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Vol.48 No.5
JournalJournal of the Magnetics Society of Japan
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2024

Magnetic Recording
Inﬂuence of Anisotropy Constant on Writability in Heated-Dot Magnetic Recording
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T. Kobayashi, Y. Nakatani, and I. Tagawa…81

Physics of Magnetism, Utilization of High Magnetic Fields
Synthesis and High-Field Magnetic Measurement of Ba2Sn2+xMe1+xFe10-2xO22

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Journal of the Magnetics Society of Japan
Vol. 48, No. 5

Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Magnetic Recording
Influence of Anisotropy Constant on Writability in Heated-Dot Magnetic Recording………………………………………………………… T. Kobayashi, Y. Nakatani, and I. Tagawa

81

Physics of Magnetism, Utilization of High Magnetic Fields
Synthesis and High-Field Magnetic Measurement of Ba2Sn2+xMe1+xFe10-2xO22………………… H. Harasawa, H. Mitamura, M. Tokunaga, K. Kakizaki, and K. Kamishima

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Copyright ©2024 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., 48, 81-87 (2024)<Paper>Influence of Anisotropy Constant on Writability
in Heated-Dot Magnetic Recording
T. Kobayashi, Y. Nakatani*, and I. Tagawa**

Graduate School of Engineering, Mie Univ., 1577 Kurimamachiya-cho, Tsu 514-8507, Japan

1-5-1 Chofugaoka, Chofu 182-8585, Japan35-1 Yagiyama-Kasumicho, Sendai 982-8577, Japan*Graduate School of Informatics and Engineering, Univ. of Electro-Communications,**Electrical and Electronic Engineering, Tohoku Institute of Technology,

We discuss the influence of the anisotropy constant on writability, taking account of 10 years of archiving andadjacent track interference in 4 Tbpsi shingled heated-dot magnetic recording (HDMR), using our stochastic
calculation employing the Néel-Arrhenius model with a Stoner-Wohlfarth dot. The bit error rate is calculated and theresult is analyzed using the mean magnetization reversal number per unit time as a function of the writing time. We
confirm the stochastic calculation result by employing a micromagnetic simulation. HDMR has a certain margin forerasure-after-write, since half of the writing time determined by field is for the magnetic dot and the rest is for thenonmagnetic spacing. HDMR also has a certain margin for the dot aspect ratio, since the dot is relatively large.
Therefore, the combination of a small anisotropy constant and a large dot volume can be used to improve write-error.
When we choose a small anisotropy constant, the mean magnetization reversal number per unit time in the opposite
direction to the recording direction is negligible. Furthermore, the writing time determined by medium is longer.
Therefore, the bit error rate caused by write-error is low for a small anisotropy constant.
Key words: HDMR, 10 years of archiving, ATI, dot height, bit error rate, anisotropy constant ratio
1. Introducti on

Many magnetic recording methods have been
proposed to solve the trilemma problem1) of conventional
magnetic recording (CMR) on granular media. Thesemethods include shingled magnetic recording (SMR),
microwave-assisted magnetic recording (MAMR), heatassisted magnetic recording (HAMR), bit patterned
media (BPM), heated-dot magnetic recording (HDMR),
namely HAMR on BPM, and three-dimensional
magnetic recording (3D MR).
The challenges to be faced when designing MR media
are(1) information stability during 10 years of archiving,known as the 𝐾𝐾! 𝑉𝑉 ⁄(𝑘𝑘𝑘𝑘) problem1), where 𝐾𝐾! , 𝑉𝑉, 𝑘𝑘, and𝑇𝑇 are, respectively, the grain or dot anisotropy constant,volume, the Boltzmann constant, and temperature,(2) information stability in an adjacent track (AT) during
writing, known as the adjacent track interference (ATI)
problem, and(3) the writing field dependence of the bit error rate(bER), namely writability.
Akagi et al. reported (3) the recording performance of
HDMR2) and 3D HDMR3,4) employing micromagnetic
simulation. They assumed the medium material to be
FePt. However, the 𝐾𝐾! value was smaller than that ofbulk FePt.
The above three challenges, namely (1), (2), and (3),must be dealt with simultaneously, since they are in a
trade-off relationship. If a small 𝐾𝐾! value is chosen, theinformation stabilities in (1) and (2) will be worse.
Corresponding author: T. Kobayashi (e-mail: kobayasi@phen.mie-u.ac.jp).

In this paper, we discuss the influence of 𝐾𝐾! on (3)writability, taking account of (1) 10 years of archiving
and (2) ATI in 4 Tbpsi shingled HDMR, using ourstochastic calculation employing the Néel-Arrhenius
model with a Stoner-Wohlfarth dot. We confirm thestochastic calculation result by employing a
micromagnetic simulation. Our calculation is applicable
to all three challenges5) including SMR and CMR. The
anisotropy constant ratio 𝐾𝐾! /𝐾𝐾"!#$ , which we
introduced6,7), is used instead of 𝐾𝐾! . The 𝐾𝐾! /𝐾𝐾"!#$ value
is the intrinsic ratio of the medium 𝐾𝐾! to the bulk FePt
𝐾𝐾! . Therefore, it becomes easy to grasp the ratio to thebulk 𝐾𝐾! . If we employ 𝐾𝐾! /𝐾𝐾"!#$ , we can choose areasonable 𝐾𝐾! value for the medium. For example,
although we can choose a 𝐾𝐾! value of 60 Merg/cm3 at
300 K for a medium with a 𝑇𝑇% value of 750 K since the
𝐾𝐾! /𝐾𝐾"!#$ value is less than 1.0, that of 70 Merg/cm3
cannot be selected since the 𝐾𝐾! /𝐾𝐾"!#$ value exceeds 1.0
as reported in a previous paper7).
2 . C a l c u l a t i o n C o n d i t i o n s a n d Me t h o d

2 . 1 Do t a r r a n g e me n t a n d me d i u m s t r u c t u r e
Figure 1 shows the dot arrangement and medium
structure in 4 Tbpsi HDMR where 𝐷𝐷& , 𝐷𝐷' , and ℎ are
the dot sizes for the down-track 𝑥𝑥 and cross-track 𝑦𝑦
directions, and the dot height, respectively. The 𝑧𝑧
direction is film normal. The bit length 𝐷𝐷( and track
width 𝐷𝐷) are both 12.7 nm. We assume that the mean
dot size 𝐷𝐷* and mean dot spacing Δ+ are the same forboth the down-track and cross-track directions, namely
𝐷𝐷* = Δ+ = 6.35 nm.
There are two cases as regards the dot sizes 𝐷𝐷& and𝐷𝐷' depending on the dot manufacturing method. In one
case, the 𝐷𝐷& and 𝐷𝐷' sizes are the same, and the 𝐷𝐷& =Journal of the Magnetics Society of Japan Vol.48, No.5, 2024

81

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period. We used 𝑇𝑇%* and 𝜎𝜎)% /𝑇𝑇%* values of 750 K and
2 %, respectively.
For simplicity, we used a thermal gradient 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 of
14 K/nm in the cross-track direction and assumed it tobe constant anywhere for ATI. A constant 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 valueof 14 K/nm in the down-track direction was also used for
writability.
The writing field 𝐻𝐻4 was assumed to be spatially
uniform, the direction to be perpendicular to the medium
plane, and the rise time to be zero.

Fig. 1 Dot arrangement and medium structure.

𝐷𝐷' size fluctuates. In the other case, the 𝐷𝐷& and 𝐷𝐷'
sizes fluctuate independently. We examined the 𝐷𝐷& = 𝐷𝐷'
case, since the bER is larger for the same ℎ value8). We
generated a random number 𝐷𝐷& = 𝐷𝐷' that had a lognormal distribution with a standard deviation 𝜎𝜎+ . We
used a 𝜎𝜎+ /𝐷𝐷* value of 15 %.

2 . 2 Ma g n e t i c p r o p e r t i e s
The temperature dependence of the medium
magnetization 𝑀𝑀, was calculated by employing mean
field analysis9), and that of the 𝐾𝐾! value was assumed
to be proportional to 𝑀𝑀,- 10). 𝑀𝑀, (𝑇𝑇% = 770 K, 𝑇𝑇 = 300 K) =1000 emu /cm3 was assumed for FePt. Based on thisassumption, the 𝑀𝑀, value can be calculated for all
values of 𝑇𝑇% and 𝑇𝑇.
𝐾𝐾! (𝑇𝑇% = 770 K, 𝐾𝐾! /𝐾𝐾"!#$ = 1, 𝑇𝑇 = 300 K) = 70 Merg/cm3
was assumed for bulk FePt. Using this assumption, we
can calculate 𝐾𝐾! for all values of 𝑇𝑇% , 𝐾𝐾! /𝐾𝐾"!#$ , and 𝑇𝑇.
No intrinsic distribution of 𝐾𝐾! was assumed. However,there was a fluctuation in 𝐾𝐾! caused by 𝑇𝑇% variation.
Since each dot has a 𝑇𝑇% variation, the 𝑇𝑇% value of each
dot was adjusted by changing the Cu composition 𝑐𝑐 for(Fe..0 Pt ..0 )123 Cu3 .
With a 𝑇𝑇% value of 750 K and a 𝐾𝐾! /𝐾𝐾"!#$ value of 0.8,
in this work we obtain a 𝐾𝐾! value of 51 Merg/cm3 andan anisotropy field 𝐻𝐻$ of 107 kOe at a readout
temperature of 330 K employing mean field analysis.
2 . 3 T e mp e r a t u r e p r o f i l e a n d wr i t i n g f i e l d
The writing temperature 𝑇𝑇4 for the dot was assumed
to be

𝑇𝑇4 = 𝑇𝑇%* + 3𝜎𝜎)% ,(1)

as shown in Fig. 1, taking account of the 𝑇𝑇% variation,
where 𝑇𝑇%* and 𝜎𝜎)% are the mean Curie temperatureand the standard deviation of 𝑇𝑇%* , respectively. The 𝑇𝑇%
distribution was assumed to be normal. Based on thisassumption, 99.9 % of dots in the writing track areheated to above their 𝑇𝑇% values during the writing82

2 . 4 S t o c h a s t i c c a l c u l a t i o n me t h o d
The information stability for 10 years of archiving has
been discussed employing the Néel-Arrhenius modelwith a Stoner-Wohlfarth grain or dot. The attempt
period 1/𝑓𝑓5 has a value of picoseconds for FePt in heatassisted magnetic recording. Since the magnetization
direction attempts to reverse with a certain probability
at each attempt period, the information stability for 10
years of archiving is extrapolated as a stack ofphenomena in picoseconds. Therefore, the NéelArrhenius model is valid for any time from the order ofa picosecond to more than 10 years. The Néel-Arrhenius
model is also valid under the condition that the writing
field is less than the anisotropy field of recording media.
Not only in ATI but in writability, the anisotropy field islarger than the writing field during most of the writing
time, since the anisotropy field of FePt is extremely large.
In HAMR including HDMR, stochastic magnetization
switching under thermal agitation is dominant even for
writability. Therefore, we have also applied the NéelArrhenius model to phenomena with a short time, andexamined ATI8,11) and writability7).
The three challenges, 10 years of archiving, ATI, andwritability, must be dealt with simultaneously.
Therefore, in this paper we discuss the influence of 𝐾𝐾!
on writability for HDMR, taking account of 10 years ofarchiving and ATI. The results for 10 years of archiving8)
and ATI8,11) have already been reported. The criterion
determining whether or not information is stable after
10 years of archiving and AT writing was assumed to be
a bER of 10-3.
We improved our stochastic calculation for writability.
We first took the shape anisotropy reported in a previous
paper12) into account. The magnetostatic field fromsurrounding dots was ignored since the Δ+ value islarge. Then we modified the attempt frequency 𝑓𝑓5 as
described below.
We assumed 𝑓𝑓5 as
3𝛾𝛾𝛾𝛾 E𝑀𝑀s 𝐻𝐻keff 𝑉𝑉|𝐻𝐻w |cos𝜙𝜙
F1−
HI
J H1 +
2(𝐾𝐾u /𝐾𝐾bulk )𝐻𝐻const
2𝜋𝜋𝜋𝜋𝜋𝜋1+𝛼𝛼|𝐻𝐻w |cos𝜙𝜙I,(2)(𝐾𝐾u /𝐾𝐾bulk )𝐻𝐻const

𝑓𝑓5 =taking account of an approximation13), where 𝛾𝛾, 𝛼𝛼, 𝐻𝐻$677 ,|𝐻𝐻4 |, and 𝜙𝜙 are the gyromagnetic ratio, Gilbert
damping constant, effective anisotropy field, writing

Journal of the Magnetics Society of Japan Vol.48, No.5, 2024

INDEX

field magnitude, and writing field angle, respectively.
We used 𝛾𝛾 and 𝛼𝛼 values of 1.76×107 Oe-1s-1 and 0.1,
respectively. When 𝜙𝜙 = 180 deg, the magnetization
reverses in the recording direction and we defined 𝑓𝑓5 as
𝑓𝑓52 . When 𝜙𝜙 = 0, the magnetization reverses in the
opposite direction to the recording direction and we
defined 𝑓𝑓5 as 𝑓𝑓58 . We introduced (𝐾𝐾! /𝐾𝐾"!#$ )𝐻𝐻%9:,;(𝐻𝐻%9:,; = 75 kOe) instead of 𝐻𝐻$677 so that the 𝑓𝑓5 value
becomes zero at 𝑇𝑇% .
The mean magnetization reversal number 𝑁𝑁 per unit
time is expressed as(3)

𝑁𝑁 = 𝑓𝑓5 expS−𝐾𝐾< T,employing the Néel-Arrhenius model, where 𝐾𝐾< is thethermal stability factor. The 𝑓𝑓5 value gives an attempt
number per unit time for magnetization reversal, andthe Boltzmann factor expS−𝐾𝐾< T is interpreted as theprobability of magnetization reversal.
When 𝜙𝜙 = 180 deg, namely the magnetization
reversal in the recording direction, 𝐾𝐾< and 𝑁𝑁 are given
by
𝐾𝐾<2 = 0 for |𝐻𝐻4 | ≥ 𝐻𝐻$677 ,𝐾𝐾𝑉𝑉|𝐻𝐻 | -

H1 − 𝐻𝐻 w I for |𝐻𝐻4 | < 𝐻𝐻$677 , and𝐾𝐾<2 = ueff
𝑘𝑘𝑘𝑘
keff
(4)
(5)

𝑁𝑁2 = 𝑓𝑓52 expS−𝐾𝐾<2 T,

respectively, where 𝐾𝐾!677 is the effective anisotropy
constant. And when 𝜙𝜙 = 0, namely the magnetization
reversal in the opposite direction to the recording
direction, 𝐾𝐾< and 𝑁𝑁 are given by
𝐾𝐾𝑉𝑉|𝐻𝐻 | -

H1 + 𝐻𝐻 w I , and𝐾𝐾<8 = ueff
𝑘𝑘𝑘𝑘
keff

𝑁𝑁8 = 𝑓𝑓58 expS−𝐾𝐾<8 T,

Table 1 Calculation conditions.

(6)

(7)

respectively.
The calculation procedure for the writing fielddependence of the bER, namely writability, is described
below. The dot temperature fell with time from 𝑇𝑇%
according to the linear velocity and 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕. The attempt
times were calculated using 𝑓𝑓5 . The probability
expS−𝐾𝐾< T for the magnetization reversal in therecording or opposite direction was calculated for every
attempt time. The magnetization direction wasdetermined by the Monte Carlo method for every
attempt time. Then the bER value was obtained. The
calculation detail has already been reported7).
The bER in this paper is useful only for comparisons.
The calculation conditions are summarized in Table 1.
The linear velocity was 10 m/s. We assumed the storage
temperature to be 350 K for 10 years of archiving, forwhich we took a certain margin into account. We used an
exposure field of 10 kOe and a time of 1 ns for ATI.
3. Cal cul at i on Resul t s
3 . 1 I mp r o v e me n t i n wr i t a b i l i t yFirst, we discuss the improvement in writability.
Write-error (WE) and erasure-after-write (EAW)14) are
important factors in writability.
WE means that the magnetization does not switch to
the recording direction during writing when the writing
field |𝐻𝐻4 | magnitude is relatively small. WE decreases
as the |𝐻𝐻4 | magnitude increases. On the other hand,
EAW means that when the |𝐻𝐻4 | magnitude is too large,
some dot magnetizations are reversed in the opposite
direction to the recording direction caused by changing
the |𝐻𝐻4 | direction after writing. WE and EAW are in a
trade-off relationship in terms of the |𝐻𝐻4 | magnitude.
The improvement in writability is restricted to 10
years of archiving and ATI.
(1) Information stability during 10 years of archiving isdetermined by 𝐾𝐾<.

,
𝐾𝐾<. = ueff
𝑘𝑘𝑘𝑘

𝐾𝐾

𝑉𝑉

(8)

𝑁𝑁. = 𝑓𝑓5. expS−𝐾𝐾<. T,(9)and 𝑁𝑁 is given by

where 𝑓𝑓5. is for |𝐻𝐻4 | = 0. There are two cases asregards 𝐾𝐾<. , namely combinations ofℎ values, and(a) large 𝐾𝐾!677 and small 𝑉𝑉 = 𝐷𝐷*(b) small 𝐾𝐾!677 and large 𝑉𝑉 values.
(2) The ATI problem is equivalent to EAW, since ATI
means writing in the adjacent track. Since WE and EAW
are in a trade-off relationship, the better the WE is, theworse the ATI becomes and vice versa. A large 𝑉𝑉 value
is also needed for decreasing ATI when we choose a small
𝐾𝐾!677 value.
If the 𝐾𝐾!677 value, namely the 𝐻𝐻$677 value, is reduced,
the 𝐾𝐾<2 value in Eq. (4) decreases even for the same
𝐾𝐾!677 𝑉𝑉 value. This is advantageous to WE since the 𝑁𝑁2
value becomes large during writing and is
disadvantageous to EAW since the 𝑁𝑁2 value also
Journal of the Magnetics Society of Japan Vol.48, No.5, 2024

83

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becomes large at the end of writing. WE and EAW are ina trade-off relationship in terms of the 𝐾𝐾!677 value evenfor the same 𝐾𝐾!677 𝑉𝑉 value.
In addition, if the 𝐾𝐾!677 value, namely the 𝐻𝐻$677 value,
is reduced, the 𝐾𝐾<8 value in Eq. (6) increases even forthe same 𝐾𝐾!677 𝑉𝑉 value. This is advantageous to WE
since the 𝑁𝑁8 value becomes small during writing.
If the EAW problem can be solved, a small 𝐾𝐾!677 value
is advantageous for improving writability as mentioned
above. A large 𝑉𝑉 value, namely a large ℎ value, isneeded for a certain 𝐾𝐾!677 𝑉𝑉 value when we choose asmall 𝐾𝐾!677 value. However, it is difficult tomanufacture a medium with a large ℎ/𝐷𝐷* value. We
assumed the maximum ℎ/𝐷𝐷* value to be about two.
In the following, we discuss these problems that arise
when we choose large and small 𝐾𝐾!677 values.

3. 2 Large ani sot ropy const ant
When taking account of 10 years of archiving and ATI
only, we can choose a dot height of 3.0 nm for a medium
with 𝐾𝐾! /𝐾𝐾"!#$ = 0.8. The ℎ/𝐷𝐷* value was 0.48.
However, when 𝐾𝐾! /𝐾𝐾"!#$ = 0.8, the bER value is high asshown in Fig. 2. We discuss the reason for this using our
calculation.
The 𝑁𝑁 value is equal to the product of 𝑓𝑓5 andexpS−𝐾𝐾< T. Figure 3 (a) shows the 𝑓𝑓5 value as a functionof the writing time, where the writing field magnitudes|𝐻𝐻4 | are 0 and 10 kOe. The medium temperature is also
shown. At a time of zero, the medium temperature is 𝑇𝑇%*and the writing field direction changes from downward
to upward, and at a time of 1.27 ns, from upward to
downward. A writing time determined by field is 1.27 ns.
The attempt frequency 𝑓𝑓5 (1/ns) is interpreted as theattempt number per nanosecond for dot magnetization
reversal. Unfortunately, the 𝑓𝑓5 value becomes zero at
𝑇𝑇% . Furthermore, the 𝑓𝑓52 value for the dot
magnetization reversal in the recording direction
becomes small by |𝐻𝐻4 |.
The Boltzmann factor expS−𝐾𝐾< T as shown in Fig. 3 (b)is interpreted as the dot magnetization reversal
probability for each attempt, where the probability isequal to one when 𝜙𝜙 = 180 deg and |𝐻𝐻4 | > 𝐻𝐻$677 . The

Fig. 2 Writing field |𝐻𝐻4 | dependence of bit error rate fora 𝐾𝐾! /𝐾𝐾"!#$ value of 0.8.

84

probability decreases rapidly as the temperature
decreases.

(a)

(b)
Fig. 3 (a) Attempt frequency 𝑓𝑓5 and medium
temperature, and (b) Boltzmann factor expS−𝐾𝐾< T as afunction of writing time for a 𝐾𝐾! /𝐾𝐾"!#$ value of 0.8,
where the writing field magnitudes |𝐻𝐻4 | are 0 and 10
kOe.

Fig. 4 Mean magnetization reversal number per
nanosecond 𝑁𝑁 = 𝑓𝑓5 expS−𝐾𝐾< T as a function of writingtime for a 𝐾𝐾! /𝐾𝐾"!#$ value of 0.8, where the writing fieldmagnitudes |𝐻𝐻4 | are 0 and 10 kOe.

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Figure 4 shows the 𝑁𝑁 = 𝑓𝑓5 expS−𝐾𝐾< T value as afunction of the writing time. The 𝑁𝑁 = 𝑓𝑓5 expS−𝐾𝐾< T (1/ns)
value is interpreted as the dot magnetization reversal
number per nanosecond. The 𝑁𝑁2 value is the meanmagnetization reversal number in the recording
direction, and 𝑁𝑁8 is that in the opposite direction to therecording direction.
When |𝐻𝐻4 | = 0, the 𝑁𝑁. = 𝑓𝑓5. expS−𝐾𝐾<. T values in therecording and opposite directions are the same. As the|𝐻𝐻4 | value increases, the 𝑁𝑁2 value increases and the𝑁𝑁8 value decreases.
A medium with 𝐾𝐾! /𝐾𝐾"!#$ = 0.8 has an 𝑁𝑁8 value asshown in Fig. 4. This means that there is a situation
where the magnetization reverses in the opposite
direction to the recording direction.
Furthermore, the writing time determined by medium,
where the 𝑁𝑁2 value is large, is much shorter than thewriting time determined by field. For example, thewriting time determined by medium, where the 𝑁𝑁2
value is larger than one per nanosecond, is 0.27 ns, andthe writing time determined by field is 1.27 ns.
As a result, the bER value is high for a 𝐾𝐾! /𝐾𝐾"!#$ valueof 0.8.
3 . 3 S ma l l a n i s o t r o p y c o n s t a n t
Generally, a reduction in 𝐾𝐾!677 is disadvantageous to
EAW as mentioned above, since the 𝑁𝑁2 value becomeslarge at the end of writing time determined by field andthe bER caused by EAW becomes large. However, the 𝑁𝑁2
value is extremely small at the end of the writing timefor HDMR as shown in Fig. 4. Therefore, HDMR has acertain margin for EAW, since half of the writing time isfor 𝐷𝐷* and the rest is for 𝛥𝛥+ . Furthermore, HDMR also
has a certain margin for the ℎ/𝐷𝐷* value, namely 0.48,
since the 𝐷𝐷* value is relatively large, namely 6.35 nm.
Therefore, the combination of small 𝐾𝐾!677 and large 𝑉𝑉
values is available for writability.
For a combination consisting of small 𝐾𝐾!677 and large
𝑉𝑉 values, 10 years of archiving and the ATI problem
must be considered. The ℎ value necessary for a bER of
10-3 after 10 years of archiving or AT writing increases

Fig. 5 Dot height ℎ to achieve a bER of 10-3 as a functionof the anisotropy constant ratio 𝐾𝐾! /𝐾𝐾"!#$ after 10 years
of archiving or AT writing.

as the 𝐾𝐾! /𝐾𝐾"!#$ value decreases as shown in Fig. 5. Theℎ/𝐷𝐷* value is 1.1 even for 𝐾𝐾! /𝐾𝐾"!#$ = 0.4, since the 𝐷𝐷*
value of 6.35 nm is relatively large.
WE decreases and EAW increases as the |𝐻𝐻4 |magnitude increases. Figure 6 (a) shows that for a
relatively small |𝐻𝐻4 | magnitude, the bER value,
namely WE, decreases as the 𝐾𝐾! /𝐾𝐾"!#$ value decreases
where the ℎ value was changed according to the resultin Fig. 5. Although a large EAW can be seen for a

(a)

(b)

(c)
Fig. 6 Writing field |𝐻𝐻4 | dependence of (a) bit error rate(bER) and (b) signal to noise ratio (SNR) for various
𝐾𝐾! /𝐾𝐾"!#$ values. (c) The bER value in (a) as a function of
the SNR value in (b).

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𝐾𝐾! /𝐾𝐾"!#$ value of 0.4 within the |𝐻𝐻4 | calculation range,
it appears at a |𝐻𝐻4 | level exceeding about 16 kOe.
We confirmed the result in Fig. 6 (a) by employing a
micromagnetic simulation. The calculation has alreadybeen reported in detail5). Figure 6 (b) shows the |𝐻𝐻4 |dependence of the signal to noise ratio (SNR) calculated
employing the micromagnetic simulation, and Fig. 6 (c)shows the bER value in Fig. 6 (a) as a function of the
SNR value in Fig. 6 (b). A good correlation can be seen
between them. Therefore, our stochastic calculation in
Fig. 6 (a) can almost entirely explain the result of the
micromagnetic simulation in Fig. 6 (b).
When 𝐾𝐾! /𝐾𝐾"!#$ = 0.4, the 𝑁𝑁8 value is negligible asshown in Fig. 7, which can be compared with the result
shown in Fig. 4 for 𝐾𝐾! /𝐾𝐾"!#$ = 0.8. When 𝐾𝐾! /𝐾𝐾"!#$ = 0.4,
this means that there is almost no situation where themagnetization reverses direction compared with therecording direction. Furthermore, the writing time
determined by medium of 0.35 ns for 𝐾𝐾! /𝐾𝐾"!#$ = 0.4 islonger than that of 0.27 ns for 𝐾𝐾! /𝐾𝐾"!#$ = 0.8. Thesemean that the recording is more guaranteed. Therefore,
the bER caused by WE is low for a relatively small |𝐻𝐻4 |magnitude as shown in Fig. 6 (a).
We also confirmed the meaning of 𝑁𝑁2 and 𝑁𝑁8 at|𝐻𝐻4 | = 10 kOe in Figs. 4 and 7 employing a
micromagnetic simulator, EXAMAG LLG (FujitsuLtd.)15), in which the Landau-Lifshitz-Gilbert (LLG)
equation is solved by the finite-element method. The
equivalent field for the energy of the thermal fluctuation
was added. The dot size and magnetic property were thesame with those in Figs. 4 and 7. The calculation steptime was 10-16 s.
Fi gur e 8 s hows t he t i me de pe nde nc e of t hemagnetization 𝑧𝑧 component 𝑀𝑀= /𝑀𝑀, , which means themagnetization motion as a function of time. The
calculation temperature was constant at 740 K, whichcorresponds to a time of 0.070 ns in Figs. 4 and 7. The
𝑁𝑁2 value shows the maximum at 0.070 ns as shown in
Fig. 4. Since the thermal gradients and linear velocities

Fig. 7 Mean magnetization reversal number per
nanosecond 𝑁𝑁 = 𝑓𝑓5 expS−𝐾𝐾< T as a function of writingtime for a 𝐾𝐾! /𝐾𝐾"!#$ value of 0.4, where the writing fieldmagnitude |𝐻𝐻4 | is 10 kOe.

86

are the same for Figs. 4 and 7, 740 K also corresponds toa time of 0.070 ns in Fig. 7. The initial magnetization
and writing field directions are the −𝑧𝑧 and 𝑧𝑧 directions,
respectively. The 𝑁𝑁2 and 𝑁𝑁8 values are about 14 and0.3 times per nanosecond, respectively, for 𝐾𝐾! /𝐾𝐾"!#$ =0.8 as shown in Fig. 4. It is expected that there will be
0.3 magnetization reversals in the opposite direction to
the recording direction within 1 ns. As expected, several
magnetization reversals can be observed within 10 ns asshown in Fig 8 (a). If we employ a definition stating thatthe magnetization is reversed when the 𝑀𝑀= /𝑀𝑀, value
reaches less than −0.9, the magnetization reversal
number is 4 times for the example in Fig 8 (a).
On the other hand, the 𝑁𝑁8 value is about 10-3 times
per nanosecond for 𝐾𝐾! /𝐾𝐾"!#$ = 0.4 as shown in Fig. 7.
There is almost no occasion where the magnetization
reverses in the opposite direction to the recording
direction. Therefore, the magnetization reverses
immediately in the recording direction after time 0, andmaintains that direction as shown in Fig. 8 (b).
The stochastic calculation result is consistent withthat employing a micromagnetic simulation. A feature of
our stochastic calculation is that it is easy to grasp thephysical implication of HAMR writing including HDMR,
and the calculation time is short.

(a)

(b)
Fig. 8 Time dependence of magnetization 𝑧𝑧 component
𝑀𝑀= /𝑀𝑀, at 740 K for (a) 𝐾𝐾! /𝐾𝐾"!#$ = 0.8 and (b) 0.4, where
the writing field magnitude |𝐻𝐻4 | is 10 kOe.

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INDEX(a)and adjacent track interference in 4 Tbpsi shingled
heated-dot magnetic recording (HDMR).
HDMR has a certain margin for erasure-after-write
since the nonmagnetic spacing is large, and a certain
margin for the dot aspect ratio since the dot size isrelatively large. Therefore, the combination of a small
anisotropy constant and a large dot volume can be used
to improve write-error.
When we chose a small anisotropy constant, the bit
error rate caused by write-error is low for a relatively
small writing field magnitude.
However, the bit error rate caused by erasure-afterwrite is high for a relatively large writing field region.
Overall, a small anisotropy constant is effective interms of obtaining a low bit error rate in HDMR.
Acknowledgement We acknowledge the support of theAdvanced Storage Research Consortium (ASRC), Japan.
Ref erences(b)Fig. 9 Mean magnetization reversal number per
nanosecond 𝑁𝑁2 = 𝑓𝑓52 expS−𝐾𝐾<2 T as a function of writingtime for various |𝐻𝐻4 | values. (a) 𝐾𝐾! /𝐾𝐾"!#$ = 0.8 and (b)0.4.
When 𝐾𝐾! /𝐾𝐾"!#$ = 0.4, the bER caused by EAW is highfor a relatively large |𝐻𝐻4 | magnitude as shown in Fig. 6(a). When the |𝐻𝐻4 | value is large, for example 20 kOe,
the 𝑁𝑁2 value is large at the end of the writing time
determined by field as shown in Fig. 9 (b) for 𝐾𝐾! /𝐾𝐾"!#$ =0.4, which can be compared with the result shown in Fig.
9 (a) for 𝐾𝐾! /𝐾𝐾"!#$ = 0.8. If a 𝐾𝐾! /𝐾𝐾"!#$ value, namely if
the 𝐻𝐻$677 value is small, the 𝐾𝐾<2 value is also small as
seen in Eq. (4) even for the same 𝐾𝐾!677 𝑉𝑉 value.
4. Concl usi ons

We examined the influence of the anisotropy constanton writability, taking account of 10 years of archiving

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Received Apr. 16, 2024; Accepted Jun. 18, 2024

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Copyright ©2024 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., 48, 88-93 (2024)<Paper>Synthesis and high-field magnetic measurement of Ba2Sn2+xMe1+xFe10-2xO22
H. Harasawa, H. Mitamura*, M. Tokunaga*, K. Kakizaki, and K. Kamishima

Graduate School of Science and Engineering, Saitama Univ., 255 Shimo-okubo, Saitama 338-8570, Japan*Institute for Solid State Physics, Univ. of Tokyo,

Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan

We report the successful synthesis of Ba2Sn2+xMe1+xFe10-2xO22, a series of single-phase materials derived bysubstituting divalent metals (Me2+=Ni2+, Co2+, Zn2+, Mg2+, and Cu2+) into the Ba2Sn2MeFe10O22 layered structure.
High-field magnetization measurements of the parent compound (Ba2Sn2MeFe10O22) unveil a unique magnetic
response, marked by a plateau at high fields, indicating a field-induced alignment of moments near barium cations.
This alignment contrasts with the antiferromagnetic arrangement of magnetic moments observed at low fields in aprevious neutron diffraction study. The decrease in magnetization with substitution suggests the absence of thepreference of Sn4+ for down-spin sites. This work paves the way for further exploration of the magnetic properties of
Ba2Sn2MeFe10O22 and its derivatives.
Keywords: QS-type ferrite, Ba2Sn2+xMe1+xFe10-2xO22, phase diagram, pulsed high magnetic fields
1. Introduction

In the field of materials science, hexaferrites standout due to their extensive historical significance andpractical applications.1-3) They are primarily oxides withiron acting as the principal magnetic ion, typically inthe high-spin Fe3+ state. Additionally, these materials
contain alkaline earth ions, such as Ba2+ or Sr2+, whichcharacterizes distinct structural units in hexaferrites.
The composite structure of hexaferrite arises fromcombining fundamental structural units.4-5) This layered
configuration induces magnetic anisotropy, a criticalfactor influencing numerous physical properties.
Typically, magnetic moments align perpendicular to thehexagonal layers, but exceptions occur, especially withthe presence of divalent transition metal ions such as
Co2+, where magnetic alignment takes place within the
hexagonal plane.1-3)
The most prevalent variation of hexaferrite is theM-type, represented by the general formula AFe12O19,
where A signifies divalent alkaline earth ions,commonly Ba2+ or Sr2+.1-2) Recognized for its strong
magnetic characteristics, M-type hexaferrite is widely
employed as a hard magnetic material, distinguished by
its relatively high coercivity and saturation
magnetization. The Y-type hexaferrite also stands out
as a significant structural variant, with the chemical
formula Ba2Me2Fe12O22, where Me represents a divalenttransition metal. The Y-type hexaferrite exhibits
stacking
arrangements
comprising
S-block(Me2+2Fe4O8)0± and T-block (Ba2Fe8O14)0± structures.4-5)
In these materials, magnetic moments align within the
hexagonal plane, allowing for free rotation in the abplane, thus giving them the characteristic of soft
magnetic materials. Their unique properties make themvaluable for applications requiring high-frequency(GHz) RF usage.6-10)
Corresponding

author:K.

Kamishima

There is another hexaferrite of the QS-type thatshares a stacking structure similar to that of theY-type.11-14) The present investigation focuses on the
QS-type hexaferrites, Ba2Sn2MeFe10O22, characterized
by a layered arrangement consisting of alternating
S-block (Me2+Fe5O8)+ and Q-block (Ba2Sn2Fe5O14)-. Table
1 provides an overview of the crystallographic unit celldetails for the QS-type hexaferrite. Previous reports
established the presence of two formula units (QSQS)
within the magnetic unit cell of this material; themagnetic structure exhibits a c-axis twice the length of
Table 1 Overview of the crystallographic unit celldetails for the QS-type hexaferrite. Each row
describes the quantity of atoms within the unit cell,
the corresponding atom block, their designated labels
in Fig. 8, and their associated coordinates for
Ba2Sn2NiFe10O22 in Ref. 13.

(e-mail:kamisima@mail.saitama-u.ac.jp).

88

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the crystallographic c-axis while sharing the samea-axis. As depicted in Fig. 8(b) later, the magnetic unit
cell comprises 18 sites labeled along the c-axis. The
magnetic moments associated with one formula unit
(QS) exhibit equivalence and antiparallel alignment,
leading to antiferromagnetism.13) Despite its existence,
Ba2Sn2MeFe10O22 has yet to be extensively investigatedin determining whether the reported microscopic
antiferromagnetic structure adequately accounts for
macroscopic magnetization.
This study aims to explain the consequences ofsubstituting 2Fe3+ with Sn4+ and Me2+ in
Ba2Sn2MeFe10O22 for the following systems: Me2+=Ni2+,
Co2+, Zn2+, Mg2+, and Cu2+. Introducing non-magnetic
Sn4+ ions is anticipated to diminish the down-spin
population, potentially inducing ferrimagnetism. To
check the result of the arrangements of these magnetic
moments, we examined the magnetization of thesubstituted samples, Ba2Sn2+xMe1+xFe10-2xO22, up to ahigh magnetic field of about 600 kOe. This method
offers valuable insights into how magnetic moments arearranged, as demonstrated in a previous study involving
a different type of substituted hexaferrite.15)
2. Experimental Procedure

The preparation of the experimental materials
involved the precise weighing of BaCO3, α-Fe2O3, SnO2,
and MeO powders to achieve a targeted composition of
Ba2Sn2+xMe1+xFe10-2xO22 (-1.0 ≤ x ≤ 2.0). The subsequent
mixing process used a wet ball mill for 24 hours,
followed by drying. The mixed powders were thenshaped into disc-shaped samples with a diameter of 12mm. The final step involved sintering the molded
samples in air at temperatures between 1000°C and
1300°C for five hours. The crystal structure wasinvestigated by powder X-ray diffraction (XRD) with
Cu-Kα radiation (1.5405 Å). The extraction of lattice
constants from the acquired X-ray diffraction peaks
relied on Cohen’s method of least-squares.16) The
magnetization measurements were carried out undervarious magnetic field strengths: up to 15 kOe by a
VSM, up to 70 kOe by a SQUID, and up to 600 kOe by apulsed magnetic field. Magnetization measurements inpulsed high magnetic fields utilized an induction
method.

Fig. 1 X-ray diffraction (XRD) patterns of
Ba2Sn2+xNi1+xFe10-2xO22 series (-1.0 ≤ x ≤ 2.0) sinteredat 1300°C.

3. Experimental results and discussions

Figure 1 presents the X-ray diffraction (XRD)
patterns of Ba2Sn2+xNi1+xFe10-2xO22 series (-1.0 ≤ x ≤ 2.0)
sintered at 1300°C. While a single phase was observed
for compositions within the range of -0.1 ≤ x ≤ 1.0 at
1200°C, shifting x negatively led to the formation of the
QS structure associated with BaSn0.9Fe5.47O11.
Conversely, increasing x resulted in forming the Snoxide with the R block, identified as BaSn2Fe4O11. Thisphenomenon is attributed to the formation of
BaSn2Fe4O11, which shares a composition close to
Ba2Sn4Ni3Fe6O22 (x = 2.0) upon reaching the cation

Fig.
2
X-ray
diffraction
patterns
of
Ba2Sn2+xCu1+xFe10-2xO22 series (-0.2 ≤ x ≤ 0.8) sinteredat 1200°C.

substitution limit for the QS block.
Figure 2 shows the X-ray diffraction patterns of
Ba2Sn2+xCu1+xFe10-2xO22 series (-0.2 ≤ x ≤ 0.8) sintered at

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Fig. 3 X-ray diffraction (XRD) patterns of theBa2Sn2+xCo1+xFe10-2xO22 series (-0.2 ≤ x ≤ 1.2) sinteredat 1200°C.

Fig. 4 X-ray diffraction (XRD) patterns of
Ba2Sn2+xMg1+xFe10-2xO22 series (-0.2 ≤ x ≤ 1.0) sinteredat 1300°C.

1200°C. The analysis reveals the formation of a single
phase for the composition range -0.1 ≤ x ≤ 0.4. However,samples with x values of 0.6, 0.8, and 1.0 undergo
melting, preventing the achievement of a single phasein these cases.
Figure 3 shows the X-ray diffraction (XRD) patternsof Ba2Sn2+xCo1+xFe10-2xO22 series (-0.2 ≤ x ≤ 1.2) sinteredat 1200°C. While a single phase was obtained forcompositions within the range of 0 ≤ x ≤ 0.8, the M-type
hexaferrite was formed at both the substitution limits ofx = -0.1 and 1.0. Although the minority phase is thesame M-type hexaferrite, it is highly possible that theM-type hexaferrite in the sample at x = -0.1 contains
more Fe3+ and less Me2+ and Sn4+ than at x = 1.0.
Figure 4 illustrates the X-ray diffraction (XRD)
patterns of Ba2Sn2+xMg1+xFe10-2xO22 series (-0.2 ≤ x ≤ 1.0)
sintered at 1300°C. Similar to Fig. 3, a single phase wasobserved for compositions within the range of -0.1 ≤ x ≤0.8. The M-type hexaferrite phase was again observedat the substitution limits, x = -0.2 and 1.0.
Figure 5 shows the X-ray diffraction patterns of
Ba2Sn2+xZn1+xFe10-2xO22 series (-0.2 ≤ x ≤ 1.0) sintered at
1300°C. Similar to the observations in Figure 3,
analysis of the patterns reveals the formation of a single
phase for the composition range -0.1 ≤ x ≤ 0.6.
Additionally, the M-type phase was observed at both thesubstitution limits, x = -0.2 and 1.0.
Figure 6 depicts a schematic diagram representing
thesingle-phasefabrication
range
for
the
Ba2Sn2+xMe1+xFe10-2xO22 series (where Me2+=Ni2+, Co2+,
Zn2+, Mg2+, and Cu2+). This diagram is based on theanalysis of X-ray diffraction (XRD) patterns obtained

from samples sintered at temperatures ranging from1100°C to 1300°C and containing varying x values
within the range of -0.2 ≤ x ≤ 1.2.
Figure 7 shows the magnetization curves of
Ba2Sn2MeFe10O22 (Me2+=Ni2+, Co2+, Zn2+, Mg2+, andCu2+) and the Fe3+ system Ba2Sn1.8Fe10.94O22 (=

90

Fig.
5
X-ray
diffraction
patterns
of
Ba2Sn2+xZn1+xFe10-2xO22 series (-0.2 ≤ x ≤ 1.0) sinteredat 1300°C.

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Fig. 7 Magnetization curves of Ba2Sn2MeFe10O22(Me2+=Ni2+, Co2+, Zn2+, Mg2+, and Cu2+) and Fe3+system Ba2Sn1.8Fe10.94O22 (= 2BaSn0.9Fe5.47O11),
measured at T=4.2 K up to H=600 kOe.
Fig. 6 Schematic diagram representing single-phasefabrication range for Ba2Sn2+xMe1+xFe10-2xO22 series(where Me2+=Ni2+, Co2+, Zn2+, Mg2+, and Cu2+).

2BaSn0.9Fe5.47O11), measured at T=4.2 K up to H=600
kOe. The magnetization curve of the Zn-based QS-type
hexaferrite did not reach full saturation, contrastingwith QS-type hexaferrites containing alternative
divalent cations. Zn2+ ions predominantly occupy
tetrahedral sites, specifically M2, M9, M11, and M18,
within the S blocks of the QS-type unit cell, whichfeatures alternating Q-, S-, Q-, and S-blocks. Notably,
these tetrahedral sites within the S block serve as
bottlenecks for transition metal ions when traced along
the block stacking direction. The presence of
non-magnetic Zn ions at these bottleneck positions cansignificantly disrupt the exchange interaction,hindering magnetization saturation compared to thatobserved in QS-type hexaferrites with different cations.
The figure demonstrates that the high-fieldmagnetization at H=600 kOe approaches a value of 20µB/f.u. for the Zn-system, 15 µB/f.u. for the Mg, Co, andFe systems, and 13 µB/f.u. for the Cu and Ni systems.
While generally in agreement with the findings of M. C.
Cadée et al. up to 400 kOe, our results present somenoticeable discrepancies. These differences likely stemfrom variations in sample synthesis conditions,particularly our approach compared to that of Cadée's,
who subjected samples to sintering at 1197°C over
several days. Such differences may induce alterations inionic distribution and, consequently, magnetic
properties, as demonstrated in the case of MgFe2O4.17)
Notably, the magnetization curves exhibit a kink-likefeature up to an applied field of 600 kOe. Theseobservations allow us to discuss the magnetic structureat H=600 kOe.
Figure 8 depicts the (a) two crystallographic unit cellsand (b) magnetic unit cell proposed by M. C. Cadée etal.13) Their analysis suggests that the cancellation ofionic magnetic moments within the magnetic unit cell
leads to antiferromagnetic behavior. Our present work
investigates whether this spin configuration canaccount for the observed magnetization at the plateau.
Considering the Zn-system as an example, thereplacement of non-magnetic Sn4+ and Zn2+ ions with 2
Fe3+ ions in two chemical formula units results in a
distribution of 20 Fe3+ magnetic moments. To achieve
agreement with the experimental value of 20 µB/f.u.,(1)
2 × (7 × 5 - 3 × 5) = 40 µB
mustbesatisfied.
This
means
that
the
two-chemical-formula-unit magnetic structure exhibits
fourteen right-pointing and six left-pointing magnetic
moments. Based on their valences and coordinationpreferences, we propose a plausible configuration (Fig.
8(c)) where Sn4+ ions occupy M8 and M12 sites, and Zn2+
ions occupy M2 and M18 sites. However, thisconfiguration yields a magnetic moment of 30 µB per
unit cell, which is inconsistent with the observed 40 µB
plateau magnetization.
The inability of the spin configuration proposed by M.
C. Cadée et al. to account for the observed plateau
magnetization necessitates a re-evaluation of themagnetic structure. While the bond length between M5
and M6 in Fig. 8(b) is significantly long, thecorresponding bond angle is 76º, as shown in Fig. 8(d).
This angle being close to 90º suggests a potential

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ferromagnetic alignment of the magnetic moments.
So, we propose a field-induced alignment of moments
near barium cations in the Q-block. Figure 8(e) depicts
this magnetic structure with aligned magnetic moments
at the M5-M6 and M14-M15 sites, while other sites

maintain antiparallel alignments, as in Fig. 8(b). In otherwords, the directions of magnetic moments at theM6-M14 sites in Fig. 8(d) oppose those in Fig. 8(b). Thisconfiguration results in a distribution of eighteen
right-pointing and eight left-pointing magnetic
moments per unit cell, leading to a ferrimagnetic
arrangement throughout the crystal. Based on
considering the local charge balance, Sn4+ and Zn2+ are
expected to occupy the positions indicated in Fig. 8(f).

Fig. 8 (a) Two crystallographic unit cells of
Ba2Sn2MeFe10O22,(b)magnetic
structureof
Ba2Sn2MeFe10O22 proposed by M. C. Cadée et al.
(1986), (c) plausible spin configuration based on (b)with Sn4+ and Zn2+ cations, (d) bond between M5 andM6 in Q block, (e) modified magnetic structure withaligned magnetic moments at M5-M6 and M14-M15
sites, and (f) plausible spin configuration based on (e)with Sn4+ and Zn2+ cations.

92

Therefore, at low magnetic fields, the dominantmagnetic structure is the one depicted in Fig. 8(b),which leads to the cancellation of the magnetic
moments within the crystal. However, at high magnetic
fields, the alignment of the M5-M6 and M14-M15
magnetic moments (as shown in Fig. 8(e)) gives rise to
the observed plateau.
We consider if the magnetic structure shown in Fig.
8(e) applies to another divalent metal substitution.
Considering the non-magnetic Mg-system, the same
configuration as in Fig. 8(e) would yield 18
right-pointing and eight left-pointing moments.
Replacing Fe3+ with four non-magnetic Sn4+ and two
Mg2+ in the Mg system requires an equation of(2)
2 × (6.5 × 5 - 3.5 × 5) = 30 µB
for the experimental value of 15 µB/f.u. This translates
to thirteen right-pointing and seven left-pointing
moments. Assigning Sn4+ and Mg2+ to the Fig. 8(e)configuration, Sn4+ likely occupies M8 and M17 due toits high valence and preference for octahedral sites.
Mg2+, being able to occupy both tetrahedral andoctahedral sites as the incomplete inverse spinel
structure of MgFe2O4 demonstrates, is assumed to havea 50% occupancy in M1, M2, M10, and M11 of the S
block.
Figure 9 shows the magnetization values of
Ba2Sn2+xMe1+xFe10-2xO22 at an applied magnetic field of
550 kOe and a temperature of 4.2 K. The magnetization
decreased with increasing substitution levels. Thisobserved reduction can be attributed to two main
factors: (1) the substituted ions, which possess smaller
magnetic moments compared to Fe3+, do not exhibit apreferential occupancy of the left-handed spin sites, and(2) the dilution of the system with non-magnetic Sn4+
ions, which disrupts the super-exchange interaction. It

Fig. 9 Magnetization of Ba2Sn2+xMe1+xFe10-2xO22 atapplied magnetic field of 550 kOe and temperature of
4.2 K.

Journal of the Magnetics Society of Japan Vol.48, No.5, 2024

INDEXis likely that introducing non-magnetic Sn4+ ions does
not diminish the down-spin population.
4. Conclusion

We report the successful achievement of single-phase
synthesis for the Ba2Sn2+xMe1+xFe10-2xO22 series, which
represents a divalent metal substitution system derived
from the Ba2Sn2MeFe10O22 QS-type hexagonal ferrite.
This achievement was realized within specific synthesis
temperature ranges (TS) and substitution level ranges(x) for the Co, Ni, Mg, Zn, and Cu systems. Furthermore,
the investigation of the magnetic properties of theBa2Sn2MeFe10O22 ferrite suggests the following
potential explanation: at low magnetic fields, thedominant magnetic structure, as described by M. C.
Cadée et al., leads to the cancellation of the magnetic
moments within the unit cell. However, at highmagnetic fields, the alignment of the magnetic moments
near barium cations in the Q block results in theobserved
plateau.
Themagnetizationof
Ba2Sn2+xMe1+xFe10-2xO22 decreased with increasing
substitution levels, which implies that introducing
non-magnetic Sn4+ ions does not diminish the down-spin
population.
Acknowledgements This work was supported by JSPS
KAKENHI Grant Number 21K04862. The high-fieldmagnetic measurements were carried out along the
proposals
No.
202211-HMBXX-0005
and202209-HMBXX-0089, and partly supported by ISSP of
the University of Tokyo.

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Journal of the Magnetics Society of Japan Vol.48, No.5, 2024

93

INDEX

Editorial Committee Members・Paper Committee Members
S. Yabukami and T. Taniyama (Chairperson), N. H. Pham, D. Oyama and M. Ohtake (Secretary)
H. Aoki
M. GotoT. GotoK. Hioki
S. Inui
M. Iwai
Y. Kamihara
H. Kikuchi
T. Kojima
H. KuraK. Masuda
Y. Nakamura
K. Nishijima
T. Nozaki
T. SatoT. Suetsuna
K. Suzuki
Y. Takamura
K. ThamT. Tanaka
N. Wakiya
S. Yakata
A. YaoS. Yamada
M. Yoshida
N. Adachi
S. Haku
K. Kobayashi
Y. SatoI. Tagawa
S. Yoshimura

K. Bessho
S. Honda
T. MakiS. Seino
K. Tajima

M. DoiS. Isogami
S. Muroga
M. Sekino
M. Takezawa

T. DoiT. Kawaguchi
M. NaoeY. Shiota
T. Takura

T. Hasegawa
T. KawaiT. Narita
T. Shirokura
S. Tamaru

K. ItoA. Kuwahata
E. Shikoh
M. Toko
R. Hashimoto
N. Kikuchi
M. Sakakibara
S. Sugahara
T. Yamazaki

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編 集 委 員・論 文 委 員
薮上 信（理事） 谷山智康（理事） Pham NamHai（幹事）
青木英恵
伊藤啓太
乾
成里
岩井守生
後藤太一
後藤
穣
佐藤
拓
仕幸英治
Kim Kong Tham
仲村泰明
西島健一
山田晋也
吉田征弘
脇谷尚樹

大竹 充（幹事） 小山大介（幹事）
神原陽一
菊池弘昭
藏
裕彰
末綱倫浩
鈴木和也
高村陽太
野崎友大
日置敬子
増田啓介

桑波田晃弘
田中哲郎
八尾
惇

小嶋隆幸
都甲
大
家形
諭

安達信泰
白倉孝典
土井達也
槙
智仁

菊池伸明
田倉哲也
白
怜士

佐藤佑樹
田島克文
別所和宏

塩田陽一
田丸慎吾
本多周太

磯上慎二
菅原
聡
土井正晶
室賀
翔

川井哲郎
清野智史
直江正幸
山崎貴大

川口昂彦
関野正樹
成田正敬
吉村
哲

小林宏一郎
田河育也
橋本良介

榊原
満
竹澤昌晃
長谷川 崇

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