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ISSN 2432-0250

Vol.42 No.3
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2018

Hard and Soft Magnetic Materials
Anisotropic Magnetic Core for the Iron Loss Reduction of Permanent Magnet Synchronous Motor
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N. Denis, S. Takeda, K. Fujitani, K. Fujisaki, and S. Odawara…062

Thin Films, Fine Particles, Multilayers, Superlattices
Magnetostrictive Behaviors of fcc-Co(001) Single-Crystal Films Under Rotating Magnetic Fields
T. Kawai, M. Ohtake, and M. Futamoto…072

Magnetostriction Behaviors of Single- and Poly-Crystalline Ni/Ni-Co Bi-Layer Films
K. Serizawa, M. Ohtake, T. Kawai, M. Futamoto, F. Kirino, and N. Inaba…078

Power Magnetics

Eﬀects of magnetic ﬁeld applied during heat treatment on magnetic properties of non-oriented electrical steel sheets
T. Kinoshita, K. Kohara, H. Shimoji, T. Sato, and T. Todaka…083

Biomagnetism / Medical Applications
Optimization of Resonant Circuit and Evaluation of Magnetic Field Uniformity with 50 mm Gap Magnetic Field Generator
R. Hasegawa, T. Nakagawa, S. Seino, and T. A. Yamamoto

広告◇東英工業株式会社◇計測エンジニアリングシステム株式会社◇ネオアーク株式会社

…090

42

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

3

2018

INDEX

Journal of the Magnetics Society of Japan
Vol. 42, No. 3
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Hard and Soft Magnetic Materials
Anisotropic Magnetic Core for the Iron Loss Reduction of Permanent Magnet Synchronous Motor… ………………………………………… N. Denis, S. Takeda, K. Fujitani, K. Fujisaki, and S. Odawara

62

Thin Films, Fine Particles, Multilayers, Superlattices
Magnetostrictive Behaviors of fcc-Co(001) Single-Crystal Films Under Rotating Magnetic Fields… …………………………………………………………………… T. Kawai, M. Ohtake, and M. Futamoto

72

Magnetostriction Behaviors of Single- and Poly-Crystalline Ni/Ni-Co Bi-Layer Films… …………………………… K. Serizawa, M. Ohtake, T. Kawai, M. Futamoto, F. Kirino, and N. Inaba

78

Power Magnetics
Effects of magnetic field applied during heat treatment on magnetic properties of non-oriented electrical steel sheets		
… …………………………………………… T. Kinoshita, K. Kohara, H. Shimoji, T. Sato, and T. Todaka

83

Biomagnetism / Medical Applications
Optimization of Resonant Circuit and Evaluation of Magnetic Field Uniformity with 50 mm Gap Magnetic Field Generator		… …………………………………………… R. Hasegawa, T. Nakagawa, S. Seino, and T. A. Yamamoto

Board of Directors of The Magnetics Society of Japan
President:

K. Takanashi

Vice Presidents:

K. Nakagawa, S. Nakamura

Directors, General Affairs:

Y. Miyamoto, K. Niiduma

Directors, Treasurer:

K. Aoshima, K. Ishiyama

Directors, Planning:

Y. Saito, S. Nakagawa

Directors, Editorial:

K. Kobayashi, T. Ono

Directors, Public Relations:

H. Itoh, S. Greaves

Directors, International Affairs: Y. Takemura, M. Nakano
Auditors:

Y. Suzuki, R. Nakatani

90

INDEX
J. Magn. Soc. Jpn., 42, 62-71 (2018)<Paper>Anisotropic Magnetic Core for the Iron Loss Reduction of Permanent
Magnet Synchronous Motor
Nicolas Denis*, Shinya Takeda*, Kohei Fujitani*, Keisuke Fujisaki*, Shunya Odawara*** Toyota Technological Institute,2-12-1 Hisakata, Tempaku-ku, Nagoya 468-8511, Japan
165 Koen-cho Kitami, Hokkaido 090-8507, Japan** Kitami Institute of Technology,

An interior permanent magnet synchronous motor (IPMSM) using a stator core made of grain-oriented (GO)anisotropic magnetic material is manufactured to evaluate the potential iron loss reduction that GO can bringcompared to the conventionally used non-oriented (NO) quasi-isotropic silicon steel. The stator core is divided into
yoke and teeth pieces that are arranged so that the GO material easy magnetization direction follows the main
magnetic flux that flows in the core during the motor operation. The motor iron loss is measured under two
conditions: 1) the IPMSM is rotated by an external motor (“drag force operation”), 2) the IPMSM is driven by apulse-width modulation (PWM) inverter without load (“no-load operation”). The manufactured motor shows 13.5 %iron loss reduction during drag force operation and 5 % reduction during no-load operation. Numerical calculation is
also carried out by 2-D finite element analysis (FEA) to confirm the experimental data.
Key words: Grain-oriented magnetic material, Iron losses, Magnetic core, Permanent magnet synchronous motor,
Silicon steel
1. Introduction
Global warming and/or polluted urban areas is one of
the biggest challenge that the society is facing today.
Electrified vehicles are presented as one of the possible
solutions but they still have to be more affordable andincrease their autonomy in order to be more widely
accepted by the society. The limited embeddable
electrical energy in batteries is still a strong limit andtherefore, the losses that occur in each part of theelectrical powertrains should be reduced as much as
possible. Interior permanent magnet synchronous
motors (IPMSM) are known to be very efficient driving
power sources for electrical vehicles but still contributeto waste of electrical energy caused by mechanicalfriction loss, coper loss and iron loss. In order to reducethe iron loss, focusing on the magnetic materials
characteristics and applications is important 1).
Non-oriented silicon steel (NO) has small magnetic
anisotropy. Moreover, its iron loss density and its
magnetization characteristic are usually measured
using the Epstein frame in which several sheets aresuperimposed with alternating direction (90°, 0°). In thisway, the measured characteristic is considered as anaverage characteristic over the sheet orientation angle
range. In other words, knowing the fact that theanisotropy is usually small, one single averagecharacteristic is usually preferred for simplification
rather that a complete characterization for every
orientation angle. On the other hand, grain-oriented
steel (GO) 2)-3) has strong magnetic anisotropy 4) that has
to be measured and characterized. GO is generally used
for electrical transformer cores. It has very small ironloss density in its easy magnetization direction.
Fig. 1 shows the magnetic characteristics of NO andGO at 50 Hz taken from catalogue data 5). The NO steel
has one single characteristic, as explained previously,
while the GO steel characteristic depends on the angle φ,62which is the angle between the magnetic flux density
vector and the easy magnetization direction. In
particular, GO has low iron loss density in the easymagnetization axis (φ = 0°, (100) direction) while high inthe transverse direction (φ = 90°, (010) direction).
Because the magnetic flux in a stator core of anelectrical motor flows multi directionally, simply
substituting NO steel by GO steel would make themagnetic flux force its way through the transverse
direction of GO at some parts. This would have forconsequence to likely increase the iron losses. This
underlinesthechallengeofdesigningandmanufacturing a motor core with GO steel. However,considering its superior magnetic properties, the authors
think that GO is worth experimental trials in scientificresearch.
A proposed solution is to assemble the stator shifting
each lamination from the previous one with a constantangle, so the easy magnetization direction appears in
different parts of the stator 6). This supposedly makes
the magnetic flux pass from one lamination to another inorder to avoid the parts which present the transverse
magnetization direction. However, it can be argued thatthe magnetic flux could be restrained, causing a loss of
performance of the motor. Moreover, in ref. 6), tests aredone using the stator as a transformer core and not as
part of an actual motor. Consequently, segmented typestators are tried in which teeth and yoke are divided 7)- 9),
however only the teeth are made of GO steel. It would beinteresting to evaluate the improvement of a stator
composed solely of GO steel. GO steel is also applied torotor cores 10)-13) for which increase of electromagnetic
torque and efficiency are reported. However, the rotor
core is usually not the major contributor of the motor
iron losses, so for the purpose of iron loss reduction,
studies and trials should focus primarily on the stator.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

Magnetic flux density B [T]Divided steel piece

Stator

2.5
2.0

T-joint partGO(35ZH135): φ = 0

1.5

Yoke partNO(35H300)

Rotor

1.0
0.5

Permanent
magnetGO(35ZH135): φ = 90

Teeth part

0.0
1

10

100
1000
10000
Magnetic field intensity H [A/m]

100000Easy magnetization
direction(a) B-H curve
5

Fig. 2 Geometry of the proposed magnetic anisotropic
motor.

Iron loss W [W/kg]

4
GO(35ZH135): φ = 90
3
2
NO(35H300)
1
GO(35ZH135): φ = 0

0
1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Magnetic flux density B [T](b) B-W curve

Fig. 1 Magnetic characteristics of NO steel (35H300) andGO steel (35ZH135) at 50 Hz.
Considering the current state of the art describedabove, this paper proposes a novel assembly for an
IPMSM stator core made completely of GO steel. The
IPMSM using the proposed stator core, illustrated in Fig.
2, will be called “magnetic anisotropic motor” hereafter.
The considerations lying under the proposed coreassembly are as follows: at first, the assumption that themagnetic flux flows mainly in the radial direction in thestator tooth and in the tangential direction in the stator
yoke is made. Based on this assumption, it is proposed todivide the yoke part and tooth part and cut GO steel
pieces accordingly. The GO steel pieces are thenarranged so that the GO easy magnetization direction
coincides mostly with the tangential direction in theyoke and, similarly, the GO easy magnetization
direction coincides mostly with the radial direction in
the teeth. This configuration has been chosen as an
attempt to maximize the correspondence between themagnetic flux direction and the GO easy magnetization
direction. In previous works, the suitable shape of the
proposed magnetic anisotropic motor was designed byusing finite element analysis (FEA) 14) . Iron loss
measurement trials have been made under “drag force
operation” (IPMSM rotated by an external motor) in theprevious work 1 5 ) but it is believed that thesemeasurements along with the analysis have to becorrected and improved. Moreover ref. 15) does notpresent any results concerning the motor rotated by apulse-width modulation (PWM) inverter, which is themost common way to drive an IPMSM.
In this paper, section II provides some important
information about the manufacturing process. The
manufacture of the stator core requires precision andlimiting the mechanical stress as much as possible iscrucial. In section III, the magnetic anisotropic motor istested under both “drag force operation” and “no-load
operation” (IPMSM driven by a PWM inverter without
mechanical load) and its capacity to reduce iron loss is
assessed. Finally, section IV presents numericalmagnetic calculation to verify the measured data.
2. Trial Manufacture of Magnetic Anisotropic Motor
The GO steel 35ZH135 is used to manufacture thestator of an IPMSM with 12-slots, 8-poles, andconcentrated windings. The detailed geometry is shownin Fig. 3 and Table I. In the proposed geometry, the slot
opening is quite large and will cause a high torque ripple.
Since no dedicated machinery was available to wind thestator, wide slot opening has been chosen to make thewinding process easier to do by hand. Since thereduction of torque ripple is not the focus of this study, it
is considered that this particular geometry does notnegatively affect the conclusions of this paper.
For the sake of comparison, a stator made of NO steel
35H300 has also been manufactured. Since the
manufacture process of the NO stator is significantly
different from that of the GO stator, it is difficult toobtain geometrical similarity to the 10 microns order.
The dimensions of the NO stator differ slightly from
Table I. RSi is equal to 38.20 mm and the axial length to46.9 mm. It is thought that the differences observed do
not influence the iron loss to the point at which acomparison is significantly unfair.
In both cases, the rotor core of the motor is made ofNO steel (35H300). Sintered NdFeB permanent magnets(PM) are used. Their characteristics are given in Table
II.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

63

INDEXTABLE II CHARACTERISTICS OF PERMANENT MAGNETS AT
ROOM TEMPERATURE.

PM residual magnetization
Coercive force
Electrical conductivity

Bm
Hc
σ

1.28 T
1.02×106 A/m
6.25×105 S/m

Lamination direction

Yoke part

Teeth part(a) With the same shape

Fig. 3 Proposed magnetic anisotropic motor (quarter sizemodel).

(b) With the different shape(a) No overlapping(b) Overlapping( is given for lap-joint)
Fig. 4 T-joint part, (a) No overlap, (b) With overlap.

TABLE I SPECIFICATIONS OF MAGNETIC ANISOTROPIC
MOTOR.

Number of poles
Number of slots
Radius of stator core (outside)
Radius of stator core (inside)
Yoke width
Teeth width
Radius of rotor
Air gap between stator androtor
PM width
Stator axial lengthWinding method

-

8
12
64 mm
38.15 mm
9.17 mm10.00 mm36.95 mm1.20 mm

WPM

20 mm
47.0 mmConcentrated

RSo
RSi
WY
WT
RR
G
-

In the GO stator core, the junction between the toothpart and the yoke parts is illustrated in Fig. 4. A joint
structure without overlap from one layer to another, as
in Fig. 4.a, would cause mechanical brittleness.
Consequently, a structure with overlaps, as in Fig. 4.b,has been chosen to ensure the stator overall solidity.
Therefore, the angle  defined in Fig. 4.b has to be taken
inferior to 90°. In the previous study 14), numericalanalysis has been performed in order to find an angle
that would ensure good tradeoff between iron loss
minimization and mechanical solidity. The selected
angle is 80°.
The manufacture process of the GO stator has beendetailed in previous papers 14)-15). This paper does not
aim at providing detailed manufacture explanations but
some points should be noted. For both the GO and NO
stators, wire electric discharge machining has been used
to cut the electrical steel sheets while avoiding highmechanical stress 16). In order to improve the mechanicalsolidity of the GO stator, compressive force was appliedfor 30 minutes after each completed layer. As aconsequence, the stacking factor of the GO stator isslightly higher (99.8%) than for the NO stator (97.7%).
GO is known to have more stress sensitivity than NO

64(a) Using NO steel(b) Using GO steel

Fig. 5 Completed stator core specimens.
but the effect is negligible in case of uniform axial
which
was
compression.
Therefore,ajig15),
manufactured so that a good geometrical accuracy canbe kept, is prepared to avoid this type of stress. Fig. 5
shows the completed stator core specimens.
It can be understood that the GO requires extra
manufacture because of the special junction between
teeth parts and yoke parts. On top of that, GO requires
more cutting using the rather expensive wire electric
discharge machining. Therefore, the proposed GO stator
core increases manufacture complexity and cost, which
is a disadvantage compared to the NO stator. However,
future development in manufacturing technology could
help to overcome these problems. Moreover, as motor
applications expand widely, the proposed GO stator core
could be useful for special applications (like aircraft orspacecraft) in which the iron loss reduction is required
while the motor core cost is less crucial.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

3. Experimental Evaluation of Magnetic Anisotropic
Motor
As explained in the introduction, the manufactured
magnetic anisotropic motor iron losses are evaluatedexperimentally under “drag force operation” and“no-load operation”. Table III shows equipment used forthe operations. The tests are explained hereafter.
3.1 Drag Force Operation
The drag force operation measurement system is
illustrated in Fig. 6. No current is supplied to the tested
IPMSM (trial motor MS). The rotor of the IPMSM isrotated by an external brushless DC (BLDC) motor. The
BLDC motor rotational speed ω and output torque T aremeasured by a revolution indicator and a torque meter,
respectively. When the rotor is rotated by the BLDC
motor, the rotating permanent magnets magnetize thestator core, which creates stator iron losses. The teeth
shape of the IPMSM stator core generates variating
magnetic flux density in the rotor and magnets whichcause rotor and magnet iron losses.
Since no electrical power is supplied to the IPMSM,
the output power supplied by the BLDC motor balances
all the IPMSM losses, namely the iron loss Wi_drag andthe mechanical friction loss Wm. Then the following
equation holds.

Pout = ωT = Wi_drag + Wm,(1)

where Pout is the BLDC motor output mechanical power.
In order to measure the mechanical loss, a rotor withdemagnetized permanent magnets is used. It has thesame shape and bearings as the rotor with magnetized
permanent magnets. When the same drag force test as
described above is carried out replacing the conventionalrotor by the demagnetized rotor, there are no iron loss
generation and the term Wi disappears in (1). Therefore,
Wm can be calculated using the following equation.

P’out = ωT’ = Wm,

3.2 No-load Operation
During no-load operation, the trial IPMSM is driven
by a 3-phase PWM inverter. As shown in Fig. 7, theinverter output power Pinverter and the IPMSM phase
RMS current In are measured using a power analyzer
whose bandwidth is 2 MHz and sampling frequency 2.2
MHz. The rotational speed is controlled using a vector
control scheme and a speed feedback provided by anencoder. The d-axis IPMSM phase current reference is
set to zero, the PWM carrier frequency to 1 kHz and the
DC bus voltage to 180 V.
Because the trial IPMSM has no mechanical load, thepower balance verifies the following equation.
Pinverter = 3RaIn2 + Wm + Wenc + Wi_inv,(3)
where Ra (0.510 Ω) is the phase resistance that has beenmeasured in DC condition just after the measurements,
Wenc is the mechanical loss of the encoder measured by
the same method as used for the estimation of Wm. Thenthe IPMSM iron loss under no-load operation Wi_inv canbe deduced.
The measurement procedure of ten consecutive trials
introduced in the last section has also been carried out toincrease the reliability of the measurements.
TABLE III EXPERIMENTAL EQUIPMENT.

Item

Manufacturer

TH-3014H

Ono Sokki

Revolution indicator MD-0118

Ono Sokki

Watt meter

TS-2800

Ono Sokki

Blushless DC motor

BXM6200-A

Oriental motor

Encoder

MES-20-1024

Microtech Laboratory

Power analyzer

PPA-5530

IwatsuPWM inverter

MWINV-9R122B

Myway Plus

Pout

0

Watt meter

Ms

(2)

where P’out and T’ are the BLDC motor output
mechanical power and torque respectively, when the
demagnetized rotor is used. The IPMSM iron losses
under drag force operation can be deduced from (1) and(2).
The torque to measure is relatively small, whichmakes the measurements more susceptible touncertainties. The torque meter chosen for the test canmeasure a maximum torque of 1 N∙m and has an
accuracy of ±2 mN∙m, which corresponds to ±0.157 W at
750 rpm and ±0.628 W at 3000 rpm for the measured
power accuracy. In order to improve the reliability of theresults, the motor runs a first for 30 minutes at a given
speed in order to reach thermal steady-state operation
and avoid measurement differences due to thermaltransient behavior. Then one measurement consists inrecording the torque and speed for 20 seconds. The
recorded data are then averaged over the 20 seconds
time span. This procedure is done 10 times. The
standard deviation of the 10 measurements is thencalculated.

Model

Torque meter

Trial motor (Ms) Torque meter
Coupling

Blushless DC motor
Coupling

Revolution
indicator

Fig. 6 Schematic diagram of the iron loss measurement
system by drag force test.
0

Velocity
Controller

Pinverter

0

PWM
InverterPower Analyzer

Coupling
Trial Motor (Ms)

EncoderFig. 7 Schematic diagram of the iron loss measurement
system by no-load test.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

65

INDEX

The iron losses measured under no-load operation are
illustrated in Fig. 9. As in the previous section, thestandard deviation of the ten measurements is also
illustrated using bars. The PWM inverter causes highorder harmonics in the magnets, rotor and stator
magnetic flux that contribute to increase the iron loss
compared to drag force operation 19)-20). Under PWM
inverter excitation also, it appears that the GO stator
decreases the IPMSM iron loss. However, the reduction
percentage is smaller compared to the drag force
condition, especially at 750 rpm (50 Hz). This can be
explained by the fact that the GO material is originallyintended for application at 50/60 Hz and has its best
reduction potential at these frequencies compared to NO.
At higher frequencies, the iron loss density reduction
worsens, as shown by Table IV.

12

20

6

GO IPMSM loss

4

15
10

2

5

Reduction

0
500

1500
2500
Speed [rpm]

3500

0

Fig. 8 Iron loss comparison between magnetic
anisotropic motor and IPMSM with NO stator coreunder drag force operation.

25
Iron losses [W]The measured iron loss data need to be confirmed bynumerical calculation. Here, a 2-dimensional (2-D)
model for magnetic field analysis and Steinmetz
equations for iron loss calculation are used. Someassumptions and simplifications are made and detailed
in the following sections, along with their possible
consequences. It should be noted that the aim of thispaper is to evaluate the potential gain of using GO steel
in the proposed configuration and numerical analysis isdone to confirm the experimental data. Since the final
purpose of the paper is not to propose a novel numericalmodel, it is considered that the simplifications andassumptions could lead to possible inaccuracies but are
acceptable given the targeted purpose.

66

25

8

30

The 2-D model is based on FEA with A-method used
as in ref. 21). The fundamental equation is expressed asfollows:

 


  
 νx
Az  Az 
 νy x   x   y   y 
(4)



  J0  
Az  v0M y  ν0
Mx
t
x
y

NO IPMSM loss

10

4. Analysis of Magnetic Anisotropic Motor

4.1 Method for Magnetic Field Analysis

30

Reduction [%]3.4 Measurement Results of No-load Test

9
8

Reduction

7

20
15

6
5

NO IPMSM loss

4

10

GO IPMSM loss

2

5
0
500

3

Reduction [%]The IPMSM iron loss is measured at 750 rpm, 1500
rpm, 2250 rpm and 3000 rpm which correspond to anelectrical fundamental frequency of 50 Hz, 100 Hz, 150
Hz and 200 Hz respectively. The results obtained forboth IPMSMs (with GO stator and with NO stator) are
shown in Fig. 8. The bars represent the standard
deviation of the ten measurements. The iron loss
reduction calculated considering the average of the ten
measurements is also presented in Fig. 8. Even though
the reduction could be considered small given theincreased manufacture complexity, a reduction isobserved and is considered to be due to the superior
characteristics of GO steel 17) and the laser scratch that
downsizes the magnetic domains and then reduce theexcess loss 18).

where Az is the vector potential on the z-axis, νx and νyare the magnetic reluctivity on the x and y axis, v0 is thespace magnetic reluctivity, J0 is the current density
supplied to the coil parts, σ is the electrical conductivityof the material, and M is the magnetization of
permanent magnets.
In the GO stator, two-axis anisotropic method is used
to model the magnetic anisotropy. It provides
satisfactory magnetic field analysis when the material is
not magnetically saturated 22). The magnetic reluctivity
νx is the reluctivity of GO in the easy magnetization axisand νy is the reluctivity in the transverse magnetization
axis. They are calculated from Fig. 1.a. Since the easy
axis and transverse axis direction change at each toothand yoke part, it is impossible to take a unique ( x, y)reference frame for the whole numerical model.
Consequently, each tooth or yoke part has its own
reference frame.

IPMSM iron loss [W]

3.3 Measurement Results of Drag Force Test

1
1500

0
3500

2500
Speed [rpm]Fig. 9 Iron loss comparison between magnetic
anisotropic motor and IPMSM with NO stator coreunder no-load operation.
TABLE IV MATERIAL IRON LOSS DENSITY OF NO (35H300)
AND GO (35ZH135) AT B = 1 T.
Exciting frequency (Hz)

50

100

200

1000

NO (W/kg)

1.06

2.54

6.59

77.8

0.415

1.25

3.90

64.1

60.9

51.0

40.8

17.6

GO easy magnetization
direction (W/kg)
Reduction ratio (%)

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

WGO = ∑ {(Khys,e,i
i =1

B2

e,i + Khys,h,i+(Ked,e,i

B2B2h,i)fi22e,i + Ked,h,iB h,i)f i}(5)

unlike(6)+Ked,i(B 2t,i + B 2r,i)f 2i}
(5),

the

magnetic

Frequency

Fig. 10 Two-frequencies method to calculate theSteinmetz constants.
100

10
10 kHz

1 kHz

5 kHz 2 kHz

1400 Hz0.1

100 Hz200 Hz
50 Hz

0.01

0.01

0.1
Magnetic flux density (T)

1

(a)

flux

density

1 kHz

100

N

WNO = ∑ {Khys,i(B 2t,i + B 2r,i)fi
whereIntercept

1000

where i is the harmonic rank, N is the rank of thehighest harmonic, fi is the frequency of the ith harmonic,
and Bh,i and Be,i are the amplitudes of the ith harmonic of
Bh and Be respectively. Khys,e,i and Khys,h,i are thehysteresis loss Steinmetz constants of the GO in theeasy
andtransverse
magnetization
directions
respectively. Ked,e,i and Ked,h,i are the eddy current loss
Steinmetz constants of the GO in the easy andtransverse magnetization direction respectively.
As the NO stator is considered to have global
magnetic isotropy, the following equation can be usedinstead of (5) for the calculation of the iron loss density.
i =1

Inclination

isIron loss density (W/kg)

N

decomposed into its radial Br and tangential Bt
components and the Steinmetz constants do not dependon the direction in the material as shown by thedisappearance of the index h and e. The Steinmetz
constants depend on the frequency as shown by theindex i, and are calculated using the “two-frequencies
method”. This method, illustrated in Fig. 10, is basicallyan interpolation using the material iron loss
characteristics of Fig. 11. Figure 10 illustrates the caseof NO but the same procedure is applied to GO for boththe easy and transverse magnetization directions. Theinterpolation is done by considering the two available
nearest frequencies to the frequency fi.

Iron loss density (W/kg)

Similarly to the Epstein frame configuration
explained in the introduction, the NO stator lamination
is done by stacking the cut sheets with different
orientation angles (made possible by the several
symmetries of the stator shape). In this way, the stator
has small local anisotropy but can be considered to havea global magnetic isotropy since the material orientation
angle differs through the stator axial length, covering
the whole angle range. As a consequence, it is possible touse a single average B-H characteristic in the FEA
model without causing large inaccuracies. In otherwords, νx and νy are considered equal in (4) for the modelof the NO stator.
Because of the interlamination insulation and the factthat a 2-D model is used, the electrical conductivity istaken null in the stator and rotor. The magnetic field
induced by the eddy current is not considered and theeddy current losses are approximated by using the
Steinmetz equations. The electrical conductivity ofpermanent magnets however is considered and themagnets eddy current losses are obtained from thecalculation of the eddy currents flowing in the magnets.
Moreover, the magnetic reluctivity of the magnets istaken equal to that of the air.
When simulating the drag force operation, J0 is taken
null since there is no current in the coils. Whensimulating the no-load operation, the phase current thathas been measured during the no-load tests are used as
input of the numerical model. In other words, thecurrent density J0 is calculated based on the measured
phase current.
To evaluate the iron loss density WGO in the GO stator,
the magnetic flux density is first decomposed into its
components in the easy magnetization direction Be andthe transverse magnetization direction Bh. In this way,
the decomposition of the magnetic flux density vector
depends on the part (yoke or tooth) that is considered. A
fast Fourier transform (FFT) is then performed to findthe harmonic components of Be and Bh 23). Finally, theiron loss density at each point is calculated using the
Steinmetz approximation 24)-25).

500 Hz10200 Hz100 Hz

1

50 Hz

0.1

0.01
0.001

0.01

0.1
Magnetic flux density (T)1(b)

Fig. 11 Material iron loss density characteristics of GO
and NO. (a) 35H300 (b) 35ZH135 easy magnetization
direction (solid curve) and transverse direction (dashedcurve).

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

67

INDEX

Finally, the stator made of GO steel has much more
cutting than the stator made of NO steel. It is known
that cutting an electrical steel sheet increases the ironloss density in the vicinity of the cutting line. In thispaper, wire electric discharge machining has been used
for cutting. The paper does not aim at quantifying theimpact of the cutting on the GO stator iron losses but itshould be noted that wire electric discharge machining
causes very low level damage and can even leave thematerial undamaged when the process is followed bystress relief annealing under nitrogen atmosphere at
820 °C for 3 hours 16). It is then assumed that thedamaged area will have only a small impact on theactual motor iron losses and consequently, the choice
has been made not to model them in the FEA for amatter of simplification.
4.2 Influence of the Clearance Between the stator Pieces
The manufacture process of the GO stator results in asmall clearance between the yoke and teeth pieces. The
magnetic flux analysis results illustrated in the previous
section is obtained using a finite element model that
ignores the clearance.
1.0
0.8
0.6

0.4
0.2

Bh (T)

Equations (5) and (6) are a sum through theharmonics of the magnetic flux density 26). The
harmonics in the stator magnetic flux caused by therectangular magnets, the harmonics in the magnet androtor magnetic flux caused by the stator slots, and theharmonics caused by the PWM inverter are taken into
account in the calculation of the motor iron losses 27).
Moreover, even though the 2-D components of themagnetic flux density are considered in (5) and (6), theadditional iron loss due to the rotation of the magnetic
flux 28) is not modeled in this paper. For more accuracy,modeling the impact of rotational magnetic flux on theiron loss is preferable. However, for the NO material,
previous works show that the approximation (6) results
in a relatively good agreement between experiment andcalculation 27),29). As for the GO material, thepermeability in the transverse direction is much lower
than in the easy magnetization direction. Therefore, thequestion of whether or not the magnetic flux is rotatingin the GO stator remains to be investigated at this stage.
It is proposed to do this investigation for the case of dragforce operation at 750 rpm. Through magnetic flux
analysis, the magnetic flux density locus is calculated atthree different points of the stator shown in Fig. 12. The
magnetic flux density locus presents the variations of
the components Be and Bh of the magnetic flux density
simultaneously through one electrical period. Fig. 13
shows the obtained results. It can be seen that for all
points, the magnetic flux is stronger in the easymagnetization direction but the component in thetransverse direction remains non-negligible, especiallyin the tooth part, showing that the magnetic flux isrotating. In order to confirm that, it is proposed toillustrate the magnetic flux lines at a given position of
the rotor. The flux lines are shown in Fig. 14. It can beseen that some flux lines in the stator tooth are in thetransverse direction especially when the tooth faces thespace between two magnetic poles. Based on theseobservations, it is acknowledged that the impact of therotational magnetic flux on the GO iron loss should be
investigated in order to improve the model accuracy.
Since it is a quite difficult task, this study is left for
future work.

-1.0

-0.5

0.0
-0.2

A
0.0

0.5

1.0

B
C

-0.4
-0.6

-0.8
-1.0
Be (T)

Fig. 13 Magnetic flux density locus in the GO statorobtained by FEA (drag force operation at 750 rpm).

B
A
C

Fig. 12 Points considered for the investigation of themagnetic flux density locus.
68

Fig. 14 Magnetic flux lines in the magnetic anisotropic
motor (drag force operation at 750 rpm).
As a first approximation, it can be said that the total

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

1.0

4.3 Calculation Results
Fig. 16 and Fig. 17 show the measurements and thenumerical analysis results of both magnetic anisotropic
and NO IPMSMs iron losses in drag force and no-loadconditions respectively. For both numerical analysis andexperiments, the magnetic anisotropic IPMSM has lower
iron losses than the NO IPMSM.
TABLE V IRON LOSS CALCULATION RESULTS OBTAINED BY
1) MODEL CONSIDERING PIECES CLEARANCE, 2) MODELWITHOUT PIECES CLEARANCE (750 RPM)
Drag
force

No-load

0.6

Bh (T)

1.134
0.356
0.04081.095
0.353
0.0391

2.86

2.81

1.250
0.526
1.086

1.212
0.521
1.077

14

Exp

12

Magnet10

Rotor
Stator

8
6

2
0

A
0.0

0.5

1.0

B
C

-0.4

-0.6

Iron loss (W)

-0.2

1.49

GO GO NO NO
sim exp sim exp

GO GO NO NO
sim exp sim exp

GO GO NO NO
sim exp sim exp

GO GO NO NO
sim exp sim exp

750 rpm

1500 rpm

2250 rpm

3000 rpm

30

0.2
-0.5

1.53

4

0.4

-1.0

With clearance[W]

Fig. 16 Numerical analysis and measurements of
IPMSM iron losses in drag force condition.

0.8

0.0

IPMSM total
iron loss
Stator loss
Rotor loss
Magnet loss
IPMSM total
iron loss
Stator loss
Rotor loss
Magnet loss

No clearance[W]

16

Iron loss (W)reluctance of the magnetic flux path is mainly
determined by the rotor/stator air gap plus the magnet
and that the small clearance does not impact the total
reluctance significantly. In this section it is proposed toevaluate the influence of the clearance on the stator
magnetic flux density and iron losses.
If one considers a space factor of 98% in a laminatedcore of 350 μm thick steel sheets, it makes aninterlamination of approximately 7 μm. The assembly of
yoke and tooth parts has been done using an accurate jig15) that ensures similar clearance between pieces while
limiting mechanical pressure in the lamination direction.
The clearance is then likely to be larger than 7 μm andslightly different at each junction. Choosing a
representative clearance seems to be difficult but
considering the above points, a model with a clearance of
10 μm is developed. Moreover, considering the tightclearance, unevenness due to imperfect cutting might
locally affect the magnetic flux density. Because of the
difficulty of modeling the unevenness of the air gap, theclearance has been chosen uniform through the whole
gap in the new model.
The magnetic flux density locus obtained with the newmodel is illustrated in Fig. 15. The pieces clearancechanges the magnetic flux density quite sensibly,
especially in the T-joint part (point B), compared to thecase in which there is no clearance (Fig. 13).
Table V gives the results of the IPMSM iron losses
calculation using both models (with and without pieces
clearance). Simulation results for both drag force andno-load operations at 750 rpm are presented. It can beseen that the iron losses are slightly lower when theclearance is included but the results remain close.
Considering the above observations, it is decided to keep
the model including pieces clearance for all thesimulations whose results are presented in the next
section.

25

Exp

20

Rotor

MagnetStator

15
10
5

-0.8
-1.0
Be (T)

Fig. 15 Magnetic flux density locus in the GO statorobtained by FEA considering the pieces clearance (dragforce operation at 750 rpm).

0

GO GO NO NO
sim exp sim exp

GO GO NO NO
sim exp sim exp

GO GO NO NO
sim exp sim exp

GO GO NO NO
sim exp sim exp

750 rpm

1500 rpm

2250 rpm

3000 rpm

Fig. 17 Numerical analysis and measurements of
IPMSM iron losses in no-load condition.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

69

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However, the iron loss difference between themagnetic anisotropic motor and the NO IPMSM is larger
for the numerical calculation than for the experiments.
In particular, at 3000 rpm for example, themeasurements show a decrease of total iron losses by
about 7.5 % in drag force condition and 6.8 % in no-loadcondition. In comparison for the same speed, FEA
results show that the magnet and rotor iron losses arevery similar for both motors but the stator iron losses
drop by about 24 % in drag force operation and 27 % in
no-load operation when the GO stator is used. As
explained in section 4.1, the rotational losses have notbeen taken into account in the FEA neither for the NO
IPMSM nor the magnetic anisotropic motor. It isthought that the rotational magnetic flux density in the
GO material may have a bigger impact than for the NO
material, which could explain the lower iron loss
decrease obtained by experiment. Moreover, bothexperiment and numerical calculation show an increaseof iron losses between the drag force and the no-load
operations. This is due to the high frequency voltage
supplied to the motor coils by the PWM inverter in
no-load condition 19)-20). The magnet eddy currents areespecially strongly affected 30).
The peak magnetic flux density and the iron loss
distributions calculated by FEA for drag force operation
at 750 rpm are presented in Fig. 18 and Fig. 19 for the
NO IPMSM and the magnetic anisotropic motor
respectively. It should be noted that the iron loss
distribution shows only the rotor and stator iron losses
but not the magnet eddy current losses because both are
made at different calculation steps. In the NO IPMSM
the magnetic flux flows from the tooth to the yoke
concentrated in the inner area and the magnetic
2T

15 kW/m3

0T

0 kW/m3(a) Magnetic flux density(b) Iron loss density

Fig. 18 Peak magnetic flux density and iron loss density
distributions of NO IPMSM at 750 rpm (drag force
operation).
2T

flux density in the outer of the tooth/yoke junction area
remains low. Comparatively, for the magnetic
anisotropic motor, the magnetic flux rotates less andremains as much as possible in the easy magnetization
direction. Therefore it flows all the way towards theouter of the T-joint area, resulting in a higher iron loss
density compared to the NO stator in this zone.
Everywhere else, the iron loss density in the GO stator issmaller than in the NO stator. For both motors, the peakmagnetic flux density in the tooth is higher than in theyoke, which results in higher iron loss density. The
difference of iron loss density between the tooth andyoke parts seems to be more accentuated in the GO
stator though. This can be explained by the fact that,besides the higher peak magnetic flux density, themagnetic flux density component in the transverse
direction is larger in the tooth part than in the yoke part(Fig. 15).
5. Conclusion
A novel permanent magnet synchronous motor using astator made of grain-oriented steel sheets has been
evaluated. In drag force test conditions at 750 rpm, theexperiments show that the iron losses of the proposed
motor are 13.5 % lower than the iron losses of its
equivalent motor using exclusively non-oriented siliconsteel. The reduction becomes 5 % in no-load condition at
750 rpm.
The GO stator requires more cutting than aconventional stator and a low damage cutting technique
is preferred knowing the sensitivity of GO to mechanicalstress. Consequently, even though GO can reduce themotor iron losses, the GO stator manufacture is morecostly, making it more suitable for special applications
like aircrafts or spaceships at this moment. Moreover,numerical analysis could be improved by taking
rotational losses and cutting damage into account.
Finally, a simple geometry has been chosen for thestator core proposed in this paper. Thus, further
optimization is still a possible future investigation inorder to fully benefit from the characteristics of the GOmaterial.
Acknowledgements
This research is partially
supported by KAKENHI (26420259) of Ministry of
Education,
Culture,Sports,ScienceandTechnology.
References

15 kW/m3

1)

2)
3)
0T

0 kW/m3(a) Magnetic flux density(b) Iron loss density

Fig. 19 Peak magnetic flux density and iron loss density
distributions of magnetic anisotropic motor at 750 rpm(drag force operation).
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Received Nov. 01, 2017; Accepted Mar. 27, 2018

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J. Magn. Soc. Jpn., 42, 72-77 (2018)<Paper>Magnetostrictive Behaviors of fcc-Co(001) Single-Crystal Films
Under Rotating Magnetic Fields
Tetsuroh Kawai1, Mitsuru Ohtake1, 2, and Masaaki Futamoto1

Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan

1

Faculty of Engineering, Kogakuin University, 2665-1 Nakano, Hachiohji, Tokyo 192-0015, Japan

2

Magnetostrictive behaviors of fcc-Co(001) single-crystal films with thicknesses ranging from 40 to 500 nm areinvestigated under rotating magnetic fields up to 1.2 kOe. The magnetocrystalline anisotropy estimated from themagnetization curves is confirmed to be lying with four-fold symmetry, and the anisotropy field is within a narrow
range of 900~950 Oe for these films. The easy and the hard axes are lying parallel to <110> and <100>, respectively.
The magnetostrictive behavior measured along [110] shows rectangular or bathtub-like waveform and the amplitude
does not change much when the magnetic field is increased. On the contrary, the behavior along [100] shows
triangular waveform and the amplitude increases with increasing the magnetic field. These characteristic behaviors
are explained by using a coherent rotation model of magnetization assuming an in-plane four-fold magnetic
anisotropy. The magnetostriction constants (λ100, λ111) estimated from the amplitudes measured at 1.2 kOe are
λ100=(85~90)×10−6 and λ111=−(40~50)×10−6, respectively for these films. The λ100 values are in agreement with that
estimated by the first-principle calculation.
Key words: fcc-Co, magnetocrystalline anisotropy, magnetostriction, single-crystal film

1.

Introduction

The crystal structure of Co metal is known to be
hexagonal close packed (hcp) at room temperature andit changes to face centered cubic (fcc) over 450°C
according to the phase diagram. On the other hand,meta-stable fcc-Co appears even at room temperature in
the films prepared by molecular beam epitaxy or
spattering process 1-4). Single-crystal films of fcc-Co(001)are prepared by hetero-epitaxial film growth on Cu(001)underlayers, and their magnetic anisotropies arereported to be with the easy and the hard axes along<110> and <100>, respectively 5-7). Magnetic propertiesof fcc-Co are different from those of hcp-Co 7, 8). However,systematic magnetostriction studies of fcc-Co(001)single-crystal films have not yet been reported.
In the present study, well defined fcc-Co(001)single-crystal films are prepared on MgO(001)single-crystal substrates by employing Pd and Cu
underlayers and the magnetostrictive behaviors areinvestigated under rotating magnetic fields up to 1.2
kOe. The experimental results are analyzed by using a
coherent rotation model of magnetization considering
the magnetocrystalline anisotropy.
2.

Experimental Procedure

Co films with thicknesses of 40~500 nm wereprepared on MgO(001) single-crystal substrates of
20×20×0.5 mm3 with Pd (10 nm) and Cu (10 nm)
underlayers at 300 °C by using a radio-frequency
magnetron sputtering system equipped with a reflection
72

high energy electron diffraction (RHEED) facility. Thebase pressures were lower than 4×10–7 Pa. Before film
formation, the MgO substrates were heated at 600 °C
for 1 hour in the ultra-high vacuum chamber to obtainclean surface, which was confirmed by RHEED. The
underlayers of Pd and Cu were employed to adjust thelattice mismatch (16%) between MgO and fcc-Co andalso to promote Co thin film growth with a metastable
fcc structure 4). The film structure was confirmed by
RHEED
and
X-ray
diffraction
(XRD)
with
Cu-Kα radiation (λ=0.15418 nm). Magnetization curves
were measured by using a vibrating sample
magnetometer (VSM). Magnetostriction measurements
were carried out by using a cantilever method underrotating magnetic fields up to 1.2 kOe 9). The rotating
speed was 5 rpm. The magnetostriction observation
directions were set along [100] and [110] of the
MgO(001) substrates. The magnetostriction coefficient λis calculated from the following formula 9).

λ=2
ΔS ⋅ ts Es ⋅ (1 + ν f ) ,⋅2
3L ⋅ t f E f ⋅ (1 − ν s )(1)where ∆S is the measured bending, L is the distance
between laser beam points (12.5 mm), t is the thickness,
E is Young’s modulus, ν is Poisson’s ratio, and thesubscripts of f and s respectively refer to film andsubstrate. For the single-crystal films and thesingle-crystal substrates, the values shown in Table 1
are employed because the elastic property ofsingle-crystal sample is anisotropic10). In thecalculations, the elastic stiffness values of fcc-Ni were
employed for the values of fcc-Co because the stiffness
values of fcc-Co were unknown 11).

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

Table 1 E and ν values of fcc-Co and MgO materials
used in the present study 10, 11)．
<100>

<110>

<100>

<110>

E [GPa]

129

227

185

215

ν

0.384

−0.0850.34

0.23

Results and Discussion

3.1 Crystal structure of Co films grown on Cu/Pd
underlayers
RHEED patterns observed for Co films grown on
Cu/Pd underlayers are shown in Fig. 1. Similar sharp
streaks are observed for the Co films of different
thicknesses ranging from 40 to 500 nm, which indicatesthat the films are single-crystals with smooth surfaces.

¯
420

400

420

¯
220

200

220

(b) 100 nm(c) 200 nm

100 nm
200 nm
500 nm20(d) 500 nm

Fig. 1 RHEED patterns observed for Co films of (a) 40,(b) 100, (c) 200, and (d) 500 nm thicknesses. The
incident electron beam is parallel to MgO[100].
Figure 2 shows the out-of-plane and the in-plane
XRD patterns observed for these Co films. The fcc(002)
and (004) peaks are clearly recognized in addition to thereflections from the MgO substrates and the Cu/Pd
underlayers. Therefore, the films are determined to befcc(001) single-crystal films. The epitaxial orientation
relationship to the MgO substrate is determined as
fcc-Co(001)[100] ∥ MgO(001)[100].
The lattice parameters determined from the peak
positions of fcc(002) in the out-of-plane and the in-plane
XRDs are shown in Fig. 3. The lattice parametermeasured parallel to the substrate surface, a, is larger
than that measured perpendicular, c, for the thickness
range between 40 and 500 nm, indicating that the
fcc-crystal is slightly deformed. This is due to thehetero-epitaxial growth of fcc-Co(001) film on the
fcc-Cu(001) under layer, where the lattice parameters offcc-Cu (a=0.3614 nm) is 2.1% larger than that of bulk
fcc-Co (a=0.354 nm) and the fcc-Co lattice is expanded inlateral direction. The difference of lattice parameters offcc-Co(001) film decreases with increasing the film
thickness as shown in Fig. 3 suggesting that the
influence on the lattice strain from the Cu underlayer isdecreasing with increasing the Co film thickness. The
full width at half-maximum of rocking curves (Δθ50) is
shown in Fig. 4 as a function of film thickness. The Δθ50
values measured from the out-of-plane and the in-plane
XRDs are decreasing with increasing the film thickness,
which indicate that the crystallographic quality is
i mp r o v e d f o r th i c k e r f c c - C o ( 001) films. Theseexperimental results confirm that the Co films preparedPd(004)

40 nm

40

60

(b)

80
2θ (deg.)

100

120

MgO(002)
Pd(002)Co(002)fcc

Log intensity (arb. unit)(a) 40 nm

WL
Kβ

Log intensity (arb. unit)

Orientation3.

MgO(002)
Pd(002)Co(004)fcc
Cu(002)
MgO(004)
Co(002)fcc
Cu(004)

MgO

MgO(004)

40 nm

Pd(004)100 nm
200 nm
WL

WL
Kβ

20

500 nm Kβ

40

60

80
2θχ (deg.)

100

120

Fig. 2 XRD patterns observed for (a) out-of-plane and(b) in-plane of Co/Cu/Pd films formed on MgO(001)substrates. The Co film thickness is 40, 100, 200, and
500 nm, respectively.

0.37
Lattice constant (nm)fcc-Co

(a)

0.36

0.35

0.34
0

Cu

a
c

fcc-Co100 200 300 400 500
Film thickness (nm)Fig. 3 Lattice constants determined from the fcc(002)
peaks in the out-of-plane XRDs (c) and the in-plane
XRDs (a) of Co films. Arrows show the lattice constantsof bulk materials of Cu and fcc-Co.

Journal of the Magnetics Society of Japan Vol.42, No.3, 201873

INDEX<110> for the (40-200) nm thick films show sharpshoulder, which means that the coherent rotation ofmagnetization is dominant in the magnetization process.
On the other hand, the M-H curve for the 500 nm thickfilm shows mild shoulder, which means that thecoherent rotation mode is slightly disturbed in the film.
The small coercivities mean that the magnetic domain
wall motions are dominant in the magnetization reverse
process under small magnetic fields less than 50 Oe.

Δθ50 (deg.)

3
2

out

1
0

in
0

100

200 300 400 500
Film thickness (nm)Fig. 4 Film thickness dependence of full width at half
maximum of rocking curve (Δθ50) observed for theout-of-plane (out) and the in-plane (in) XRDs of Co
films.
in the present study are single-crystal films with
fcc(001) orientation involving very small lattice
deformation which decreases with increasing the film
thickness.
3.2 Magnetization curves of fcc Co(001) films
The magnetization curves of fcc Co(001) films
measured with the magnetic field aligned parallel to[100] and [110] are shown in Fig. 5. All the films areshowing similar types of M-H curve with the easy andthe hard axes parallel to [110] and [100], respectively.
The anisotropy filed matches to the saturation field forthe cubic (001) film with four-fold anisotropy 12). The
anisotropy field (Ha) is estimated to be ranging from 900
to 950 Oe for the film thickness between 40 and 500 nm.
The anisotropy field is nearly equal to those reported in
the references 5-7). The coercivities of these films are
ranging between 40 and 50 Oe, which are far smaller
than the H a values (900-950 Oe). Such kind ofmagnetization curves can be expressed by using themodified coherent rotation model 12). However, the detailof magnetization curve is slightly different depending on
the film thickness. The M-H curves along
1.0
0.5(a) 40 nm(b) 100 nm: <110>: <100>: <110>: <100>

0
−0.5
M/Ms

−1.0
1.0
0.5

(c) 200 nm(d) 500 nm: <110>: <100>0: <110>: <100>−0.5−1.0−2.0 −1.00−2.0 −1.0
1.0 2.0
Magnetic field (kOe)

0

1.0

2.0

Fig. 5 Magnetization curves measured for fcc-Co(001)films with the thickness of (a) 40, (b) 100, (c) 200, and(d) 500 nm, respectively.
74

3.3 Magnetostrictive behavior of fcc-Co(001) films
Figure 6 shows the magnetostrictive behaviors
measured along fcc[110] and [100] for the 40 nm thickfilm under rotating magnetic fields. The output voltageof 1 V corresponds to 0.2 μm bending of the sample. The
rotating angle, 0, corresponds to [010] for λ//[110] and to[110] for λ//[100]. The output voltages are quite small,λ// fcc[110]0.2 kOe

λ // fcc[100]0.04 V

0.3 kOe

0.5 kOe

0.5 kOe

0.7 kOe

0.7 kOe

1.0 kOe

1.0 kOe

1.2 kOe

0

90

180

0.04 V
0.2 kOe

0.3 kOe

Output (V)4

1.2 kOe

090
270
Rotation angle (deg.)

180

270

360

Fig. 6 Measured magnetostrictive behaviors of 40 nm
thick fcc-Co(001) single-crystal film under rotating
magnetic fields. The magnetostriction observation
direction is along fcc[110] and [100], respectively.
since the film thickness is very small (40 nm) incomparison to that of MgO base substrate (0.5 mm),whereas the S/N ratio is good. The waveform along [110],
namely along the easy magnetization axis, isrectangular under small magnetic fields up to 0.3 kOe
and changes to bath-tub like with increasing themagnetic field, while the amplitude is kept at almost asimilar level in the investigated magnetic field range.
However, the waveform along [100], namely along thehard magnetization axis, is triangular in theinvestigated magnetic field range and the amplitude
increase with increasing the magnetic field up to 1 kOe.
The waveforms are different from ideal sinusoidal evenunder a high magnetic field of 1.2 kOe, which is larger
than the magnetic anisotropy field. The output phasewith respect to the magnetic field angle is opposite
when measured along [110] and [100] directions, which

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEXλ // fcc[110]Output (V)

0.1 V

0.2 kOe

0.2 kOe

0.3 kOe

0.3 kOe
0.5 kOe

0.7 kOe

0.7 kOe180

1.2 kOe

090
270
Rotation angle (deg.)

180

270

360

Output (V)

0.3 kOe

0.5 kOe

0.5 kOe

0.7 kOe

0.7 kOe

1.2 kOe

90

180

0.1 V

0.2 kOe

0.3 kOe

1.0 kOe0

λ //fcc [100]0.1 V

1.0 kOe
1.2 kOe
090
270
Rotation angle (deg.)

0.1 V

0.2 kOe

0.3 kOe

0.3 kOe

0.5 kOe

0.5 kOe
0.7 kOe

1.0 kOe

1.0 kOe

1.2 kOe

1.2 kOe

90

180

0
90
270
Rotation angle (deg.)

180

270

360

Fig. 9 Measured magnetostrictive behaviors of 500 nm
thick fcc-Co(001) single-crystal film under rotating
magnetic fields. The magnetostriction observation
direction is along fcc[110] and fcc[100], respectively.

Fig. 7 Measured magnetostrictive behaviors of 100 nm
thick fcc-Co(001) single-crystal film under rotating
magnetic fields. The magnetostriction observation
direction is along fcc[110] and fcc[100], respectively.

0.2 kOe

0.1 V

0.1 V

1.0 kOe

λ // fcc[110]λ // fcc[100]0.7 kOe00.5 kOe

1.2 kOe90

0.2 kOe

λ // fcc[100]1.0 kOe0λ // fcc[110]Output (V)means that the sign of magnetostriction constant is
opposite between the two orientations.
Figure 7 shows the magnetostrictive behaviors
measured for the 100 nm thick film. The output
amplitude is increasing in proportional to the film
thickness. The waveforms measured along [110] and[100] resemble to those for the 40 nm thick film, namely
the output waveform changes from rectangular tobath-tub like with increasing the magnetic field and theoutput intensity is kept almost at a similar amplitude
along [110], whereas the output waveform measured
along [100] is triangular and the amplitude increases
with increasing the magnetic field.

180

270

360

Fig. 8 Measured magnetostrictive behaviors of 200 nm
thick fcc-Co(001) single-crystal film under rotating
magnetic fields. The magnetostriction observation
direction is along fcc[110] and fcc[100], respectively.

The output phases are reversed similar to the case of 40
nm thick film (Fig, 6). The waveforms for the 200 nm
thick film shown in Fig. 8 are also similar to those forthe 100 nm thick film. However, the waveforms for the
500 nm thick film are slightly different from those for
40 or 100 nm thick films. The waveform along [110] is
not rectangular but bath-tub like even under a small
magnetic field of 0.2 kOe. In the case that themagnetization process is based on a coherent rotationmode, the waveform should be rectangular under asufficiently small magnetic field compared with its
anisotropy field as reported in the previous report 13). It
is notable that the films with sharp rectangular M-H
curves (Fig. 5), which are of the 40 and 100 nm thickfilms, show rectangular waveforms and the film withmild square M-H curve measured for the 500 nm thickfilm (Fig. 5) shows a bath-tub like waveform even undera small magnetic field. Therefore, the behavior of 500
nm thick film suggests that the magnetization process isdeviating slightly from the coherent mode.
These unique magnetostrictive behaviors can be
explained by considering coherent rotation ofmagnetization under a rotating magnetic field withtaking into account the magnetocrystalline anisotropy12,
13). In the case that the intensity of rotating magnetic
field is comparable to the magnetocrystalline anisotropy
field, the magnetization tends to keep its direction
parallel to the easy magnetization axis and tends toleave its direction from the hard magnetization axis.
Only in the case where the intensity of rotating
magnetic field is strong enough to overcome theanisotropy field, the magnetization will rotate under an
influence of the applied rotating magnetic field and themagnetostrictive waveform is expected to be sinusoidal.

Journal of the Magnetics Society of Japan Vol.42, No.3, 201875

INDEX+ 3⋅ λ111 ⋅ (α1 ⋅ α2 ⋅ β1 ⋅ β2 + α2 ⋅ α3 ⋅ β2 ⋅ β3 + α3 ⋅ α1 ⋅ β3 ⋅ β1 )(2).

Here λ100 and λ111 are the longitudinal magnetostriction
for [100] and [111] directions, α’s are the direction
cosines of the magnetization with respect to the crystal
axes, and β’s the direction cosines of the measured
length change. Since the change in length is a functionof direction cosine of magnetization in this equation, it
is based on a coherent rotation model. In a coherent
rotation model, the free energy is given by the following
equation considering magnetocrystalline anisotropy
energy (K1) and Zeeman energy (Ms·Hex).

1
E = ⋅ K 1 ⋅ (1 − cos 4θ ) + M S ⋅ H ex ⋅ cos (φ − θ )
8
.

(4)

In the case, the direction depending part of the change
in length depends only on λ100, namely λ100 can be
estimated from the measured amplitude along [100].
In order to calculate the change in length, we needto know the angle θ under an applied rotating magnetic
field. The angle θ is determined so as to minimize thefree energy, E in the equation (3). The calculated results
are shown in Fig. 10 for h=1 and 2, where h is defined
as h=Hex/Ha. Therefore, the calculated results for h=1
are corresponding to the experimental results underH e x =1.0 kOe and can explain the characteristic
waveforms such as bath-tub like or triangular. The
magnetostriction constants, λ 100 and λ 111 can be
estimated from the amplitudes of output. Fig. 11 shows
the output amplitude as a function of applied magnetic
field up to 1.2 kOe. The amplitude along [110] keeps
almost a same level and is well saturated in the

76

[010]

3
λ100
2

1×10−6(b)h =1.0
1×10−63
λ111
2

h =2.0090
180 270 360
Rotating angle (deg.)

Fig. 10 Calculated magnetostrictive behaviors along(a) [110] and (b) [100]. λ100 and λ111 are assumed to be
10×10−6. K1 is assumed to be negative. h is defined as
h=Hex/Ha, where Ha is anisotropy field.

150

(a)
500 nm100
200 nm50

100 nm
40 nm

0
(b)

100

500 nm
200 nm50
0100 nm40 nm

00.2 0.4 0.6 0.8 1.0 1.2
Magnetic field (kOe)

Fig. 11 Magnetic field dependence of output amplitude
measured along (a) [110] and [100] of fcc-Co(001)single-crystal film sample with the thickness of 50, 100
200, and 500 nm, respectively.

Magnetostriction constant

(5)

¯
[100]

h =2.0This equation shows that the direction depending part
depends only on λ111, namely λ111 can be estimated fromthemeasured
amplitude
along[110].
The
magnetostrictive behavior along [100] can also be
calculated. In this case, the equation (2) is rewritten as
the following equation.

δl 1= ⋅ λ100 ⋅ (1 + 3 cos 2θ )
l 4
.

¯
[010]
h =1.0(3)

Here θ and ϕ are the direction of Ms and Hex withrespect to the [100] axis in the (001) plane, respectively.
For an observation direction of the change in length
along [110] in the (001) plane, the equation (2) isrewritten as the following equation.

δl 1
3= ⋅ λ100 + ⋅ λ111 ⋅ sin 2θ
l 4
4
.

[100]

(a)

Output (mV)

δl 3
1⎞
⎛ 2 2
2
2
2
2
= ⋅ λ100 ⋅ ⎜ α1 ⋅ β1 + α2 ⋅ β2 + α3 ⋅ β3 − ⎟
l 2
3⎠
⎝

[010]

Elongation

These behaviors are similar to those for bcc(001)single-crystal films with four-fold magnetocrystalline
anisotropy 12, 13).
A phenomenological model is described as follows.
The change in length by magnetostriction is given by
the following equation for a cubic crystal 14).

150

λ100

100
50
0

λ111

−50
−100

0

100 200 300 400 500
Film thickness (nm)Fig. 12 Film thickness dependences of magnetostriction
constants λ100 and λ111 estimated for fcc-Co(001)single-crystal films.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

magnetic field range. However, the amplitude along[100] increases with increasing the magnetic field andthe amplitudes for 40 nm, 100 nm, and 200 nm thickfilms are almost saturated at 1 kOe but that for 500 nm
thick film is still approaching to saturation at 1.2 kOe.
The estimated magnetostriction constants are shown in
Fig. 12. The λ100 shows large positive value ranging
from 85 to 90×10−6 and shows small film thickness
dependence. The λ111 shows negative value ranging from−40 to −45×10−6 and also shows small film thickness
dependence. The large positive value is consistent to thevalue calculated by a first principle method 15).
4.

Conclusion

The magnetostrictive behaviors of fcc-Co(001)single-crystal films are investigated under rotating
magnetic fields. The magnetostrictive behaviors alongfcc[110] show rectangular or bath-tub like waveform
and the amplitude is kept at almost a similar level,
while the behaviors along fcc[100] show triangular andthe amplitude increases with increasing the magnetic
field. The behaviors can be explained by the coherent
rotation model of magnetization assuming a four-foldmagnetocrystalline anisotropy in (001) plain. The
magnetostriction constant λ100 is determined to be large
positive ranging from 85 to 90×10−6, which agrees with thatobtained by theoretical calculation. λ111 is negative ranging
from −40 to −45×10−6. The thickness dependences of λ100
and λ111 are confirmed to be very small for the
fcc-Co(001) films.

References
1) C. M. Schneider, P. Bressler, P. Schuster, and J.
Kirschner: Phys. Rev. Lett. 64, 1059 (1990).
2) B. Heinrich, J. F. CVochran, M. Kowalewski, J. Kirscher, Z.
Celinski, A. S. Arrot, and K. Myrtle: Phys. Rev. B, 44, 9348
(1991).
3) G. R. Harp, R. F. C. Farrow, D. Weller, T. A. Rabedeau,
and R. F. Marks: Phys. Rev. B, 48, 17538 (1993).
4) M. Ohtake, O. Yabuhara, J. Higuchi, and M. Futamoto: J.
Appl. Phys., 109, 07C105 (2011).
5) P. Krams, F. Lauks, R. L. Stamps, B. Hillebrands, and G.
Guntherodt: Phys. Rev. Lett. 69, 3674 (1992).
6) D. Weller, G. R. Harp, R. F. C. Farrow, A. Cebollada, and J.
Sticht: Phys. Rev. Lett. 13, 2097 (1994).
7) T. Suzuki, D. Weller, C.-A. Chang, R. Savoy, T. Huang, B.
A. Gurney, and V. Speriosu: Appl. Phys. Lett. 64, 2736
(1994).
8) M. Takahashi and T. Miyazaki: Proc. 5th ICMTF (April
1972 at Mt. Fuji Area, Japan) B2-1 (1972).
9) T. Kawai, M. Ohtake, and M. Futamoto: Thin Solid Films,
519, 8429 (2011).
10) T. Kawai, T. Aida, M. Ohtake, and M. Futamoto: IEEE
Trans. Mag. 51, 2007004 (2015).
11) C. Kittel: Introduction to Solid State Physics 8th edition,
Chapter 3, p. 78 (John Wiley & Sons Inc., 2005).
12) T. Kawai, T. Aida, M. Ohtake, and M. Futamoto: J. Magn.
Soc. Jpn., 39, 181 (2015).
13) T. Kawai, T. Aida, M. Ohtake, and M. Futamoto: IEEE
Trans. Mag. 50, 2008004 (2014).
14) S. Chikazumi: Physics of Ferromagnetism, p.121 (Syokabo,
Tokyo, 1961).
15) R. Q. Wu, L. J. Chen, A. Shick, and A. J. Freeman: J. Magn.
Magn. Mater. 177-181, 1216 (1998).
Received Mar. 23, 2017; Accepted Feb. 22, 2018

Acknowledgements The authors would like to thankProf. N. Inaba of Yamagata University for supporting
the VSM measurements.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

77

INDEX
J. Magn. Soc. Jpn., 42, 78-82 (2018)<Paper>Magnetostriction Behaviorsof Single- and Poly-Crystalline Ni/Ni-Co Bi-Layer Films
Kana Serizawa1,2, Mitsuru Ohtake1, Tetsuroh Kawai1,2, Masaaki Futamoto2, Fumiyoshi Kirino3, and Nobuyuki Inaba4
Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan

1

Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan

2

Graduate School of Fine Arts, Tokyo University of the Arts, 12-8 Ueno-koen, Taito-ku, Tokyo 110-8714, Japan

3

Faculty of Engineering, Yamagata University, 4-3-16 Jyonan, Yonezawa, Yamagata 992-8510, Japan

4

Ni(tNi nm)/Ni50Co50(100–tNi nm) bi-layer films are prepared on Cu/Pd/MgO(001) single-crystal substrates at
300 °C and on Cu/Pd/glass substrates at room temperature by varying the layer thickness, tNi, in a range of 0–100
nm. The effect of layer thickness ratio on the magnetostriction is investigated. As tNi value increases from 0 to 100
nm, the magnetostriction coefficient observed for single-crystal film along fcc[100], λ100, monotonically decreases
from a positive value of +1 × 10–4 (tNi = 0 nm) to a negative value of –6 × 10–5 (tNi = 100 nm), whereas that measured
along fcc[111], λ111, remains almost similar (–4 × 10–5 to –2 × 10–5). The magnetostriction coefficient ofpoly-crystalline film decreases from –3 × 10–6 to –2 × 10–5 with increasing tNi value from 0 to 100 nm. The present
study has shown that control of magnetostriction coefficient is possible by combining materials with positive andnegative coefficients.
Key words: Ni, Ni-Co alloy, thin film, magnetostriction coefficient, λ100, λ111
1.

Introduction

Soft magnetic materials have been used for
applications to magnetic devices, transformers, etc. In
order to improve the performance, it is required toreduce the magnetostriction that causes vibration and is
one of the origins for energy loss.
Ni-based alloys with fcc structure such as Ni-Fe
and Ni-Co are typical soft magnetic materials. In the
Ni-Co binary alloy system, fcc structure can bestabilized in the full compositional range throughhetero-epitaxial thin film growth on Cu underlayer1–3).
In our previous study3), Ni100–xCox single-crystal films offcc(001) orientation were prepared on Cu(001)underlayers by varying Co content, x, from 0 to 100
at. %. The magnetostriction coefficient of λ100 increased
from a negative value of –3 × 10–5 to a large positive
value of +1 × 10–4 with increasing Co content, whereasthat of λ111 stayed almost constant around –2 × 10–5.
The compositional dependences were similar to the caseof bulk Ni-Co alloy system4).
Magnetostriction seems to be reduced by combining
materials with negative and positive magnetostriction
coefficients. In the present study, single- andpoly-crystalline Ni/Ni50Co50 bi-layer films are preparedby varying the layer thicknesses while keeping the total
thickness at 100 nm. The effect of layer thickness ratioon the magnetostriction coefficient is investigated.
2. Experimental Procedure
2.1 Film preparation
A radio-frequency magnetron sputtering system78

equipped with a reflection high-energy electron
diffraction (RHEED) facility was used for film formation.
Single- and poly-crystalline films were respectively
prepared on MgO(001) single-crystal substrates of 0.3
mm thickness at 300 °C and on glass substrates of 0.14
mm thickness at room temperature. 5-nm-thick Pd
buffer layers and 10-nm-thick Cu underlayers weresequentially deposited on the substrates. Then, Ni(tNi
nm)/Ni50Co50(100–tNi nm) bi-layer films were formed on
the underlayers. The Ni and the Ni50Co50 layer
thicknesses were varied from 0 to 100 nm. The totalbi-layer film thickness was fixed at 100 nm to obtainenough bending to detect by using our magnetostriction
measurement system. The sputter deposition condition
was similar to the case of our previous work3).
The crystal structure and the crystallographic
orientation were determined by RHEED. The resulting
film structure was investigated by X-ray diffraction(XRD) with Cu-Kα radiation (wave length: 0.15418 nm).
The magnetization curves were measured by vibrating
sample magnetometry.
2.2 Magnetostriction measurement
Magnetostriction was measured by employing alaser displacement meter fixed on a vibration isolated
table to measure the small cantilever bending with anaccuracy of 1 nm. The output sensitivity was 1 V per 0.2
μm bending. A rotating magnetic field of 1.2 kOe wasapplied in the film plane. The rotating speed was 5 rpm.
Magnetostriction coefficient, λ, is expressed5.6) as

λ = {ΔS ts2 Es (1 + υf)} / {3 L2 tf Ef (1 – υs)} ,Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

(1)

INDEX

where ΔS is the measured bending, L is the distance
between laser beam points, t is the thickness, E is theYoung’s modulus, υ is the Poisson’s ratio, and thesubscripts of f and s respectively refer to film andsubstrate.
When the magnetostriction of fcc(001) single-crystal
film is measured under a rotating magnetic field, a
relationship among λ, λ100, and λ111 is given7) as thefollowing formula,(a) tNi = 0 nm (Ni50Co50)(d) tNi = 75 nm(b) tNi = 25 nm(e) tNi = 100 nm (Ni)(c) tNi = 50 nm(f)

λ = (3/2) λ100 [α12 β12 + α22 β22 + α32 β32 – (1/3)]

the incident electron beam is parallel to Cu[100] (||MgO[100]). Figure 1(f) shows the schematic diagram ofdiffraction pattern calculated for fcc(001) single-crystal
surface with reconstructed structure of c(2×2). The
observed diffraction patterns are in agreement with thesimulated pattern. Therefore, Ni(tNi nm)/Ni50Co50(100–tNinm) single-crystal films grow epitaxially on theu n d e r l a y e r s. T h e c r y stal l o g r aph i c o r i e n tati o nrelationship is determined as Ni(001)[100] f c c ||Ni50Co50(001)[100]fcc || Cu(001)[100]fcc. Figure 2 shows
the 2θ/ω-scan out-of-plane XRD patterns. fcc(002) andfcc(004) reflections from the Ni(tNi nm)/Ni50Co50(100–tNinm) films are recognized around the diffraction angles,
2θ, of 51° and 122°, respectively. It is noted that fcc(004)reflections from the Ni and the Ni50Co50 layers are
separately observed for the bi-layer films [Figs. 2(b)–(d)].
The result indicates that atomic mixing at the
Ni/Ni 5 0 Co 5 0 interface is not so high. The lattice
constants of Ni layers in films with tNi = 25, 50, 75, and
100 nm are estimated to be 0.3514, 0.3516, 0.3518, and
0.3519 nm, whereas those of Ni50Co50 layers in films
with tNi = 0, 25, 50, and 75 nm are calculated to be
0.3528, 0.3529, 0.3529, and 0.3528 nm, respectively.

tNi = 0 nm
(Ni50Co50)(a)Intensity (arb. unit)

for Ni(tNi nm)/Ni50Co50(100–tNi nm) films with different
tNi values formed on Cu/Pd/MgO(001) substrates. Here,

002

022

(b)

Ni(004)

Ni50Co50(004)Ni(004)and/or

Ni50Co50(004)tNi = 25 nm(c)tNi = 50 nm(d)tNi = 75 nm
tNi = 100 nm
(Ni)

(e)
20

WL

Figures 1(a)–(e) show the RHEED patterns observed

Kβ

Results and Discussion

MgO(004)3.

and/or(4)

Ni(002)λ = (1/4) λ100 + (3/4) λ111 sin2ψ .

044
c(2×2)

Fig. 1 (a)–(e) RHEED patterns observed for Ni(tNi
nm)/Ni50Co50(100–tNi nm) films with tNi = (a) 0, (b) 25,(c) 50, (d) 75, and (e) 100 nm formed on Cu/Pd/MgO(001)substrates. (g) Schematic diagram of RHEED pattern
simulated for fcc(001) single-crystal surface withreconstructed structure of c(2×2). The incident electron
beam is parallel to (a)–(e) Cu[100] (|| MgO[100]) or (f)fcc[100].
Ni50Co50(002)

(3)

004

022

Kβ WL

λ = (1/4) λ100 (1 + 3 cos2ψ) ,044c(2×2)

MgO(002)where α is the cosine of angle between themagnetization and the three crystallographic axes (a, b,c) and β is the cosine of angle between the direction ofrelative change in length and the axes. When theobservation directions are fcc[100] and fcc[110], (β1, β2,β3) values are respectively (1, 0, 0) and (1/ 2 , 1/ 2 , 0),
whereas (α1, α2, α3) values are (cosψ, sinψ, 0) for bothcases. Here, ψ is the angle of magnetization direction
with respective to fcc[100]. By substituting α and β
values to Eq. 2, the following relations are given,

_

(3)

_

+ 3 λ111 (α1 α2 β1 β2 + α2 α3 β2 β3 + α3 α1 β3 β1) ,

40

60

80
120
100
Diffraction angle, 2θ (deg.)

118

122

126

Fig. 2Out-of-plane XRD patterns of Ni(tNi
nm)/Ni50Co50(100–tNi nm) films with tNi = (a) 0, (b) 25,(c) 50, (d) 75, and (e) 100 nm formed on Cu/Pd/MgO(001)substrates. The intensity is shown in logarithmic scale.
The small reflections noted as Kβ and WL are due toCu-Kβ and W-Lα radiations included in the X-ray source,
respectively.
These values are similar to the bulk values (aNi = 0.3524
nm8), aNi50Co50 = (aNi8) + afcc-Co9))/2 = 0.3534 nm),suggesting that the strains in Ni and Ni50Co50 layers are
small.

Journal of the Magnetics Society of Japan Vol.42, No.3, 201879

Ni(200)

0(a-2) tNi = 0 nm(d-1) tNi = 75 nm(b-2) tNi = 25 nm(c-2) tNi = 50 nm(d-2) tNi = 75 nm

40
50
60
70
Diffraction angle, 2θ (deg.)

–1

0

1

2 –2

–2
–1
1 (c)

–1

0

1

2

0

1

2

(e)
tNi = 100 nm
(Ni)

(b)
tNi = 25 nm

0

1

2 –2

–1

Magnetic field, H (kOe)fcc[110]

0

(Ni)

30

(d)
tNi = 70 nm

tNi = 0 nm
(Ni50Co50)

tNi = 50 nm(e-2) tNi = 100 nm(e-1) tNi = 100 nm (Ni)

–1
–2

80

Fig. 3 (a-1)–(e-1) RHEED and (a-2)–(e-2) XRD patternsof Ni(tNi nm)/Ni50Co50(100–tNi nm) films with tNi = (a) 0,(b) 25, (c) 50, (d) 75, and (e) 100 nm formed on
Cu/Pd/glass substrates. The XRD intensity is shown inlogarithmic scale.

Figures 3(a-1)–(e-1) and (a-2)–(e-2), respectively,
show the RHEED and the XRD patterns of Ni(tNi
nm)/Ni50Co50(100–tNi nm) films formed on Cu/Pd/glass
substrates. Ring-like RHEED patterns and XRD
patterns showing fcc(111) and fcc(200) reflections areobserved. The results show that poly-crystalline films
with fcc structure are formed on glass substrates.
Figure 4 shows the in-plane magnetization curvesof single-crystal films. The films are easily magnetizedwhen the magnetic field is applied along fcc[110],
whereas the magnetization curves measured alongfcc[100] saturate at higher magnetic fields. There wereno clear differences in the magnetization curves
measured along fcc[100]_ and fcc[010] and measured
along fcc[110] and fcc[110] (not shown here). Therefore,
the single-crystal films show four-fold symmetries inin-plane magnetic anisotropy, which is reflecting themagnetocrystalline anisotropy of fcc crystal with theeasy magnetization axes parallel to fcc<111>. Figure 5
shows the magnetization curves of polycrystalline films.
There were no differences in the curves measured along
in-plane
directions
(not
shown
here).
The
poly-crystalline films show isotropic in-plane magnetic
properties. The single- and poly-crystalline films arenearly saturated at a magnetic field of 1.2 kOe, which isused for magnetostriction measurements.
Figures 6(a) and (h) show the output waveforms ofmagnetostriction of Ni50Co50 (tNi = 0 nm) and Ni (tNi =100 nm) single-crystal films measured along fcc[100]
80

–1
–2

–1

0

1

Magnetic field, H (kOe)fcc[100]

2

Fig. 4Magnetization curves measured for Ni(tNi
nm)/Ni50Co50(100–tNi nm) films with tNi = (a) 0, (b) 25,(c) 50, (d) 75, and (e) 100 nm formed on Cu/Pd/MgO(001)substrates. The vertical dotted lines show the strengthof magnetic field (±1.2 kOe) used for magnetostriction
measurements.
10Normalized magnetization, M/Ms(c-1) tNi = 50 nm

Intensity (arb. unit)(Ni50Co50)

Normalized magnetization, M/Ms(b-1) tNi = 25 nm

1 (a)and/orNi(111)

and/or

Ni50Co50(111)(a-1) tNi = 0 nm (Ni50Co50)

Ni50Co50(200)

INDEX

–1
–2

(a)
tNi = 0 nm
(Ni50Co50)–1(d)tNi = 70 nm

0

1

2 –2

1 (b)
tNi = 25 nm
0

–1
–2

–1

–1

0

1

2

0

1

2

(e)
tNi = 100 nm
(Ni)

0

1

2 –2

0

1

2

1 (c)
tNi = 50 nm–1

Magnetic field, H (kOe)

0
–1

–2

–1

Magnetic field, H (kOe)

Fig. 5Magnetization curves measured for Ni(tNi
nm)/Ni50Co50(100–tNi nm) films with tNi = (a) 0, (b) 25,(c) 50, (d) 75, and (e) 100 nm formed on Cu/Pd/glass
substrates. The vertical dotted lines show the strengthof magnetic field (±1.2 kOe) used for magnetostriction
measurements.
under the in-plane rotating magnetic field of 1.2 kOe,
respectively. Phase of waveform is different between thetwo cases, suggesting that the Ni50Co50 and the Ni films
have positive and negative λ100 values, respectively.
Figures 6(a)–(d) show the output waveforms of

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEXdll0.05 v

100dll(a) tNi = 0 nm

(Ni50Co50)

0.1 v
110

(a) tNi = 0 nm

(Ni50Co50)(b) tNi = 25 nm(d) tNi = 60 nm(b) tNi = 25 nm

OutputOutput(c) tNi = 50 nm(c) tNi = 50 nm(e) tNi = 62 nm(f) tNi = 75 nm(ｄ) tNi = 75 nm(g) tNi = 85 nm(h) tNi = 100 nm(e) tNi = 100 nm

(Ni)

0

90
180
270
Rotation angle, φ (deg.)3600Fig. 6
Output waveforms of magnetostriction
measured for Ni(tNi nm)/Ni50Co50(100–tNi nm) films withtNi = (a) 0, (b) 25, (c) 50, (d) 60, (e) 62, (f) 75, (g) 85, and(h) 100 nm formed on Cu/Pd/MgO(001) substrates. The
observation direction is along fcc[100].
(×10–6)140
Magnetostriction coefficient

120
100

(a) λ100
Bulk

80
60
40
20
0

(c) λ

–20
–40
–60
–80

(b) λ111

0(Ni50Co50)

Bulk

25
50
75
Ni layer thickness，tNi (nm)

(Ni)

100
(Ni)

Fig. 7 Ni layer thickness dependences of (a) λ100, (b)λ111, and (c) λ values of Ni(tNi nm)/Ni50Co50(100–tNi nm)[(a), (b)] single- and (c) poly-crystalline films. The bulk
values of λ100, λ111, and λs cited from Ref. 4.
single-crystal films with tNi = 0, 25, 50, and 60 nm. As
tNi value increases from 0 to 60 nm, the amplitude of
output gradually decreases, which indicates that theλ100 value decreases. The magnetostriction is apparently
reduced by combing the Ni50Co50 crystal with positive
λ100 value and the Ni crystal with negative λ100 value.
Figures 6(d)–(f) show the waveforms of single-crystal
films with tNi = 60, 62, and 75 nm. These films show

90
180
270
Rotation angle, φ (deg.)360

Fig. 8Output waveforms of magnetostriction
measured for Ni(tNi nm)/Ni50Co50(100–tNi nm) films withtNi = (a) 0, (b) 25, (c) 50, (d) 75, and (e) 100 nm formed
on Cu/Pd/MgO(001) substrates. The observation
direction is along fcc[110].
small amplitudes. The phase of waveform reverses withincreasing tNi value from 60 to 75 nm. The sign ofmagnetostriction changes from positive to negativearound t N i = 62 nm. Figures 6(f)–(h) show the
waveforms of single-crystal films with tNi = 75, 85, and
100 nm. The amplitude increases with increasing tNi
value. Figure 7(a) summaries the λ 100 values ofsingle-crystal films as a function of tNi. Here, the λ100
values are calculated by using Eq. 3. The λ100 value
monotonically decreases from a positive value of +1 ×
10–4 (tNi = 0 nm) to a negative value of –6 × 10–5 (tNi =100 nm) with increasing tNi value. Figure 8 shows the
waveforms of single-crystal films with different tNi
values measured along [110]. The amplitude and thephase of waveform do not vary depending on tNi value.
Figure 7(b) shows the variation of λ 111 value as afunction of tNi, where the λ111 values are calculated byusing Eq. 4. The λ111 value slightly increases from –4 ×
10–5 to –2 × 10–5, as tNi value increases from 0 to 100
nm.
Figure 9 shows the waveforms of poly-crystalline
films. As tNi value increases, the amplitude increases,
though the phase dose not change. Figure 7(c) shows the
λ values, which are estimated by using Eq. 1. The λvalue decreases from –3 × 10–6 to –2 × 10–5 withincreasing tNi value from 0 to 100 nm.
The present study demonstrates that reduction of

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

81

INDEX

magnetostriction is possible by combining materials
with negative and positive magnetostriction coefficients.

dllConclusion

Single- and poly-crystalline Ni/Ni50Co50 bi-layer
films are prepared by varying the layer thicknesses
while keeping the total thickness at 100 nm. The effectof layer thickness ratio on the magnetostriction isinvestigated. The λ100 values of Ni50Co50 (tNi = 0 nm) andNi (tNi = 100 nm) single-crystal films are positive (+1
×10–4) and negative (–6 × 10–5), respectively. As tNivalue increases from 0 to 62 nm, the λ100 value
decreases from positive to nearly 0. With further
increasing tNi value, the λ100 value decreases to negative.
On the other hand, the λ111 value remains almost
similar (–4 × 10–5 to –2 × 10–5). The λ value ofpoly-crystalline film decreases from –3 × 10–6 to –2 ×
10–5 with increasing tNi value from 0 to 100 nm. The
present study demonstrates that reduction ofmagnetostriction is possible by combining materials
with negative and positive magnetostriction coefficients.
Acknowledgment A part of this work was supported by
Chuo University Grant for Special Research.

(Ni50Co50)(b) tNi = 25 nm(c) tNi = 50 nm

Output4.

(a) tNi = 0 nm(d) tNi = 75 nm(e) tNi = 100 nm

(Ni)

0.2 v
0

90
180
270
Rotation angle, φ (deg.)360

Fig. 9Output waveforms of magnetostriction
measured for Ni(tNi nm)/Ni50Co50(100–tNi nm) films withtNi = (a) 0, (b) 25, (c) 50, (d) 75, and (e) 100 nm formed
on Cu/Pd/glass substrates.

References
1) H. A. M. de Gronckel, K. Kopinga, W. J. M. de Jonge, P.
Panissod, J. P. Schillé, and F. J. A. den Broeder: Phys. Rev.
B, 44, 9100 (1991).
2) M. Ohtake, O. Yabuhara, J. Higuchi, and M. Futamoto: J.
Appl. Phys., 109, 07C105 (2011).
3) K. Serizawa, T. Kawai, M. Ohtake, M. Futamoto, F. Kirino,
and N. Inaba.: IEEE Trans. Magn., 53, 2004204 (2017).
4) S. Ishio, T. Kobayashi, H. Saito, S. Sugawara, and S.
Kadowaki: J. Magn. Magn. Mater., 164, 208 (1996).
5) E. Klokholm: IEEE Trans. Magn., 12, 819 (1976).

826) T. Kawai, M. Ohtake, M. Futamoto: Thin Solid Films, 519,
8429 (2011).
7) B. D. Cullity and C. D. Graham: Introduction to Magnetic
Materials (Addision Wesley, Reading, MA, 1992).
8) M. Matsui and K. Adachi: J. Magn. Magn. Mater., 10, 152(1979).
9) W. F. Schlosser: Phys. Status Solidi A, 17,199 (1973).
Received Oct. 16, 2017; Accepted Mar. 21, 2018

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX
J. Magn. Soc. Jpn., 42, 83-89 (2018)<Paper>Effects of magnetic field applied during heat treatment on magnetic
properties of non-oriented electrical steel sheets
T. Kinoshita, K. Kohara *, H. Shimoji **, T. Sato *, and T. Todaka *Sumitomo Heavy Industries, Ltd., 19, Natsushima-cho, Yokosuka-shi, Kanagawa, 237-8555, Japan* Faculty of Science and Technology, Oita Univ., 700 Dannoharu, Oita, 870-1192, Japan** Dept. of Oita Industrial Research Institute., 4361-10, 1-chome, Takaenishi, Oita, 870-1117, JapanTo improve the magnetic properties of non-oriented electrical steel sheets, the effects of applying heat treatment ina magnetic field on controlling the crystallographic orientation were studied. The heat treatment temperature wascontrolled to be 1023, 1123, and 1273 K. The magnetic field applied during the treatment was parallel to the rolling
direction of sheet samples, and the magnetic field strength was 10 T at maximum. The samples heat treated in amagnetic field under the temperature condition of 1123 K or higher showed a remarkable change in magnetic
properties as the textures changed. Even when a magnetic field was not applied, the grain growth was accelerated byheat treatment, iron loss was reduced, and permeability under low excitation conditions was improved. However, thepermeability at 1.6 T or higher decreased. In this paper, it is shown that iron loss could be further reduced byapplying a strong magnetic field during the cooling step of the heat treatment. It is also found that applying a strong
magnetic field throughout the heat treatment, i.e. heating and cooling, inhibited grain growth, increased iron loss,
and decreased magnetic permeability.
Key words: magnetic heat treatment, crystallographic orientation, iron loss
1. Introduction
There is an international demand for effective
utilization of energy, especially for downsizing andimproving efficiency of rotating electric motors(hereinafter referred to as electric motors), which
account for a large proportion of total electric power
consumption. The efficiency of electric motors is
specified by the IEC standards, and the efficiency classis defined from the IE1 (standard efficiency) to the IE3(premium efficiency). It is expected that demand forhigher efficiency of electric motors will further increasein future.
Responding to the needs, effort to improve efficiencyof electric motors and decrease energy losses, e.g. corelosses, should be considered. Iron loss is known toincrease due to the influence of residual stress duringiron core processing, thereby deteriorating the magnetic
properties.
In order to reduce iron loss withoutchanging the iron core material, it is expected that
reduction or utilization of residual stress is necessary.
Strain relief annealing is an effective method to
reduce residual stresses. In non-oriented electrical steel
sheets, deterioration of magnetic properties due toprocessing strain is known to be improved by heat
treating at about 1020 K1). However, strain relief
annealing leads to texture changes within the material.
A structure including hard axis of magnetization basedon magneto-crystalline anisotropy appears in the planeof the electrical steel sheet, resulting in thedeterioration of magnetic properties at 1.5 T or higher.
Thus, it may not be possible to take full advantage ofmaterial properties with simple heat treatment2,3).
Therefore, the authors' group has studied heat

treatment in a magnetic field which offers the possibilityof controlling the texture of the magnetic material
during heat treatment.
It is well known that magnetic properties of magnetic
materials are improved by heat treatment in a magnetic
field4), In addition, some literatures reported that thematerial’s texture could be controlled with such heat
treatment processes 5,6). However, there are few detailed
reports on the magnetic properties under alternating
excitation of non-oriented electrical steel sheets
heat-treated in a magnetic field. Moreover, detailed
mechanism of the phenomenon is not well understoodand there are only a few reports on their industrial
application. The authors in present study investigatedthe effects on the magnetic properties under alternating
excitation of samples heat-treated in a magnetic field byusing commercially available electromagnetic steel
plates. In our previous reports, samples of sufficient
size could not be produced due to the structuralFig. 1

Schematic diagram of magnetic heat
treatment apparatus.

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83

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constraints of heat treatment equipment, and there wasonly qualitative discussion7). Subsequently, quantitativeevaluation methods of samples with shape constraints
were studied, and the magnetic properties in the
direction of the magnetic field applied during heat
treatment were measured with a small-sized single
sheet tester (SST) 8). In this paper, by comparing
magnetic properties with and without a magnetic field
during heat treatment, we make clear quantitatively
magnetic properties depending on heat treatment
conditions, i.e. temperature and magnetic field.
2. Experimental method and apparatus
2.1 Heat treatment apparatus in a magnetic field
Fig. 1 shows a schematic view of the heat treatment
apparatus. The heat treatment apparatus in a magnetic
field consisted of a superconducting magnet (10 T-CSM)
with an inner diameter of 100 mm, and a quartz glass
tube with outer diameter of 14 mm and inner diameterof 12 mm of which one end was closed. The quartz glass
tube was inserted into an electric furnace with an outer
diameter of 50 mm and an inner diameter of 22 mm.
The structure could be depressurized to less than 10-3 Pawith a turbo molecular pump. Samples were preparedby cutting a non-oriented electrical steel sheet 50A470(JIS C 2552) to 10 mm × 50 mm by electrical dischargemachining, and set at the center of the magnetic field in
the quartz tube using a holding jig made of quartz sothat the field direction of the magnetic field was parallelto the longitudinal direction of the sample. Thus, theuniformity of the magnetic field during the heat
treatment at the sample position was sufficiently
maintained. The temperature around the sample wasmeasured using a Pt-Rh thermocouple.
Fig. 2 shows the temperature profile and appliedmagnetic field pattern. In this test, the temperature wasraised to the set temperature at a rate of T/t1 = 500 K/hr,
and after reaching the set temperature, the sample washeld for (t2 - t1) = 1 hr, and then cooled to room
temperature at a rate of T / (t3 - t2) = 100 K/hr. A
constant magnitude of magnetic field was kept
throughout the heating and cooling cycle until thesample was cooled to room temperature.
2.2 Small-sized Single Sheet Tester (SST) 8)
Fig. 3 shows the measurement system of SST, and Fig.
4 shows the schematic diagram of the apparatus
configuration. As an excitation coil, polyester copper
wire (PEW), 1.0 mm, was wound for 380 turns on theepoxy resin frame. As a yoke, 20 electrical steel sheets(50A470) cut out by electrical discharge machining wereused, and laminated and adhered in the direction of thepaper surface of Fig. 3 to a thickness of 10 mm or more.
By using the stacked yokes, leakage of magnetic flux isprevented and generation of eddy currents is reduced.
Samples were formed by electrical discharge machiningof electrical steel sheets (50A470) to be 10 mm × 50 mm,
with the rolling direction being the longitudinal
direction of the sample. A measurement sample placedin the central part of the excitation coil is excited byalternating magnetic flux in the longitudinal direction
to measure the alternating magnetic properties of 50Hz.
As shown in Fig. 3, feedback control can be performed inthis system, and a sinusoidal magnetic flux density
waveform in the sample is maintained. The magnetic
flux search coil (B-coil), of 3 turns is wound at thecentral portion of the sample, and the magnetic flux

Fig. 3Fig. 2

84

Schematic diagram of magnetic field
during heat treatment.

Fig. 4

System for measuring magnetic properties of
SST.

Schematic diagram of SST configuration.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEXdensity B is thereby detected. The magnetic fieldstrength H is calculated from the excitation current
detected by the shunt resistance. The effective magnetic
path length l is determined as the yoke inner dimension(40 mm). Based on the above conditions, multiple
samples were measured a number of times, and theaverage value was taken as the measurement result.
3. Experimental results and discussion
3.1 Effect of heat treatment temperature
To understand the effects of heat treatment in amagnetic field on the magnetic properties of theelectrical steel sheets, heat treatment in the absence of amagnetic field was firstly carried out. The heat
treatment temperatures for comparison were 1023, 1123,
and 1273 K. Samples were heated at 330 K/hr, held for 1
hr, and then cooled to room temperature at 100 K/hr.
Same cooling and heating rate was used regardless ofthe heat treatment temperature. Fig. 5 shows the ironloss measurement results of the samples fabricated ateach heat treatment temperature. It was found thatthe iron loss decreased under all conditions as comparedwith ones before heat treatment. In addition, the ironloss also decreased as the heat treatment temperature
increased. Next, magnetic permeability characteristics
depending on the heat treatment temperature were
investigated. Fig. 6 shows the measurement results ofthe magnetic permeability. Compared with the relative
permeability of the electrical steel sheets before heat
treatment, the relative permeability increased with theexcitation magnetic flux density of 1.5 T or less under all
the temperature conditions. In addition, the magnetic
permeability increased as the heat treatment
temperature increased. Reduction of the iron loss andincrease of the relative permeability may be attributed
to grain growth9).
Fig. 7 shows an image of crystal grains observed with
an optical microscope. As expected, the crystal grains
became coarser compared with those before heat
treatment. The grain size of the sample heat-treated at1273 K increased to nearly 1 mm. Thus, the increase of
the magnetic permeability can be explained by the
relative reduction of crystal grain boundary areas,
which constitute an energy barrier, resulting in the
reduction of iron loss due to facilitated magnetic domain
wall movement. As for the excitation magnetic flux
density of 1.6 T or higher, the iron loss was reduced, but
the magnetic permeability decreased as compared withthat before heat treatment. The reason that thepermeability decreases in the high magnetic field of≥1.6 T is due to the fact that the 90° magnetic domains
with respect to the excitation direction are increased by
the heat treatment. Normally the <100> direction, i.e. theeasy direction of crystal magnetization, is largely
distributed within the plane in order to reduce
spontaneous magnetization in thickness direction.
However the heat treatment promoted isotropic grain
growth resulting in increased <100> crystals in theFig. 5Iron loss properties of heat treated samples.

(a) Results of measuring relative permeability.

(b) Magnetic permeability change in heat treatedsamples with respect to magnetic permeability
before heat treatment.
Fig. 6

Magnetic permeability properties of heat treatedsamples.

(a) 1023 K(b) 1273 K
Fig. 7
Crystal grain of specimen section observed byusing optical microscope.

Journal of the Magnetics Society of Japan Vol.42, No.3, 201885

INDEX

Fig. 8(a) 1123 K(a) 1123 K(b) 1273 K(b) 1273 K

Change rate of iron loss characteristics ofsamples heat treated in magnetic field.

thickness direction.
3.2 Effect of magnetic field during cooling process
It was found that the magnetic properties of electricalsteel sheets subjected to simple heat treatment
deteriorated at the exciting magnetic flux density of ≥1.6
T. The reason for poor properties is the spontaneous
magnetization in the thickness direction of the steel
sheet due to isotropic grain growth. Therefore, byapplying a magnetic field during heat treatment,
spontaneous magnetization in the thickness direction of
the steel sheet is expected to be suppressed, resulting ingood magnetic properties even in a high excitation field.
The anisotropy induced by heat treatment of soft
magnetic materials in a magnetic field is often explainedin terms of magnetic atom pair ordering mechanism.
According to the model for binary alloys proposed
independently by Néel10) and Taniguchi11), thedirectional diffusion takes place with a preferred
direction of magnetic atom pairs imposed by the
direction of magnetization during the heat treatment
and/or subsequent cooling. This explanation should beappliedtomaterials
withdirectional-ordered
crystallographic microstructure. Since, the material
used in this study has a few percent of silicon and it isseldom the ordered lattice structure, the above model is
not considered to be dominant. A previous study
reported that texture could be controlled by applying amagnetic field to electrical steel sheets during the86

Fig. 9Change rate of magnetic permeability
characteristics of samples heat treated inmagnetic field.

cooling step of the heat treatment12). Hence, theapplication of magnetic field during cooling step
improves the magnetic properties of electrical steel
sheets. In the present study, the heat treatment
temperature of the sample was set to 1123 K and 1273
K at which the iron loss reduction effect was particularlymarked, and a magnetic field was applied during cooling.
The applied magnetic field strength was set to 1 T, 5 T,
10 T, and the effects of the heat treatment temperatureand the magnetic field strength applied during coolingon magnetic properties were investigated. Fig. 8(a)shows the changing rate of iron loss characteristics ofthe samples heat-treated at 1123 K in a magnetic field
relative to one of the sample heat-treated in the absenceof a magnetic field. At 1 T and 5 T, the iron loss
increased with its ratio greater than 1, but at 10 T, theiron loss was reduced in all regions. Although thedetailed mechanism is not completely understood, theapplication of a magnetic field during cooling clearlyaffected the magnetic properties. In the sample
subjected to heat treatment in a magnetic field at 1273
K, as shown in Fig. 8(b), the iron loss is reduced inalmost all regions by applying the magnetic field.
Although at 1123 K, a correlation with the magnetic
field strength was not confirmed, at 1273 K it was foundthat iron loss could be further reduced by increasing themagnetic field strength.
This experimental result
suggests that raising the heat treatment temperature
increases the sensitivity of the sample to the magnetic
field.

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INDEX

Next, the change in the relative permeability due toheat treatment in the magnetic field was examined. Fig.
9(a) shows the measurement result of the changing rateof the relative magnetic permeability of the sample
heat-treated in the magnetic field at 1123 K, and Fig.
9(b) shows the result at 1273 K. As seen from Fig. 9(a),at ≤1.3T, the relative magnetic permeability of thesamples heat-treated in the magnetic field decreased,
and the decrease rate of the sample heat-treated at 1 T
is the largest. Although a slight increase in magnetic
permeability was observed between 1.4 T and 1.6 T, therelative permeability ratio at ≥1.8 T decreased to lessthan 1. In Fig. 9(b), by applying a magnetic field(neglecting 1 T), the magnetic permeability decreased in
the sample heat-treated at 1273 K under relatively low
excitation conditions and increased under highexcitation conditions. The behavior of this relative
permeability was observed independently at different
temperature in heat treatment. However, the changing
rate of the relative permeability with respect to themagnetic field was larger at higher temperature i.e.
1273 K. Similar to iron loss, the sensitivity of magnetic
properties to the magnetic field during heat treatment ishigher for samples heat treated at high temperature.
The change in magnetic properties could be possible
due to change in texture of the sample caused byapplication of the magnetic field during heat treatment.
In order to evaluate the texture of a sample heat-treatedin the magnetic field, X-ray pole figure measurement
was performed. Fig. 10 shows the {110} X-ray pole figure
measurement results for the samples (a) before heat
treatment, and (b), (c), after heat-treated at 1123 K and
1273 K, respectively. In Fig. 10, the region enclosed by
the red line is a strong intensity position, indicating thepresence of a texture. At 1123 K, only minor changes
were found compared with before heat treatment. At
1273 K, the texture was greatly changed and highintensity diffraction lines could be seen at the center ofthe {110} pole figure, indicating that {110} increased in
the plane parallel to the surface of the steel sheet. Since(a) Raw material(b) 1123 K(c) 1273 K
Fig. 10{110} pole figure analysis of magnetic
heat-treated non-oriented electrical steel sheet.

{110} is the plane orientation including both the <100>direction which is the easy magnetization direction andthe <111> direction which is the hard magnetization
direction, it is expected that magnetization properties
improved in the <100> direction. However, in thelongitudinal direction of the sample which is themeasurement direction, i.e. in the direction of themagnetic field during heat treatment, improvement ofmagnetization properties could not be confirmed. The
induced magnetic anisotropy in the non-oriented
electrical steel sheets is considered to be a large
influence of crystal orientation. The sample subjected toheat treatment in the magnetic field undergoes arecrystallization process accompanied with preferredorientation, whereby the crystal orientation distributionchanges and anisotropy appears. As the conditions
under which the anisotropy was induced, in the present
experiments, both of a sufficient temperature condition
for causing recrystallization and a strong magnetic field
capable to give non-negligible influence on the
scattering by the temperature are necessary. We believe,by clarifying the relationship between magnetic field
applied during heat treatment and the resulting crystal
orientations, crystal directions that improve magnetic
properties of steels could be determined andpreferentially textured within the material.
3.3 Effect of magnetic field applied during heating
An electrical steel sheet made of iron to which a few
percent of silicon is added becomes a paramagnetic
substance at and above the Curie temperature. The
sheet does not exhibit spontaneous magnetization,suggesting that it is not likely to easily get affected by amagnetic field above the Curie temperature. However,Bacalchuk et al. reported that application of a magnetic
field in the temperature range showing paramagnetism
was effective to control texture13). In addition, byapplying a magnetic field in the ferromagnetic state,individual crystal grains may generate magnetostrictionand expand or contract according to the crystal
orientation. An energy barrier is then formed at the
crystal grain boundaries which interferes with grain
growth14,15), resulting in deterioration of magnetic
properties. Hence, the effects of the magnetic field may
not necessarily be obtained under ferromagnetic
conditions in soft magnetic materials against thatmagnetic properties are expected to improve by heat
treatment in a magnetic field. As described in theprevious section, the effects of the magnetic field are
more pronounced when applied during heat treatment
at ≥1123 K, which is believed to exceed the Curie
temperature. Therefore, by comparing the magnetic
properties of a sample to which a magnetic field wasapplied only during the cooling to a sample produced bycontinuous application of a magnetic field throughout
heating and cooling, we examined the heat treatment
condition under which the magnetic field was more
effective with respect to material’s magnetic properties.
The measurement condition are selected to be 1 T and
10 T at 1273 K of which the effects of the magnetic field

Journal of the Magnetics Society of Japan Vol.42, No.3, 201887

INDEX

Fig. 11

Change rate in the iron loss of the sample
applied throughout heating and cooling to oneof the sample applied the same magnetic fieldstrength during cooling at 1273 K.

Fig. 12

Change rate in the magnetic permeability of thesample applied throughout heating and coolingto one of the sample applied the same magnetic
field strength during cooling at 1273 K.

during cooling is particularly observed in the previous
section.
Fig. 11 shows the iron loss characteristics of thesample in which the magnetic field was applied during
heating. The magnetic field strength during the heat
treatment was maintained at 1 T and 10 T. Reported
iron loss values are relative to those of the samples inwhich the magnetic field was applied only during cooling.
It is seen that with at the magnetic field of 1 T, the ironloss was reduced by applying the magnetic field
throughout during heat treatment.
Regardingmagnetic permeability, as seen in Fig. 12, thepermeability was improved by about 50 % under an
excitation condition of ≤1.5 T. This is believed to be theresult of crystal growth during heat treatment underthe magnetic field. The reason why the magnetic
permeability decreased at ≥1.6 T is because of theincrease in the 90° magnetic domain as mentioned
previously. On contrary, heat treatment with appliedmagnetic field of 10 T led to iron loss increase of 13 % incomparison with that when the magnetic field wasapplied during cooling only. However, with increasing
magnetic flux density, magnetic permeability ratio
decreased in the range of 0 to 1.5 T.

88

3.4 Consideration on effect of magnetic field annealing
The following two reasons can be considered asreasons why the magnetic properties were deteriorated
in the sample when the magnetic field was applied
throughout heat treatment, compared with that of thesample when the magnetic field was applied duringcooling. Firstly, sufficient grain growth may not havebeen achieved under the influence of the magnetic field.
This could be because the crystal grains in the electricalsteel sheet expand or contract due to magnetostriction
and form an energy barrier in the crystal grainboundary. The second reason may be an increase in the
90° magnetic domain. It is known that when a soft
magnetic material is heat-treated in a magnetic field, its
magnetic domain structure changes remarkably 16).
Since λ111 which is a typical magnetostriction constant ofiron is a negative value17), the sample may contract inthe magnetic field direction if a strong magnetic field isapplied at a temperature below the Curie temperature.
By maintaining the contracted state while being
exposed to a high temperature, crystal grains grow witha relatively large number of 90° magnetic domains,resulting in microstructural texturing. We believe that
this phenomenon would be better understood andexplained in future works by detailed observation of
crystal grains and boundaries inside the sample andobserving the changes in magnetic domains.
Furthermore, in addition to the magnetic field
application conditions verified in this paper,
experiments will be carried out the application of amagnetic field only during heating up to certain
temperature and only during keeping, we make clear asuitable heat treatment condition, which is mosteffective to material’s magnetic properties.
4. Conclusion
In this paper, the effects of heat treatment in an
applied magnetic field on the magnetic properties of thecommercial electrical steel sheet (50A470) were reported.
Upon heat treating in the absence of magnetic field,
grain growth was promoted and iron loss was reducedwith increasing heat treatment temperature. The
relative permeability, however, decreased at thealternating excitation condition of ≥1.6 T. The
magnitude of the influence of the magnetic field variedwith heat treatment temperature, and greater effects
were seen at higher temperature. These effects also
varied depending on whether the magnetic field wasapplied throughout the heat-treatment or during coolingalone. Iron loss was seen to increase and magnetic
permeability decrease with 10 T magnetic field applied
throughout heating and cooling, as compared with 10 T
applied during cooling only. The results demonstratethat the strength of magnetic field and whether themagnetic field is applied during cooling or throughout
the heat treatment process are both importantparameters.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

Results confirmed the change in texture of
non-oriented electrical steel sheet due to heat treatment
in magnetic field, ultimately affecting the magnetic
properties under alternating excitation.
In future
works, we will clarify the phenomenon whereby themagnetic properties change due to heat treatment in amagnetic field by analyzing detailed observation of
crystal orientation distribution and crystal grainboundaries using EBSD or XRD, by observing thechange of magnetic domain structures using Kerr effect,and by measuring the two-dimensional magnetic
properties.
Acknowledgements The heat treatment samples in
the magnetic field in this paper were the result of a joint
use study (Issue No. 16H0066) of the High Field
Laboratory for Superconducting Materials attached toInstitute of Materials Research, Tohoku University. We
would like to thank Kohki Takahashi, Associate
Professor, for his collaboration with this research, fromwhom we received valuable advice on sample
fabrication.
References
1)
2)

JFE Steel Corporation, ELECTRICAL STEEL SHEETS, p.21
(2010).
A. Kutsukake, Y. Kido, T. Ikeda, T. Kinoshita, T. Todaka.,
The Papers of Technical Meeting on Magnetics, IEE Japan,
MAG-16-086 (in Japanese), pp.23-28 (2016).

M. Wada: National Technical Report, 50, pp.878-882(1984).
4) S. Koshiba et al.: Hitach Review, 16, pp.1-5 (1956).
5) N. Masahashi, M. Matsuo, K. Watanabe: J. Mater. Res., 13,
pp.457-461 (1998).
6) H. O. Martikainen and V. K. Lindroos: Scandinavian J.
Metallurgy, 10, pp.3-8 (1981).
7) T. Kinoshita, T. Todaka, H. Shimoji, T. Sato: J. Jpn. Soc.
Applied Electromagnetics and Mechanics (in Japanese), 25,
pp.162-167 (2017).
8) T. Kinoshita, K. Kouhara, H. Shimoji, T. Sato, T. Todaka,
The Papers of Technical Meeting on Magnetics, IEE Japan,
MAG-17-083 (in Japanese), p.25 (2017).
9) H. Denma, Y. Ishihara, T. Todaka, M. Doi: J. Magn. Magn.
Mater., 215-216, pp.106-109 (2000).
10) L. Néel: J. Phys. Radium, 15, pp.225-239 (1954).
11) S. Taniguchi, M. Yamamoto: Sci. Rept. Res. Inst. Tohoku
Univ., A6, p.330 (1954).
12) H. Komei, Trans. JIM., 9, pp.88-92 (1968).
13) C.M.B. Bacaltchuk, G.A. Castello-Branco, M. Ebrahimi, H.
Garmestani and A.D. Rollett: Scripta Mater., 48,
pp.1343-1347 (2003).
14) T. Watanabe, T. Suzuki, S. Tanii, H. Oikawa: Phil. Mag.
Lett., 62, pp.9-7 (1990)
15) Y. Xu, H. Ohtsuka, K. Ito, H. Wada, J. Magn. Soc. Jpn. (inJananese), 24, pp.651-654 (2000).
16) J. Marcin et al.: Acta Electorotechnica et Informatica, 13,
DOI: 10.2478/aeei-2013-0020 (2013).
17) S. Chikazumi: “Physics of Ferromagnetism”, 2, p.125(Syokabo, Tokyo,1974).
3)

Received Nov. 22, 2017; Revised Jan. 23, 2018; Accepted Feb.
14, 2018

Journal of the Magnetics Society of Japan Vol.42, No.3, 201889

INDEX
J. Magn. Soc. Jpn., 42, 90-95 (2018)<Paper>Optimization
Optimization of Resonant Circuit and Evaluation of Magnetic Field
Uniformity with 50 mm Gap Magnetic Field Generator
R. Hasegawa, T. Nakagawa, S. Seino and T. A. Yamamoto

Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Heating mediators for magnetic hyperthermia treatment (MHT) are dependent on magnetic field strength.
Therefore, a hyperthermia applicator that generates a homogeneous magnetic field is required. We fabricated a 50
mm gap magnetic field generator (hereinafter called the 50 mm prototype), and the guideline for optimizing
combination of parameters of the resonant circuit was suggested to maximize the estimated heating index (product of
frequency and magnetic field strength). We found that a 7×2-turn coil is optimal for the 50 mm prototype. We consider
that this optimization method is applicable for designing a full-scale hyperthermia applicator. The uniformity ofmagnetic field strength distribution in the 50 mm prototype was measured by a pickup coil, and we show
experimentally that magnetic circuit type magnetic field generator is appropriate for the MHT applicator. The
feasibility of a full-scale MHT applicator was increased by the suggestion of guideline for high-estimated heating index
operation and the demonstration of magnetic field homogeneity.
Key words: hyperthermia, magnetic field generator, magnetic circuit, resonant circuit, uniform magnetic field
1. Introduction
Hyperthermia therapy has gained attention in recent
years as a new cancer treatment. In current clinicalpractice, it is performed with induction heating in theradio frequency range (8 MHz or 13.56 MHz) anddielectric heating in the microwave range (430 MHz or
2450 MHz) 1). In this study, we focused on magnetic
hyperthermia treatment (MHT), which can heat thecancer tissue locally using relatively low frequencies(100 kHz to 1 MHz). The treatment procedure is asfollows. A heating mediator such as an electricalconductor 2), magnetic fluid 3), or bulk magnetic material
4) is inserted around the cancer tissue. An alternating
magnetic field is applied to the heating mediator fromoutside the body and the mediator is heated by eddycurrent loss, Neel and Brownian relaxations, orhysteresis loss. The target temperature of the heating
mediator is between 42 and 45 °C 5) 6).
The specific absorption rate (SAR) of heating mediators
is proportional to the magnetic field strength to a powerof between 1.5 and 2.3 3) 6)-8). As magnetic field strength
has a large influence on SAR, a homogeneous magnetic
field is required and the heating mediator must be
capable of being heated correctly anywhere in the body.
Therefore, a hyperthermia applicator is required togenerate a homogeneous (±5%) magnetic field over alarge area (5–10 L 5)). Additionally, for the widespread
adoption of MHT, it is desirable that the hyperthermia
applicator should be as simple as possible. However, afull-scale MHT applicator requires a large-capacity
power supply. This is why that a MHT applicator that
operates on condition of high-estimated heating index isrequired. Estimated heating index is product of
frequency and magnetic field strength and inproportional to SAR of heating mediator.
The guideline for high-estimated heating index
90

operation is required when designing a full-scale MHT
applicator. There has been no study that focuses on
estimated heating index and no suggestion about theguideline for optimizing resonant circuit of MHT
applicator. We consider that optimizing resonant circuit
improves estimated heating index of MHT applicator. We
evaluated the resonant characteristics with the 50 mm
prototype. Assuming that SAR is proportional to the
product of frequency and magnetic field strength, theguideline for optimizing circuit parameters thatmaximize estimated heating index was suggested.
Moreover, we applied this guideline to 50 mm prototype
and confirmed that the optimal resonant circuit
parameter was uniquely determined. This guideline is
helpful for designing a full-scale MHT applicator.
In previous research, it has been shown that magnetic
field uniformity in the magnetic circuit type magnetic
field generator by the electromagnetic field analysis9). In
this paper, we experimentally demonstrated magnetic
field uniformity in the 50 mm prototype to consolidate
validity of the magnetic circuit type magnetic field
generator. By the suggestion of the guideline for highestimated heating index operation and the experimental
demonstration of magnetic field uniformity, thefeasibility of a full-scale MHT applicator was improved.
2. Experiment equipment
As a preliminary stage for fabrication of a full-scale
MHT applicator, we fabricated a prototype that has
50 mm gap and magnetic poles with a cross-sectional
area of 90×90 mm2 (Fig. 1). The purpose of this prototype
is the evaluation of the resonant circuit, the verificationof the guideline for optimizing the resonant circuit andthe demonstration of magnetic field uniformity. Too
narrow gap makes it difficult to measure the magnetic
field distribution. To evaluate the magnetic field

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

distribution by the multi-point with a pickup coil (spatial
resolution: x-axis 1.3 mm, y-axis 10 mm, z-axis 10 mm),the gap width was 50 mm. The circuit was composed of apair of E-type ferrite cores (TDK, PC40), and excitationcoils were wound about the magnetic poles. The pair of
excitation coils was connected in series. We refer to thenumber of turns of the coil as (number of turns on oneside) × 2. The excitation coil was composed of copper pipe
(inner diameter 2 mm and outer diameter 3 mm) tocirculate cooling water.
Fig. 2 shows the simplified equivalent circuit of theresonant circuit. Lc, Cc are inductance (Lc =0.9 µH) andcapacitance (Cc =360 pF) of the 50 Ω coaxial cable. AC
resistance of excitation coil Re was only considered as
resistance component because it has the most significant
influence on impedance characteristic. The combined
impedance between terminals A and B is expressed by
Eq. (1). The impedance between terminals A and B was
measured using an LCR meter (HIOKI, 3532-50). s                                                             

(1)

The excitation current Ie is expressed Eq. (2).
| |               1 


(2)



Fig. 1 Magnetic circuit type magnetic field
generator.
High-frequency
power supply

Lc

Cm

A

50Ω

Ie
V

Lm
B

150

Excitation
coil

Matching box

Le

Cc

Maximum
value of Re{Z }10016 μH (3×2-turn)
60 μH (6×2-turn)

50
0

Re

Coaxialcable
Fig. 2 Simplified equivalent circuit.

3.1 Characteristics of resonant circuit
We evaluated the changes in impedance locus byvarying the resonant circuit parameters. Fig. 3 shows themeasured impedance locus when the inductance of
excitation coil Le was changed. In the resonance band, theimpedance locus starts near the imaginary axis andmoves in a clockwise direction with increasing frequency
before returning to the imaginary axis. To maximize thepower factor and minimize the reflected power, theimpedance locus should pass through the matching point(50+j0 Ω) and a matched frequency should be chosen. For
example, the impedance locus of a 3×2-turn coil should
be reduced and a 10×2-turn coil should be expanded for
impedance matching, as shown in Fig. 3.
The size of the impedance locus was evaluated from the
maximum value of the real part impedance Re  .
Fig. 4(a) shows that the size of impedance locus reduces
with increasing inductance. Fig. 4(b) shows therelationship between inductance of the excitation coil andthe resonant frequency fr. A diamond indicium wascalculated value that was obtained from the impedancelocus by Eq. (1). The experimental value of the 50 mm
prototype was plotted using a filled circle. We define theresonant frequency fr as the frequency at which the phaseof impedance becomes 0 from a positive value. When thephase did not equal 0, the minimum frequency was
adopted and plotted using an unfilled indicium. Whencalculating the impedance locus by Eq. (1), the measured
frequency characteristic of AC resistance of the 50 mm
prototype was applied to the resistance Re. As for the
calculation value in Fig. 4(a), there is the variation toapproximate curve due to the resistance frequency
characteristic that has the measurement error. The
difference between the calculated value andexperimental value, shown in Figs. 4(a), 5(a) and 6(a),was due to the parasitic capacitance between the internal
wiring and the metal housing of the matching box.
Fig. 4 shows that the trend of the calculated value
agrees with that of experimental value. The resonant
frequency fr is inversely proportional to the inductance ofthe excitation coil (Fig. 4(b)). Coils with a small
inductance (a small number of turns) have higher
operating frequencies but weaker magnetic fields.
Conversely, a coil with large inductance (a large number

Im{Z} (Ω)

  Re  Im 

3. Experimental results

166 μH

-50
-50

0

60 μH
84 μH
106 μH139 μH

50
100
Re{Z} (Ω)

84 μH (7×2-turn)
106 μH (8×2-turn)

16 μH

150

139 μH (9×2-turn)
166 μH (10×2-turn)200

Fig. 3 Measured impedance locus.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

91

INDEX

3×2-turn

150

Experimental value
Simplified equivalentcircuit

100
50
0

6×2-turn
7×2-turn

10×2-turn8×2-turn
9×2-turn

0

50
100
150
Inductance Le (μH)

200

weaker. Therefore, there is also a trade-off between
frequency fr and magnetic field strength H.
Fig. 6(a) shows the relationship between matching
inductance Lm and the size of the impedance locus.
As shown in Fig. 6, the trend of the calculated value
qualitatively agrees with that of the experimental value.
The impedance locus expands monotonically withincreasing Lm. Fig. 6(b) shows the relationship between
matching inductance Lm and resonant frequency fr. In thechange from Lm = 4.09 µH to 5.24 µH, the change ofexperimental fr is only -3.8 kHz because the influence of
Lm on fr is small. This is in contrast to the significant
changes in impedance locus (Fig. 6(a)). It is found that Lm
is uniquely determined for impedance matching at the
aaa
1500
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaQQQQ

Resonant frequency fr (kHz)Maximum value of Re{ Z } (Ω)

of turns)have a stronger magnetic field but a lower
operating frequency. There is therefore the trade-off
relationship between frequency fr and magnetic fieldstrength H.
Fig. 5(a) shows the relationship between matchingcapacitance Cm and the size of the impedance locus.
Fig. 5(b) shows the relationship between matchingcapacitance Cm and resonant frequency. As shown in
Fig.5, the trend of the calculated value qualitatively
agrees with that of the experimental value. Resonant
frequency fr increases with decreasing Cm (Fig. 5(b)).
However, an increasing fr brings increasing AC
resistance Re. Eq. (2) shows that excitation current Ie
decrease with increasing Re; the magnetic field becomes
aaaaaaaa
200
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Experimental value
Experimental value(no phase inversion)
Simplified equivalent circuit
Simplified equivalent circuit(no phase inversion)

1000

500

0

0

50
100
150
Inductance Le (μH)200(b) Resonant frequency fr(a) Maximum value of Re

200
150
100
Experimental value

500Simplified equivalentcircuit0

500 1000 1500 2000 2500 3000
Matching capacitance Cm (pF)

Resonant frequency fr (kHz)Maximum value of Re{ Z } (Ω)

Fig. 4 Relationship between inductance of excitation coil and resonant characteristics.

800
700
600
500
400
300
200
100
0

Experimental value
Experimental value(no phase inversion)
Simplified equivalentcircuit0

500 1000 1500 2000 2500 3000
Matching capacitance Cm (pF)(b) Resonant frequency fr(a) Maximum value of Re

120
100
80
60
40
20
0
4.0

Simplified equivalentcircuit
Experimental value
4.2 4.4 4.6 4.8 5.0 5.2
Matching inductance Lm (μH)(a) Maximum value of Re

5.4

Resonant frequency fr (kHz)Maximum value of Re{ Z } (Ω)

Fig. 5 Relationship between matching capacitance and resonant characteristics.

600
590
580
570
560
550
4.0

Simplified equivalentcircuit
Experimental value
4.2 4.4 4.6 4.8 5.0 5.2
Matching inductance Lm (μH)(b) Resonant frequency fr

Fig. 6 Relationship between matching inductance and resonant characteristics.

92

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

5.4

18
16
14
12
6×2 turns
7×2 turns
8×2 turns
9×2 turns

10
8
6
0

500
1000
1500
2000
Matching capacitance Cm (pF)(a) Excitation current Ie

5.0
4.5
4.0
3.5
3.0
9×2 turns
2.5
8×2 turns
7×2 turns
2.0
6×2 turns
1.5
estimated
0
500
1000
1500
2000
of aaaaaaaaaa
Matching capacitance Cm (pF)
Magnetic field strength
H (kA/m-rms)

3.2
3.2 Guideline for optim
optimizing
ptimizing circuit parameters
According to our investigation of resonant circuit
characteristics, we found that there is a trade-off
between magnetic field strength, resonant frequency.
Therefore, we consider that there is an optimal
combination of the resonant circuit parameter. In thissection, we show the guideline for examining the optimal
combination of circuit parameters that maximizes theestimated heating index while maintaining matchingconditions by changing various parameters.
We show the optimization procedure below. Firstly, we
set Le and Cm. After that, impedance locus was adjusted
to the matching point with Lm. Secondly, a fixed input
power was applied; in this paper 180 W. Thirdly, theexcitation current Ie and frequency fr were measured andmagnetic field strength H was calculated. Fourthly, theestimated heating index was evaluated from the productof frequency f and magnetic field strength H. This seriesof flow was executed until the maximum value of
estimated heating index was found.
The multiplier of f and H differs depending on the typeof heating mediator. For instance, the SAR of anelectrical conductor is proportional to    , that of amagnetic fluid is proportional to  3) 6), and that of abulk magnetic material is proportional to .–. 7) 8).
We evaluated    for an electrical conductor and 
for a magnetic fluid or bulk magnetic material.
We applied the above-described procedure to the 50
mm prototype and acquired Ie, H and fr in a plurality of
combinations of circuit parameters. Fig. 7(a) shows therelationship between matching capacitance andexcitation current when the input power is 180 W. The
excitation current having a larger number of turns issmaller when Cm is greater than 500 pF. Coils having alarger number of turns can generate a strong magnetic
field even though the exciting current is small (Fig. 7).
However, although increasing the number of turns
increases the strength of the magnetic field, thefrequency is reduced as a result (Fig. 8). Additionally,
although it is better for a stronger magnetic field toincrease Cm (Fig. 7(b)), an increase in Cm reduces thefrequency (Fig. 8).
Figs. 9 and 10 show the estimated heating index foreach type of heating mediator. The optimal combinationof parameters in terms of maximizing the estimatedheating index varies depending on the heating mediator.
This is because the influence of frequency and magnetic
field strength on SAR differs depending on the mediator.

(b) Magnetic field strength H

Fig. 7 Excitation current and magnetic fieldstrength when input power is 180 W.

Resonant frequency fr (kHz)time of choosing Le and Cm. Therefore, we adjust thematching inductance Lm for impedance matching.
Figs.4, 5 and 6 show the characteristic of theequivalent circuit qualitatively agrees with that of theexperimental resonant circuit with the 50mm prototype.
Therefore, we show that the simplified equivalent circuit
is appropriate to describe circuit characteristics and theabove resonant circuit characteristic is applied to otherexcitation coils, such as a full-scale applicator.

Excitation current Ie (A-rms)

INDEX

1000
6×2 turns
7×2 turns
8×2 turns
9×2 turns

800
600
400
200
0
0

500
1000
1500
2000
Matching capacitance Cm (pF)

Fig. 8 Relationship between matching capacitanceand resonant frequency.
The SAR of electrical conductors is proportional to   and is significantly affected by frequency. Hence,the combination using Cm = 500 pF is optimal because of
the higher frequency. The SAR of a magnetic fluid or bulk
magnetic material is proportional to  because
magnetic field strength has a significant impact on their
SAR. Hence, the combination using Cm = 1000 pF is
optimal because of the stronger magnetic field. It was
found that the optimal combination of the resonant
circuit was uniquely determined for each of the heating
mediators. We consider that this guideline is helpful for
designing a full-scale and high-estimated heating index
operation MHT applicator.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

93

120

4.0 x 10 6Distribution ofmagnetic field strength (%)

Estimated heating indexf 2H 2 (THz・A/m-rms)

INDEX

Maximum value

3.5 x 10 6
3.0 x 10 6
2.5 x 106

2.0 x 10 6

6×2 turns
7×2 turns
8×2 turns
9×2 turns

1.5 x 10 6
1.0 x 10 6
0

100
80
60
40

0

(a) zx-plane distribution

500
1000
1500
2000
Matching capacitance Cm (pF)

Analytical result
Experimental result

20
-20

-10
0
10
Position (mm)20(b) Line distribution along x-axis

Fig. 11 Magnetic field distribution by experimentand analysis (zx-plane).

8

Maximum value

76
6×2 turns
7×2 turns
8×2 turns
9×2 turns

5
4
3
0

500
1000
1500
2000
Matching capacitance Cm (pF)

Fig. 10 Estimated heating index for magnetic
fluid and bulk magnetic material.

(a) xy-plane distribution
120
Distribution ofmagnetic field strength (%)

Estimated heating index
fH 2(THz・A/m-rms 2)

Fig. 9 Estimated heating index for electricalconductor.

100
80
60
40
Analytical result
Experimental result

20
0

-80

-40
0
40
Position (mm)80(b) Line distribution along y-axis

94

Fig. 12 Magnetic field distribution by experimentand analysis (xy-plane).

120
Distribution ofmagnetic field strength (%)

3.3 Experimental demonstration of magnetic field
distribution
To demonstrate the validity of the magnetic circuit
type magnetic field generator, we measured the magnetic
field distribution with a pickup coil. The pickup coil was
manufactured with 11 turns of a polyurethane copper
wire (φ = 0.12 mm). The cross-sectional area of the coilwas 1 cm2. The magnetic field strength was obtained bymeasuring the effective value of the induced
electromotive force of the pickup coil. Furthermore,
electromagnetic field analysis was performed using thefinite element method (ANSYS, Maxwell ver.12). The
number of turns of the exciting coil was 7×2, the exciting
current was 8.3 A RMS, and the operating frequency was
450 kHz. The experimental magnetic field strength was
2.5 kA/m RMS at the center point of the 50 mm prototype（x=0, y=0, z=0) and the analytical value was 2.3 kA/m
RMS, thereby demonstrating good agreement with theexperimental value. The magnetic field strength was
normalized by the center point to investigate distribution.
Fig. 11 shows the surface distribution of the magnetic
field strength in the zx-plane, which was obtained byanalysis, and the experimental line distribution of themagnetic field. The magnetic field has uniformity towithin ±5% between magnetic poles. Figs. 12 and 13 show
the surface distribution in the xy-plane and yz-plane andthe experimental results. As shown in Figs. 11 to 13, the

100
80
60
40
Analytical result
Experimental result

20
0

-80

-40
0
40
Position (mm)80(b) Line distribution along z-axis(a) yz-plane distribution

Fig. 13 Magnetic field distribution by experimentand analysis (yz-plane).

experimental results agree with the analysis results forany axis. A homogeneous magnetic field is distributed ina cylindrical shape. The diameter of the cylindrical area
is 59 mm, and the volume is 0.14 L. Assuming thatmeasurements of the 50 mm prototype are scaled up 6
fold to human body size, the volume of uniform magnetic
field becomes 30 L (≈ 0.14 L × 63). This meets the 10 L
requirement. Thus, this design of magnetic circuit typemagnetic field generator is appropriate for MHT
applications.

Journal of the Magnetics Society of Japan Vol.42, No.3, 2018

INDEX

4. Conclusion
Conclusion
We fabricated a 50 mm prototype with a magnetic
circuit and evaluated the characteristics of the resonant
circuit. By measurement of resonant circuit
characteristic and equivalent circuit analysis, we show
the generality of the resonant circuit of the 50 mm
prototype. Therefore, the resonant circuit characteristicthat was shown in this paper can be applied to otherexcitation coils, such as a full-scale MHT applicator. It
was found that there is the trade-off relationshipbetween frequency fr and magnetic field strength H. The
guideline for optimizing resonant circuit parameters was
suggested by assuming that the product of frequency andmagnetic field strength equates to the estimated heating
index.
We applied this guideline to the 50 mm prototype. The
7×2-turn coil (84 µH), Cm = 500 pF (for electricalconductor) and Cm = 1000 pF (for magnetic fluid or bulk
magnetic material) is optimal for the 50 mm prototype.
We found that the optimal combination is uniquelydetermined. We consider that this guideline can beapplied to a full-scale MHT applicator, because thisguideline has generality.
Furthermore, we evaluated the distribution ofmagnetic field strength using the 50 mm prototype. It
was demonstrated that a 50 mm prototype can generate
a 0.14-L volume uniform magnetic field that has
uniformity to within ±5%. The validity of the magnetic
circuit type magnetic field generator was experimentallyconfirmed.
The feasibility of the a full-scale MHT applicator wasincreased by the guideline for high-estimated heating
xxxx

index operation and the experimental demonstration ofmagnetic field homogeneity in the magnetic circuit typemagnetic field generator.
Acknowledgement
Part of this work was supported by JSPS KAKENHI
Grant Number 16K13666.
References
1) Y. Tanaka: Hyperthermia Gan Onnetsuryouhou Guidebook(in Japanese), Japanese Society for Thermal Medicine,p.4(Sinryou Bunko, Kobe, 2008)
2) T. Yoshioka, T. Nakagawa, M. Horiki, S. Seino, T. A.
Yamamoto, T. Gondo, T. Hashimoto, M. Ohori, and M. Abe:J. Magn. Soc. Jpn., 35, 330-334 (2011)3) E. A. Périgo, G. Hemery, O. Sandre, D. Ortega, E. Garaio, F.
Plazaola, and F. J. Teran: Applied Physics Reviews 2,041302 (2015)4) M. Horiki, T. Nakagawa, T. Yoshioka, S. Seino, T. A.
Yamamoto, M. Abe: J. Magn. Soc. Jpn., 35, 22-26 (2011)5) A. Jordan, R. Scholz, K. Maier-Hauff, M. Johannsen, P.
Wust, J. Nadobny, H. Schirra, H. Schmidt, S. Deger, S.
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7) M. A. Laughton, M. G. Say: Electrical Engineer's ReferenceBook, p.2/13 (Newnes, Oxford, 2003)
8) W. Tong: Mechanical Design of Electric Motors, p.376 (CRC
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Magn. Soc. Jpn., 38, 102-106 (2014)
Received Dec.
Dec. 12,
12, 2017
2017; Revised Jan.
Jan. 22,
22, 2018
2018; Accepted Feb.
Feb. 07,
07,
201
2018

Journal of the Magnetics Society of Japan Vol.42, No.3, 201895

INDEX

Editorial Committee Members・Paper Committee Members
K. Kobayashi and T. Ono (Director), T. Kato, K. Koike and T. Taniyama (Secretary)
A. Fujita
H. GotoH. Hashino
S. Honda
S. Inui
S. Kasai
A. Kikitsu
H. Kikuchi
T. Kimura
T. Kubota
T. Nagahama
H. Naganuma
M. Naoe
M. Ohtake
N. PhamT. SatoT. SatoS. Seino
K. Sekiguchi
M. Sekino
Y. Shiratsuchi
M. Sonehara
T. Tanaka
K. Yamamoto
H. Yuasa
N. Adachi
S. Isogami
Y. Kota
H. Nakayama
K. Tajima
K. Yamazaki

K. Bessho
K. KamataT. MakiT. Narita
M. Takezawa
S. Yoshimura

M. DoiH. KatoE. Miyashita
D. Oyama
T. Takura

T. DoiK. KatoT. Morita
J. Ozeki
M. Tsunoda

Y. Kanai
K. Miura
Y. Sasayama
T. Shima

T. Hasegawa
T. KodaS. Muroga
T. Saito
S. Yabukami

N. Inaba
S. Kokado
T. Nakagawa
R. Sugita
T. Yamamoto

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乾
成里
大竹
充
葛西伸哉
金井
靖
喜々津哲
菊池弘昭
木村
崇
笹山瑛由
佐藤
拓
佐藤
岳
嶋
敏之
白土
優
清野智史
関口康爾
田中哲郎
直江正幸
永沼
博
長浜太郎
橋野早人
PHAM NAMHAI
三浦健司
山本健一
湯浅裕美
安達信泰
古門聡士
土井正晶
森田
孝

磯上慎二
小田洋平
中川
貴
薮上
信

稲葉信幸
齊藤敏明
中山英俊
山崎慶太

小瀬木淳一
杉田龍二
成田正敬
山本崇史

小山大介
田倉哲也
長谷川崇
吉村
哲

加藤宏朗
竹澤昌晃
別所和宏

加藤和夫
田島克文
槙
智仁

窪田崇秀
関野正樹
藤田麻哉

後藤博樹
曽根原誠
本多周太

鎌田清孝
角田匡清
宮下英一

神田哲典
土井達也
室賀
翔

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Journal of the Magnetics Society of Japan
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