flat plate (thickness: 0.9 mm; width: 8 mm) withdouble pancake winding. This model is denoted as the
single-coil model.
We also prepared a model in which the coil conductors
are divided to suppress the eddy current (Fig. 4 (b)). The
coils are manufactured by winding five flat copper plates(thickness: 0.9 mm; width: 1.6 mm) in parallel. Thismodel is denoted as the parallel-coil model. As shown in
Fig. 5 (b), the coils wound around one tip of the core aredenoted as A1, A2, ... A5 starting from the layer on the
tip side. Similarly, the coils wound around the other tipof the core are denoted as B1, B2, ... B5. For analysis of
the parallel coil, two methods for connecting coils wereapplied. As shown in Fig. 6, one connection method(straight connection) is to connect the coils of a given
layer (A1-B1, A2-B2, ... A5-B5). The other connection
method (cross connection) is to connect a coil from thetip-side layer to a coil from the base-side layer (A1-B5,
A2-B4, ... A5-B1). The parallel-coils with straight andcross connections are denoted as parallel coil (straight)
and parallel coil (cross), respectively.
The current density distribution in the conductor
when a 1.1 kA, 2.35 kHz sinusoidal current is supplied
to these coils was analyzed. The value of current is for
entire coil not for each coil layer. The current condition
was determined by measuring the waveform of theactual current flowing through the prototype coil during
magnetic stimulation. The current supplied to a coilused for treatment is an intermittent biphasic pulse.
However, the results of an analysis with a continuous
sinusoidal current are applicable to coil development15).

2.2 Results of numerical analysis

Fig. 4 (a) Single- and (b) parallel-coil models (units:mm).

Fig. 7 shows the current density distribution inside
the conductor of each coil on line C shown in Fig. 5. The
current density distribution shown in the figure wasobtained at the phase at which the current density
inside the conductor was maximum. The level indicatedby "Ideal" shows the current density for a current
flowing evenly through the conductor.
The results for the single coil in Fig. 7 show that thecurrent density is biased toward the tip side of the core.
The current density reaches a value nine times the ideal
density. This current density distribution is equivalent
to a state in which a current is flowing through a
conductor that is thinner than the actual one and theeffective resistance of the conductor increases, greatly
increasing heat generation. In addition, because Jouleheat is proportional to the square of the current density,
the region of the coil close to the tip of the core generates
particularly strong heat. It is found that the direction of
the current density is opposite to that of the suppl y

Fig. 5 Partial cross-section views of (a) single- and (b)parallel-coil models along the cutting plane shown in Fig.
4. This figure shows a view near one side of a core tip.

Fig. 6 Methods for connecting coil layers.

86

Fig. 7 Current density distribution inside various typesof coil during magnetic stimulation.

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

INDEX

current in the region of the coil apart from the tip of thecore. This opposite current density reduces magnetic
flux in the core and generates unnecessary Joule heat.
The cause of this bias is considered to be the eddy
currents inside the conductor induced by the magnetic
flux generated from the tip of the core. Fig. 8 shows avector diagram of the magnetic flux calculated under aforced condition where eddy current does not occur inthe coils. It can be seen that a strong magnetic flux
passes through the coil portion between the tips of thecore. The induced eddy current flows to cancel out thismagnetic flux.
The results for the parallel coil (straight) in Fig. 7
show that the maximum current density is suppressedcompared with that for a single coil. This suppression is
likely due to the subdivision of the conductor, whichinterrupts the eddy current flow. More specifically, thecurrent density in the A1 layer is high, and the current
flow in the A5 layer is opposite to the supply current. It
is considered that the magnetic flux through the coilinduces a positive electromotive force in the A1 (B1)layer and a negative electromotive force in the A5 (B5)layer. The eddy current induced by the electromotive
force overlaps the current from the current supply, andthe current density distribution shown in Fig.7 isappeared. In Fig. 9, the behavior of the eddy current flowin the parallel coil (straight) is simplified and illustrated.
In the figure, each layer of coil is expressed as one turn
coil to make it easy to understand. All layers of coil areconnected in parallel at the points where the pulse
current is supplied from a pulse current supply. So there
is an eddy current path through A1–B1–B5-A5 layer.
Focusing on the surface bordered with the closed curveof the eddy current path, the surface has a large area,
and all white arrows that indicate the direction ofmagnetic flux are incident on same face of the surface. Itmeans that, when a magnetic flux is generated from thecore, a large amount of eddy current is induced on theeddy current path. Therefore, the results of thisnumerical analysis show that it is impossible tosufficiently flatten the deviation of the current density
by merely subdividing the conductor.

Moreover, the results for the parallel coil (cross) in Fig.
7 show that the current density is suppressed to a level
close to the ideal distribution. This suppression is likely
due to the electromotive force in the A1 (B1) layer, whichmakes the current flow in the positive direction, and theelectromotive force in the B5 (A5) layer, which makes
the current flow in the reverse direction; these currents
cancel each other out.
Table 1 shows the heat generated by various types ofcoil after one pulse of magnetic stimulation calculated in
the numerical analysis. The values for the single coil, 5.5,
and 3.4 J, respectively. Compared to the single coil, heatgeneration is suppressed by 52% using the parallel coil(cross).parallel coil (straight), and parallel coil (cross)are 7.1,
The results of the numerical analysis show that themain cause of the heat generation in a U-core coil is theeddy current induced inside the coil conductor via themagnetic flux generated from the tip of the core. It was
shown that dividing the coil conductor and using a crossconnection between coils provides a current density
distribution close to the ideal level, suppressing heatgeneration.

Fig. 9 Simplified eddy current path model for theparallel coil (straight) for eddy current induced bymagnetic flux from the core.
Table 1 Solid loss for various types of coil
Coil Model
Quantity of heatgenerated by 1 pulse (J)Single Coil
7.1
(Conventional coil)
Parallel Coil (Straight)
5.5

Fig. 8 Vector diagram of magnetic flux on cutting plane
under the condition of no eddy current.

Parallel Coil (Cross)

3.4

Ideal Coil
(Uniform current density)

1.9

Journal of the Magnetics Society of Japan Vol.43, No.4, 201987

INDEX

Because the cause of heat generation is an eddy
current induced by the magnetic flux passing throughthe coil, heat generation could be reduced by suppressed
the eddy current using litz wire manufactured bytwisting a thin enameled wire. However, in general, litz
wire has a space factor of about 50% to 60%, and thus it
is expected that the effective direct current resistance ofthe coil will roughly double when litz wire is used. Even
if the current of each strand flows evenly and an ideal
current distribution is obtained, because heat generation
is proportional to the resistance value, it is expected toroughly double. Therefore, it is thought that the heatgeneration is the same as or greater than that in theparallel coil (cross). In addition, for litz wire, each fineelement wire is insulated by a resin coating film, so forthe heat inside to be dissipated to the outside, it must
pass through several layers of the insulation film. Whenthe temperature rises, it is thus difficult to decrease thetemperature inside the coil 16).

3. Temperature Test using Prototype Coils
3.1 Method

The three types of coil used in the numerical analysis
were manufactured and their temperature rise wasmeasured. The temperature rise over the entire coilsurface was measured using thermography. In addition,
two K-type thermocouples were installed at the upperand lower ends of the coil, respectively, and thetemperature was recorded with a data logger. The
temperature measurement points are shown in Fig. 10.
The conditions for pulse current conduction were set tothose that obtain the highest frequency assumed to be
used for subjects. Specifically, a cycle in which 30 pulses
were generated per second for 2 seconds and thenstopped for 2 seconds was repeated. The waveform ofeach pulse is 1 cycle of sinusoidal wave. The coil surface
temperature was measured during the cycle. The
supplied pulse current was set so that the amplitude
would be 1.10 kA. The value of amplitude was for entire
coil not for each coil layer. The pulse current was
supplied from a pulse current supply using capacitor
discharge. The wavelengths of pulse current were422-434 µs and the inverses of the wavelengths areequivalent of 2.30-2.38 kHz of frequency.

Fig. 10 Temperature measurement points on coil.

88

In this condition, the magnetic flux densities at 1mm
above tip core of single coil, parallel coil (straight), andparallel coil (cross) were 0.92 T, 0.90 T, and 0.93 T,
respectively, and that at 16mm above were 0.21 T, 0.21
T, and 0.21 T, respectively. Considering 1mm of the
thickness of resin cover for insulation, it means that themagnetic flux density on the patient skin exceeds 0.90T,
and that at the region 15mm inward from skin exceeds
0.20 T. Because the amplitude of magnetic flux density
over 0.20 T is enough to stimulate nerve 17), these coils
can stimulate nerves at depth of 15mm.
The generation of pulses was started after the surface
temperature of the coil was confirmed to be about room
temperature (22 °C ± 2 °C).

3.2.1 Results of thermography test

Figures 11-13 show thermographic images taken after
600 and 1200 pulses for the three types of coil,respectively.
The experimental results for the single coil (Fig. 11)
show large heat generation in the upper coil, which isconsistent with the numerical analysis results. In the
numerical analysis results, because the current density
was strongly concentrated on the tip side of the upper
coil, the temperature rise seemed to be also concentrated
at the tip side. However, in the experiment, the upperand lower coils almost uniformly increased intemperature, respectively. This is thought to be causedby the coil not being finely divided and the heat being
diffused throughout the upper and lower coils because of
the high thermal conductivity of copper.

(a)

(b)
Fig. 11 Temperature distribution in single coil measured
using thermography. Temperature distributions after(a) 600 and (b) 1200 pulses.

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

INDEX

(a)

(a)

(b)
Fig. 12 Temperature distribution in parallel coil(straight) measured using thermography. Temperature
distributions after (a) 600 and (b) 1200 pulses.

(b)Fig. 13 Temperature distribution in parallel coil (cross)measuredusing
thermography.
Temperature
distributions after (a) 600 and (b) 1200 pulses.

The experimental results for the parallel coil (straight)(Fig. 12) show that the top layer of the upper and lower
coils generates strong heat, consistent with thenumerical analysis, which showed that the current
density concentrates on the top layer of the upper andlower coils. In this coil, because the coil conductor is
divided, diffusion of heat by thermal conduction is weak.
The heat at the top layer is not transmitted to otherlayers; therefore, there is only a local temperature riseat the top layer.
The experimental results for the parallel coil (cross)(Fig. 13) show almost uniform current flow in each layer,
which is consistent with the numerical analysis.
Considering localized heat generation for the straightconnection, the main cause of this uniform temperaturerise seems to be the uniform current density, not the fast
thermal diffusion in the coil.

The temperatures at the coil tip side after 1200 pulses
for the single coil, parallel coil (straight), and parallel
coil (cross) were 110.4 °C, 112.3 °C, and 67.6 °C,
respectively, corresponding to temperature rises fromroom temperature (22 °C) of 88.4 °C, 90.3 °C, and 45.6 °C,
respectively. These results roughly agree with thenumerical analysis results shown in Table 1.
Considering the amount of heat generation, thetemperature rise should be lower in the parallel coil(straight). The reason of unexpected increment of
temperature rise in the parallel coil (straight) is the heatin the top layer does not diffuse throughout the coil.

Fig. 14 Temperature increase on coil surface measured
by thermocouples.

3.2.2 Results of test with thermocouples

Figure 14 shows the results of measuring the timecourse of the surface temperature of each coil type withthermocouples. This figure shows also the number ofgenerated pulses. The measurements were carried out
three times for each coil type. Table 2 shows the means
and standard deviations of the number of pulses
required for the surface temperature to increase from
30 °C to 80 °C measured at each measurement point
three times.
Table 2 Number of pulses required for coil surface
temperature to increase from 30 °C to 80 °C.
Coil model
Position
Average ± SD
Single coilA
635 ± 31
B
1635 ± 32
A
Parallel (Straight)
575 ± 9B
2000 ± 160
A
Parallel (Cross)1830 ± 150
B2995 ± 262

Journal of the Magnetics Society of Japan Vol.43, No.4, 201989

INDEXAs shown in Fig. 14, for the single coil and the parallel
coil (straight), the temperature on the tip side of the coil(A) sharply rises, and that on the base side of the coil (B)also rises but with a delay. There is a large difference
between the temperatures at points A and B, indicatingthat the rise in temperature is biased toward the tip ofthe coil. Even with the results in Table 2, for the single
coil and the parallel coil (straight), the required numberof pulses at points A and B are greatly different. The
inverse of the required number of pulses corresponds
roughly to the amount of heat generated at a point. The
difference of required number of pulses thus indicatesthat heat generation in these coils is strongly biased.
The results for the parallel coil (cross) in Fig. 14 showthat although the temperature rise at point A is faster,
the difference between temperatures at points A and B
is always smaller compared with that for the other twocoil types. That is, heat generation bias on the surface ofthe coil is weaker than other two coil types.
Because the part in contact with the patient is on the
tip side of the coil, for practical coils, the temperaturerise in this part must be small. As shown in Table 2, atpoint A, the pulses required for the temperature toincrease from 30 °C to 80 °C for the single coil and theparallel coil (straight) are about 600 pulses; that for theparallel coil (cross) is more than 3 times this value. In
other words, the latter coil can generate more than 3times the number of pulses compared with those of theformer two coils.

4. Conclusion
The heat generation in a U-shaped core coil during
magnetic stimulation was investigated using numericalanalysis and experiments. The numerical analysis
results reveal that the main cause of the heat generationis the eddy current generated inside the coil conductor
by the magnetic flux generated from the core tip.
Moreover, an ideal current density distribution can beobtained by dividing the conductor and using anappropriate connection between the divided conductors
so that the electromotive forces induced in the
conductors cancel each other.
Prototypes of the coil models were manufactured andtested. The experimental results were consistent with
the numerical analysis, confirming that heat generation
can be greatly suppressed by dividing the conductor andusing a proper connection between the divided
conductors.
A clinical trial on a dysphagia patient with astimulation coil based on the proposed technology iscurrently underway at Fujita Health University.
Considering the actual use at the rehabilitation clinic, it

90

is desirable to generate 6,000 pulses in 15 minutes, so
further improvement of the stimulation coil is required.
In this study, the conductor was divided into fivesections and evaluated. However, it may be possible toreduce the bias of the current density further and makea coil with lower heat generation by using finely divided
parallel winding coils. However, if the division isexcessive, the conductor space factor and the heatdissipation efficiency may decrease. The optimal
winding parameters should thus be determined using
numerical analysis.
Acknowledgements We thank Adam Przywecki, B.Eng,
from Edanz Group (www.edanzediting.com/ac) for
editing the English text of a draft of this manuscript.
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Received Feb. 22, 2019; Accepted Apr. 09, 2019

Journal of the Magnetics Society of Japan Vol.43, No.4, 2019

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. Honda
S. Isogami
K. KamataH. Kikuchi
T. Kimura
T. Kouda
S. Kokado
Y. Kota
T. MakiT. Morita
S. Muroga
T. Nagahama
H. Nakayama
T. Narita
D. Oyama
J. OzekiN. PhamT. Sasayama
K. Sekiguchi
T. Shima
Y. Shiratsuchi
T. Takura
S. YamadaK. Yamazaki
N. Adachi
S. Inui
E. Miyashita
T. SatoM. Tsunoda

K. Bessho
K. ItoY. Nakamura
S. Seino
S. Yabukami

M. DoiH. KatoK. Nishijima
T. Suetsuna
S. Yoshimura

T. DoiK. KatoT. Nozaki
K. Tajima

Y. Kanai
T. Kubota
M. NaoeT. SatoT. Yamamoto

K. Hioki
A. Kuwahata
M. Ohtake
T. Tanaka

N. Inaba
K. Masuda
T. Saito
M. Takezawa

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Journal of the Magnetics Society of Japan
Vol. 43 No. 4 (通巻第 304号) 2019年７月１日発行

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