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Vol.43 No.3
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2019Power Magnetics (Letter)
Core Losses of a Nanocrystalline Motor Under Inverter and Sinusoidal Excitations
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A. Yao, T. Sugimoto , and K. Fujisaki…42

Iron Loss and Hysteresis Properties under High-Temperature Inverter Excitation
A. Yao and T. Hatakeyama…46

Hard and Soft Magnetic Materials
Magnetostriction Behaviors of Fe100–xCox Alloy Epitaxial Thin Films under Rotating Magnetic Field
K. Serizawa, M. Ohtake, T. Kawai, M. Futamoto, F. Kirino, and N. Inaba…50

Thin Films, Fine Particles, Multilayers, Superlattices
Suppression of Jahn‒Teller Distortion by Chemical Pressure of SiO2 and Local Structure Analysis of
CuFe2O4 Nanoparticles

K. Fujiwara, S. Kimura, S. Miyano, T. Ide, and Y. Ichiyanagi…59Power Magnetics
Integrated CMOS Switch Buck DC-DC Converter Fabricated in Organic Interposer with Embedded
Magnetic Core Inductor
T. Akiyama, S. Ishida, T. Shirasawa, T. Fukuoka, S. Hara, H. Yoshida, M. Sonehara, T. Sato, and K. Miyaji

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

…64

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

3

2019

INDEX

Journal of the Magnetics Society of Japan
Vol. 43, No. 3
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTSPower Magnetics (Letter)
Core Losses of a Nanocrystalline Motor Under Inverter and Sinusoidal Excitations………………………………………………………………………… A. Yao, T. Sugimoto , and K. Fujisaki

42

Iron Loss and Hysteresis Properties under High-Temperature Inverter Excitation……………………………………………………………………………………… A. Yao and T. Hatakeyama

46

Hard and Soft Magnetic Materials
Magnetostriction Behaviors of Fe100–xCox Alloy Epitaxial Thin Films under Rotating Magnetic Field……………………………… K. Serizawa, M. Ohtake, T. Kawai, M. Futamoto, F. Kirino, and N. Inaba

50

Thin Films, Fine Particles, Multilayers, Superlattices
Suppression of Jahn–Teller Distortion by Chemical Pressure of SiO2 and Local Structure Analysis of
CuFe2O4 Nanoparticles…………………………K. Fujiwara, S. Kimura, S. Miyano, T. Ide, and Y. Ichiyanagi

59Power Magnetics
Integrated CMOS Switch Buck DC-DC Converter Fabricated in Organic Interposer with Embedded
Magnetic Core Inductor…………………… T. Akiyama, S. Ishida, T. Shirasawa, T. Fukuoka, S. Hara,
H. Yoshida, M. Sonehara, T. Sato, and K. Miyaji

Board of Directors of The Magnetics Society of Japan
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Y. Suzuki, R. Nakatani

64

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J. Magn. Soc. Jpn., 43, 42-45 (2019)
LetterCore losses of a nanocrystalline motor under inverter and sinusoidal excitations
A. Yao, T. Sugimoto∗ , and K. Fujisaki∗∗

Department of Electrical and Computer Engineering, Toyama Prefectural University, 5180, Kurokawa, Imizu 939-0398, Japan
Department of Advanced Science and Technology, Toyota Technological Institute, 2-12-1, Hisakata, Tenpaku-ku, Nagoya 468-8511, Japan

In this paper, we focus on an evaluation of core losses in permanent magnet synchronous motors (PMSMs) made of nanocrystalline
magnetic materials under inverter and sinusoidal excitations. To discuss the core loss properties of a nanocrystalline motor, comparison
with PMSMs made of amorphous magnetic materials and non-oriented (NO) silicon steel sheets is also performed. Under sinusoidal
excitation, the core losses of the nanocrystalline motor were about 0.7 and 0.5 times smaller than those of the amorphous and NO
motors, respectively. In particular, we found that the nanocrystalline motor reduced the core loss on the basis of time harmoniccomponents in comparison with not only the NO motor but also the amorphous motor. On the basis of our results, the nanocrystalline
motor is expected to be suitable for use in high-speed and high-frequency regions.
Key words: core loss, iron loss, nanocrystalline magnetic materials, PMSM, non-oriented steel sheets, amorphous magnetic materials
1

Introduction

The losses in the driving electric motors mainly consist of mechanical, copper, and core losses (iron losses). Recently, in orderimportant to estimate the core losses caused by time harmoniccomponents of the motor with NMM.
This study focuses on the experimental evaluation of corelosses of permanent magnet synchronous motor (PMSM) withto reduce core losses of the motors, the motors based on corewith amorphous magnetic materials (AMM) 1–12) and nanocrystalline magnetic materials (NMM) 13–15) have been developed andexamined. NMM and AMM exhibit lower iron loss 16) than nonoriented (NO) silicon steel sheets. In particular, NMM oﬀers po-

NMM cores excited by inverter and sinusoidal inputs. In ordertential reduction of core loss, compared to AMM. In our study,
we examine core loss properties of the motor with NMM under

estimate core losses caused by higher harmonic components

inverter and sinusoidal excitations.
In order to control the rotational torque and speed of the motor,
pulse width modulation (PWM) inverters are usually used. In the

NMM.

recent times, several researchers have shown that the iron lossesof the magnetic core under PWM inverter excitation increase due
to time harmonic components 17–29) . Therefore, it is necessary toestimate the influence of time harmonic components in the motorwith NMM to develop the low loss motor systems.

In our study, we use three kinds of motor cores. Figure 1 shows
stator and rotor cores made of NMM (FT-3M), NO electrical steel

to discuss the core loss properties of the PMSM with NMM,
we compare the PMSMs with NO and with AMM under PWM
inverter and sinusoidal excitations. By comparing core losses
under inverter and sinusoidal excitations, we experimentally(in particular, time harmonic components) of the PMSM with

2 Experimental method

sheets (35H300), and AMM (SA-1) that consist of Fe-Si-B-CuNb, Fe-Si, and Fe-Si-B, respectively. Table 1 shows the specifications of three diﬀerent materials used for those cores. From here

Previous studies have addressed that the motor with NMM
core exhibits low core losses “under PWM inverter excitation”
13, 15). Thus, the next phase is to correctly understand the coreloss properties of the motor with NMM core “under sinusoidal
excitation”. Since the motor core loss under sinusoidal excita-on, the PMSMs with the stator and rotor cores made of NMM,
NO sheets, and AMM is called NMM-PMSM, NO-PMSM, andtion does not have time harmonic components, the evaluation of
the sinusoidal-excited motor can obtain the smallest core losses

are used. The stacking factors of NMM-, NO-, and AMM-cores
are about 80 %, 100 %, and 90 %, respectively. Table 2 showsof the motor core at the same experimental conditions (the same
speed, torque, and vector control method) 12) .
In addition, by comparing losses under inverter and sinusoidal

the characteristics of the motor (stator and rotor) cores. Figure 2
shows the schematic of cross-sectional view of motor cores. See
Refs. 2, 12, 14, 15) for the details of design and fabrication process

excitations, we can experimentally estimate the core losses
caused by time harmonic components 12) . Because of a deterioration of the iron losses caused by the manufacture process andso on 15) , it is diﬃcult to accurately obtain the core loss of the
NMM motor based on iron losses of the materials by numericalof rotor and stator cores.
Figure 3 shows the schematic of the PMSM and its control sys-

simulations. Therefore, based on the experimental results, it ismental system, we perform two excitation method tests. The first42

AMM-PMSM, respectively. Here, these three PMSMs made of
diﬀerent materials are the same design. In these PMSMs, the
Sm-Fe-B bonded magnets (S5P-12ME, Aichi Steel Corporation)

tem under no-load condition. Here, we can perform good accuracy of core loss measurement in no-load condition in comparison with the case in load condition 15) . By using this experi-

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Table 1 Specifications of diﬀerent materials used for cores.
NMM

NO

AMM

Density ϕ [kg/m3 ]

FT-3M
7300

35H300
7650

SA-1
7180

Reference
Composition

Fe-Si-B-Cu-Nb

Fe-Si

Fe-Si-B

Thickness [µm]Relative permeability

18
70,000

350
1,400

25
5,000

Saturation magnetic
flux density [T]

1.23

2.0

1.56

Table 2 Motor specifications.
Characteristic

SymbolValue

Radius of stator core
Radius of rotor coreAir gap

Rs
Rr
G

64 mm
37 mm
1.25 mmYoke width
Tooth widthWyWt

9.2 mm10 mm

Axial core length
Permanent magnet length
Permanent magnet width

LPM
WPM

47 mm
20 mm
2 mm

Poles / Slot number
Fig. 1

Photographs of motor cores assembled with nanocrys-talline magnetic materials (left, FT-3M), non-oriented (NO) silicon steel sheets (center, 35H300), and amorphous magnetic materials (right, SA-1). (a) stator and (b) rotor cores.
test is to measure the core loss of the PMSM excited by the threephase sinusoidal wave, which is supplied by three linear amplifiers (HSA 4014, NF). The second test is to measure the coreloss of the PMSM excited by the PWM inverter wave using threephase PWM inverter (MWINV-9R122B, Myway). Here, a standard vector control is utilized for the speed control. See Refs. 12)
for the details of the control method.
The core loss under no-load condition Pcore is given by
Pcore = Pin − Pcu − Pm ,Pin = Pu + Pv + Pw ,

(1)
(2)

Pcu = (Iu2 + Iv2 + Iw2 )R,(3)

where Pin denotes the active input power, Pcu is the copper loss,
Pm is the mechanical loss, Iu,v,w are respectively the u, v, and w
rms currents, Pu,v,w are respectively the u, v, and w input powers,
and R (= 0.5 Ω) is the winding resistance. Here, the copper wire
has a diameter of 1 mm. The approximation formula for the skin√depth is given as 2ρ/ωµ, where ρ (= 1.68 × 10−8 Ω·m) is theresistivity, ω is the frequency, and µ (= 1.26 × 10−6 H/m) is thepermeability. Here, the skin depth of the copper wire is obtained
as about 1.5 mm at 2 kHz. Thus, it is thought that the copper wireis almost unaﬀected by the skin eﬀect. In this study, by using
a rotor without magnetization, the mechanical loss Pm is measured. In our study, the mechanical losses are estimated as about

0.34, 0.88, and 1.4 W at 750, 1500, and 2250 rpm, respectively(see Ref. 1) for the details of the mechanical loss measurement
method.).
It is well known that the core loss under inverter excitation depends on fundamental, space harmonic, and time harmonic components. On the other hand, the core loss under sinusoidal excita-

8 / 12Winding method

Concentrated

tion relates to only fundamental and space harmonic components.
Thus, the core losses caused by time harmonic components Wthc
can be obtained by 12)
Wthc = Winv − Wsin ,(4)where Winv denotes the core loss under PWM inverter excitationand Wsin is that under sinusoidal excitation.
Under PWM inverter excitation, the carrier frequency fc , theswitching dead-time, and the DC bus voltage Vdc are set to 1 kHz,
3500 ns, and 250 V, respectively. In our study, three rotational
speeds (750, 1500, and 2250 rpm) are evaluated. The rotational
speeds of 750, 1500, and 2250 rpm correspond to electrical frequencies of 50, 100, and 150 Hz, respectively. The PMSM undersinusoidal and inverter excitations shown in Fig. 3 is operated
by zero d-axis current control. Note that the core losses causedby time harmonic components (space harmonic components) depend mainly on losses at about 2 kHz (at three times electricalfrequency).
3 Results and discussion
Figure 4 shows the core loss characteristics of three PMSMs
with respect to the rotational speed under sinusoidal excitation.
Here, the rms current values of the NMM- and AMM-PMSMs(NO-PMSM) are about 0.14, 0.16, and 0.18 A (0.13, 0.14, and0.16 A) at 750, 1500, and 2250 rpm, respectively. Then the corelosses are caused by fundamental and space harmonic compo-

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Fig. 6 Core losses caused by time harmonic components of three
PMSMs with respect to rotational speed. These results were obtained from Eq. (4) on basis of experimental results.
Fig. 2 Schematic of cross-sectional view of motor cores.
core losses of about 0.43 W at 750 rpm, of about 1.0 W at 1500
rpm, and of about 1.7 W at 2250 rpm, respectively. Under sinusoidal excitation, the core loss of the NMM-PMSM is about 0.7
and 0.5 times smaller than that of the AMM- and NO-PMSMs,
respectively.
Figure 5 shows the core loss properties of three PMSMs fed byinverter input as a function of the rotational speed. Here, the NOPMSM (AMM-PMSM) exhibits the rms current of about 0.27,
0.51, and 0.80 A (0.31, 0.59, and 0.92 A) at 750, 1500, and 2250
Fig. 3 Schematic of PMSM and its excitation (control) system.
In our study, we use two excitation methods. One method issinusoidal excitation by using three linear amplifiers and othermethod is inverter excitation by using three phase PWM inverter.

rpm, respectively. The rms current values of the NMM-PMSM
at 750, 1500, and 2250 rpm are about 0.33, 0.63, and 0.99 A,
respectively. For sinusoidal and inverter excitations, the current
caused by fundamental wave is almost the same value. See Appendix for the details of waveforms, magnetic flux density, andthe related values. Under inverter excitation, the core losses arecaused by fundamental, time harmonic and space harmonic components. In the experiments, the tested NMM-PMSM presents
small core loss in comparison with that of the AMM- and NOPMSMs. The core losses of the NMM-PMSM are 0.78 W at 750
rpm, 1.7 W at 1500 rpm, and 2.5 W at 2250 rpm, respectively.
The core losses of the NMM-PMSM is about 0.6 and 0.4 times

Fig. 4 Experimentally measured core losses of three PMSMs(NO, AMM, and NMM) as a function of rotational speed undersinusoidal excitation.

of those of the AMM- and NO-PMSMs, respectively. Here, themagnet losses of the PMSMs accounts for less than 1 % of thetotal core losses 15) because the Sm-Fe-B bonded magnets haveextremely low loss.
We now discuss the core losses caused by time harmonic components of three PMSMs obtained with Eq. (4). Figure 6 shows
the obtained Wthc results at each measurement point. The corelosses caused by time harmonic components of the NMM-PMSM
are drastically smaller than those of the AMM- and NO-PMSMs.
The average core loss reduction caused by time harmonic com-

Fig. 5 Experimentally obtained core losses of three PMSMs
with respect to rotational speed under inverter excitation.
nents. For each rotation speed, the NMM-PMSM exhibits excellent low core loss in comparison with that of the AMM- and NOPMSMs. The NMM-PMSM excited by sinusoidal input exhibits

44

ponents of the NMM- and AMM-PMSMs under PWM inverter
excitation is about 70% and 45% as compared to the core loss of
the NO-PMSM, respectively. In average, the Wthc of the NMM, AMM-, and NO-PMSMs accounts for 40 %, 48 %, and 53 %of the core losses, respectively. Thus, we found that the NMMPMSM can achieve core loss reduction caused by time harmoniccomponents, which correspond to losses in the high-frequency
region, in comparison with not only the NO-PMSM but also the

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AMM-PMSM. Therefore, the NMM-PMSM is expected to besuitable for use in high-speed and high-frequency regions.
4 Conclusion
We for the first time examined the fabricated nanocrystalline
motor under both sinusoidal and inverter excitations. In addition, the NO and amorphous motors were compared to discuss
the core loss properties of the nanocrystalline motor. Under sinusoidal excitation, the core loss of the NMM-PMSM was about 0.7
and 0.5 times smaller than that of the AMM- and NO-PMSMs,
respectively. In particular, we found that the NMM-PMSM canrealize core loss reduction caused by time harmonic components,
which correspond to high-frequency region, in comparison withnot only the NO-PMSM but also the AMM-PMSM. These results open the way to further research for ultimate low loss motor system based on the nanocrystalline motor, especially in thehigh-speed motor. In our future works, we will perform the evaluation of building factor 21, 30) to understand the core losses of
the PMSM caused by factors such as the manufacturing process
based on both experiments and numerical simulations. In near
future, we will examine the core loss, the rated power, the rated
torque, the torque capacity, and the eﬃciency properties underload condition. The more precise measurement of mechanicalloss and the loss and current for each frequency will be investigated.
Acknowledgment This work was partly supported by the Ministry of Education, Culture, Sports, Science and Technology Program, Japan, for private universities, the Nagamori Foundation
Research Grant, JFE 21st Century Foundation, JSPS KAKENHI
Grant Number 18K13749, 18K04112, and the New Energy andIndustrial Technology Development Organization (NEDO).
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Appendix: Waveforms and magnetic flux density
Appendix Figs. 1 (a) and (b) show voltage and current waveforms at 750 rpm of three PMSMs under PWM inverter excitation. Here, the maximum magnetic flux densities in the teeth
parts of the NMM-, NO-, and AMM-PMSMs (under both excitations) are about 0.6, 0.4, and 0.5 T, respectively. The average
diﬀerence between magnetic flux densities under sinusoidal andinverter excitations is about 3 % or less.

Appendix Fig. 1 Waveforms under inverter excitation at 750
rpm: (a) voltage, (b) current.
Recieved Jan. 21, 2019; Accepted Feb. 15, 2019

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J. Magn. Soc. Jpn., 43, 46-49 (2019)
LetterIron Loss and Hysteresis Properties under High-Temperature Inverter Excitation
A. Yao and T. Hatakeyama
Department of Electrical and Computer Engineering, Toyama Prefectural University, 5180, Kurokawa, Imizu 939-0398, Japan

We experimentally and numerically examined the magnetic properties of magnetic materials under room- and high-temperature
inverter excitations. We show that the iron loss and hysteresis properties of magnetic materials under pulse width modulation (PWM)
inverter excitation depend strongly on the temperature dependence of semiconductor characteristics. The iron loss under PWM inverter
excitation decreased as the temperatures of semiconductors (Si-insulated gate bipolar transistors and Si-diodes) increased. In addition,
it was found that the rate of change of iron loss based on the temperature dependence of semiconductor characteristics at a high carrier
frequency was larger than that at a low carrier frequency.
Key words: iron loss, hysteresis property, inverter, high-temperatures, play model
1

Introduction

the experimental iron loss properties as a function of carrier fre-High-temperature (HT) motor drive systems have been used inquency of a NO ring excited by HT inverter. Furthermore, byusing the play model18–20) with the Cauer circuit15, 21–25) whichharsh temperature environments such as automotive, aerospace,and fire sites 1–3) . In the motor drive system, in order to control
the rotational speed, pulse width modulation (PWM) inverters

takes into account power semiconductor properties26) , we numerically investigate the magnetic hysteretic properties under RT and
HT inverter excitations.

are normally utilized. Several researchers have recently shownthat due to the higher harmonic components the iron losses in the

2 Experimental and numerical methods

magnetic core under PWM inverter excitation increase in comparison with sinusoidal case 4–14) . In the HT motor system, theinverter and magnetic material cores are exposed to HT. To real-

Figure 1 shows a schematic of the experimental setup used
to measure the iron loss characteristics under RT and HT
inverter excitations. The single phase PWM inverter consistsize HT and high eﬃciency motor drive system, it is to understandmagnetic properties of magnetic materials fed by inverter in harshof Si-insulated gate bipolar transistors (IGBT) and Si-diodes

temperature environments. To separate the eﬀects of temperature
properties of the semiconductors and the magnetic materials on
the magnetic properties, it is necessary to consider the following(GT20J341). We use a ring specimen made of laminations ofstandard NO electrical steel sheets (35H300) 11) . Here, the semiconductors (Si-IGBTs and Si-diodes) of the inverter are exposed
to ambient temperature variations in a temperature-controlled

two steps: (1) to evaluate magnetic properties of “magnetic materials at HT” under “room temperature (RT) inverter” excitationand (2) to investigate magnetic properties of “magnetic materials

oven (STH-120) to evaluate iron loss properties based on thetemperature dependence of the semiconductor characteristics.
Note here that the ring specimen (magnetic core) is set at RT.

at RT” fed by “HT inverter”. In the recent times, we have examined magnetic properties in magnetic materials at HT under “RTinverter” excitation12, 15) . The next step is to understand magnetic
properties of RT magnetic materials fed by “HT inverter”. This
paper aims to estimate the iron loss and hysteretic properties of aThis ring specimen has two (primary and secondary) coils
wound with round wires that are used as an exciting-coil and a

non-oriented (NO) material, which is conventionally used as the
motor core, under RT and “HT inverter” excitations.
We recently have shown that the power semiconductor properties aﬀect iron loss and hysteresis properties of magnetic materials under PWM inverter excitation16, 17) . It is well known thatthe power semiconductor properties depend strongly on the temperature. Here, in order to estimate the relation between power
semiconductor and iron losses properties under HT inverter excitation, it is necessary to correctly understand the influence ofcarrier frequency that relates to the number of switching times.
In this paper, we experimentally and numerically examine theiron losses and hysteretic properties of magnetic materials under
RT and HT (300◦ C) inverter excitations. This paper addresses
46

B-coil. Tab. 1 shows the characteristics of the ring specimen andsemiconductors.
In the experiments, by integrating H and B, the iron losses
Wring of the ring specimen are given by15, 17)
∫
1
HdB,
Tρ
N1 I
,
H=
l ∫
1
B=
Vdt,
N2 S

Wring =

(1)
(2)
(3)

where ρ (= 7650 kg/m3 ) denotes the density of the NO electricalsteel sheet, T (= 0.02 s) is the period, N1 (= 264) is the number ofturns of the exciting coil, l (= 0.36 m) is the magnetic path length,
N2 (= 264) is the number of turns of B-coil, S (= 87.5 mm2 ) is
the cross section area of the ring, I is the current flowing in the
primary coil of the ring specimen, and V is the B-coil voltage.

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A/D converter

Oven
Inside oven

Vdc

S1

S3

S2

S4

I
Ring coreat room temperatureV

Primary coil Secondary coil
264turns
264turns

PWM inverter

Fig. 1 Schematic of ring specimen, inverter, and measurement
system for obtaining the experimental iron loss and hysteresis

(b)

(a)

Fig. 2 I − V characteristics at RT and 300◦ C of the Si-IGBT and

Si-diode measured by using SMU. (a) Si-IGBT. (b) Si-diode.

properties under room-temperature (RT) and high-temperature(HT) inverter excitations. Semiconductors (Si-IGBTs and Sidiodes) of inverter were set in oven and exposed to ambient tem-erties 26) . By using the play model with the Cauer circuit, thehysteresis loop is described byperature variations. Ring core was set at RT.

′

Table 1 Specifications of ring specimen and semiconductors.
Characteristic

Symbol

Value

ρ
S
d
l
N1
N2

35H3007650 kg/m3
87.5 mm2
7 mm
0.36 m
264 turns
264 turns
GT20J341

Material
Density
Cross section area
HeightAverage magnetic path length
Primary coil winding
Secondary coil winding
Semiconductors

the switching dead time are set to 0.5, 0.2 T, and 3500 ns, respectively. The fundamental frequency f0 is set to 50 Hz. The ringtests are carried out at carrier frequencies fc of 1, 4, 12, and 20
kHz. See refs. 15, 17) for the details of the iron loss measurements.
In our paper, the rate of change of iron loss η based on semiconductor temperature is defined by

RT
Wring

,

(5)
(6)
(7)

where HDC (B) denotes the static (DC) hysteretic property repre-

fundamental and higher harmonic components. In the following
experiments and numerical simulations of ring tests, the modulation index, the maximum magnetic flux density of the ring, andη=7(Bk − Bk−1 ) + 2L hk−1
2
7RE ∆t + 2L′′
3L (hk2 − hk−1
2 ),+35RE ∆t
Bk
HDC (B) =
,
L
12
RE =
,
ασd2

sented by the play model, L is the inductance that correspond to′the magnetic permeability in the model, ∆t is the time division, L
is the equivalent inductance to express the magnetic flux caused

By using Eq. (1), we can calculate the iron loss caused by bothRT300
− WringWring

HAC (B) = HDC (B) +

(4)

RT
300
where Wring
and Wring
are the iron losses at RT and 300◦ C, re-spectively.
In our paper, in order to measurement the temperature dependence of I − V characteristics of the semiconductors (Si-IGBTs

and Si-diodes), we use the series precision source/measure unit
(SMU) (B2902A, Keysight). The Si-devices under test are placed
inside the oven (STH-120) and are exposed to ambient temperature variations.
In order to express hysteretic properties under RT and HT inverter excitations by numerical simulations, we use the dynamic
hysteresis model that combines the play model with the Cauer
circuit 24, 25) which takes into account power semiconductor prop-

by eddy currents, k is the step number, and RE is the resistanceto represent eddy currents. Here d (=0.35 mm) is the thickness
of NO sheet, σ (=1.923 × 106 S/m) is the electrical conductivity
at RT of NO sheet, and α (= 2.14) is the anomaly factor at RT to
express anomaly eddy currents15) . Here, the parameters and DC
hysteresis loops of magnetic material cores at RT are applied to′
the numerical simulations. In our paper, L at fc = 1, 4, 12, and20 kHz is set to 3.53, 1.44, 0.558, and 0.348 mH, respectively.
Here, we apply I − V characteristics of the semiconductors to
the current calculated from H using Eq. (2) and then can obtain
numerical hysteresis curves including the power semiconductor
properties. See ref. 15) for details of numerical and parameter
estimation methods.
3 Results and discussion
Figures 2(a) and 2(b) show the I − V characteristics at RT and300◦ C of the Si-IGBT and Si-diode measured using the SMU.
For the I − V characteristics of Si-IGBT, the collector current Ic
is measured by sweeping the collector-emitter voltage Vce at Vge(gate-emitter voltage) = 8 V. For the I − V characteristics of Si-

diode, the current is measured by sweeping the voltage at Vge = 0
V. The current of the Si-IGBT and Si-diode at HT is larger thanthat at RT under the same voltage condition. It is assumed this isdue to the fact that many carriers can overcome the barrier at HT.
Figure 3 shows the B-coil voltage V waveform of the ring specimen (shown in Fig. 1) at fc = 20 kHz under RT and HT inverter

Journal of the Magnetics Society of Japan Vol.43, No.3, 201947

INDEX

excitations. As shown in the magnified figure in Fig. 3, the onvoltage (almost 0 V) at 300◦ C is smaller than that (about 1 V) at
RT because the voltage at 300◦ C becomes low compared to thatat RT under the same current condition, as shown in Fig. 2 (SeeRoom temperature
300℃

ref. 17) for details of on-voltages).
Figure 4(a) shows the experimental hysteresis curves obtainedby the ring test system shown in Fig. 1. The blue and red lines
correspond to curves at fc = 20 kHz under RT and HT (300◦ C)
inverter excitations, respectively. In the experiments, ringing
noises and the slight unbalance of the semiconductor characteristics occur. The corresponding numerical hysteresis curves results
are shown in Fig. 4(b). Here, by using the I − V characteristics
shown in Fig. 2, power semiconductor properties are taken into

On-voltage at HTαOn-voltage at RT

βFig. 3 Induced voltage waveforms of ring specimen (shown in
Fig. 1) under RT and HT (300◦ C) inverter excitations at fc = 20
kHz. Magnified figure shows on-voltages.
Area ofminor loop

Room temperature
300℃

αaccount in our numerical simulations. The calculated hysteresis
curves are consistent with the experimental results. Here, we

βrealize the experimental and numerical representation of thehysteretic phenomena of soft magnetic materials excited byinverter at RT and HT. The ring specimen excited by the inverter
at RT and 300◦ C exhibits iron losses of about 81.1 and 71.6
mW/kg at fc = 20 kHz, respectively. The trace of α → β in theminor loop shown in Fig. 4(a) corresponds to that in voltage
waveform in Fig. 3. Here, the trace of α → β is operated inoﬀ-mode of inverter. When the inverter switches operate inoﬀ-mode, the area of the minor loops decreases with the increaseof semiconductor temperature because the on-voltage at 300◦ C
is smaller than that at RT (See refs. 15, 17) for details of the minor(a)
Room temperature
300℃

loop in oﬀ-mode.). The iron loss under PWM inverter excitation
decreases with increase of temperature of the semiconductors
because the area of the minor loop under HT inverter excitation
becomes small in comparison with that at RT (See ref. 15) for
details of the relation between area of loop and iron loss.).

Fig. 4 (a) Experimental hysteresis curves of ring specimen(shown in Fig. 1) excited by PWM inverter at RT and 300◦ C.

Based on both experiments and numerical simulations, we forthe first time found that the iron loss and hysteresis propertiesof magnetic materials under PWM inverter excitation depended

on minor loops.). (b) Corresponding numerical hysteresis curves
generated from play model with Cauer circuit.

strongly on the temperature dependence of semiconductor
characteristics in not only on-mode but also oﬀ-mode.
Figure 5 shows the iron losses of the ring specimen with respect to carrier frequency under RT and HT inverter excitations.
The blue and red points correspond to the iron losses of NO ringfed by inverter at RT and 300◦ C, respectively. The carrier frequency property of the iron loss relates to semiconductor temperature. We quantitatively evaluated the iron losses of RT magnetic
materials under RT and HT (300◦ C) inverter excitations.
Figure 6 shows the rate of change of the iron loss η calculated
from Eq. (4). Note that η at a high carrier frequency is larger
than that at a low carrier frequency. η increases with increasing
carrier frequency. It is considered that the number of switchingtimes increases with the increase of carrier frequency and thenthe influence of the temperature dependence of the semiconductor characteristics at the high carrier frequency becomes large.
Based on our coupled studies of magnetic and semiconductor

48

(b)

Carrier frequency was 20 kHz. Magnified figure shows the minor loop of hysteresis curves (See refs. 15, 17) for more details

properties, it is thought that the core losses of the HT motor system under this experimental condition can be reduced at the highcarrier frequency.
Consequently, this work shows for the first time that the ironloss and hysteresis properties of magnetic materials under PWM
inverter excitation depend strongly on the semiconductor temperature. These results open the way to further research in HT
and high eﬃciency motor system based on coupled studies ofmagnetic and semiconductor properties. It is expected that byusing our numerical simulations we can calculate the magnetic
hysteretic and iron loss properties fed by HT inverters based onother new materials such as silicon carbide (SiC) and gallium nitride (GaN). In addition, since we can achieve to represent thenumerical magnetic hysteretic properties under RT and HT inverter excitations, it will be possible to estimate the loss repartition (e.g. between the hysteresis and eddy current losses) 15, 26)

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

INDEX

atures. In future research, the iron loss and hysteresis properties
of HT magnetic materials under HT inverter excitation will be
addressed.
Acknowledgment This work was partly supported by the JSPS
KAKENHI ♯18K13749, JST OPERA, JFE 21st Century Foundation, and the Nagamori Foundation Research Grant. We are
grateful to Prof. T. Matsuda (Toyama Prefectural University) for
his support in the measurement of semiconductors and Dr. S.
Fig. 5Iron losses of ring specimen as function of carrier fre-quency at RT and 300◦ C. Tests were performed at carrier frequencies of 1, 4, 12, and 20 kHz.

Fig. 6Rate of change of iron loss η based on semiconductor

temperature calculated by using Eq. (4).
of magnetic materials excited by inverter at RT and HT by using our numerical simulations. Also, for electrical power conversion system such as DC-DC converter (especially in high frequency applications), the semiconductor devices are used in HT
environments27) . Therefore, it is expected that our coupled studies of magnetic and semiconductor properties may be useful to
reduce iron losses not only in HT motor but also in electrical
power conversion system.
4 Conclusion
We experimentally and numerically examined magnetic properties of magnetic materials under RT and HT inverter excitations. We for the first time found that the iron loss and hysteresis
properties of magnetic materials under PWM inverter excitation
depended strongly on the temperature dependence of semiconductor characteristics. In addition, we showed that the rate ofchange of iron loss based on the temperature dependence of semiconductor characteristics at the high carrier frequency was larger
than that at the low carrier frequency. These results open theway to further research for loss reduction of not only HT motor but also electrical power conversion system based on coupledstudies of magnetic and semiconductor properties. In our future
works, we will evaluate the impact of power semiconductor characteristics on iron loss properties in the driven motor and in otherparameter settings. In addition, further experimental and numerical investigations are necessary under a wider range of temper-

Odawara (Kitami Institute of Technology) for fruitful discussion.
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Recieved Jan. 23, 2019; Revised Mar. 1, 2019; Accepted Mar.
9, 2019

Journal of the Magnetics Society of Japan Vol.43, No.3, 201949

INDEX
J. Magn. Soc. Jpn., 43, 50-58 (2019)<Paper>Magnetostriction Behaviors of Fe100–xCox Alloy Epitaxial Thin Films
under Rotating Magnetic Field
Kana Serizawa1,2, Mitsuru Ohtake1, Tetsuroh Kawai1, Masaaki Futamoto2, Fumiyoshi Kirino3, and Nobuyuki Inaba4
1Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan
2
3

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

Graduate School of Fine Arts, Tokyo University of the Arts, 12-8 Ueno-koen, Taito-ku, Tokyo 110-8714, Japan
4

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

Fe100–xCox (x = 0, 30, 50 at. %) alloy thin films are prepared on MgO substrates of (001), (110), and (111) orientations by
ultra-high vacuum magnetron sputtering. The influences of film orientation and composition on the magnetic anisotropy and themagnetostriction are investigated. Fe100–xCox(001) single-crystal and (211) bi-crystal films are respectively obtained on MgO(001) and(110) substrates. Fe100–xCox(110) films are epitaxially grown on MgO(111) substrates with two types of variants with the
crystallographic orientation relationships similar to Nishiyama-Wasserman and Kurdjumov-Sachs. The (001) single-crystal and the(211) bi-crystal films, respectively, show four- and two-fold symmetric in-plane magnetic anisotropies, which are reflecting themagnetocrystalline anisotropy of Fe100–xCox crystal with the easy magnetization axes parallel to <100> or <111>. On the contrary,isotropic in-plane magnetization properties are observed for the (110) films due to an influence of the variant structure. The
magnetostriction is measured under rotating magnetic field by using a cantilever method. As the Co content increases from 0 to 50
at. %, the magnetostriction coefficients, λ100 and λ111, respectively increase from +10–5 to +10–4 and from –10–5 to +10–5 for both
Fe100–xCox(001) single-crystal and (211) bi-crystal films. Large λ100 values are also indicated for the Fe100–xCox(110) epitaxial films (x= 30, 50). The present study shows that it is possible to obtain large magnetostriction of 10–4 by control of the film orientation andcomposition.
Key words: Fe-Co alloy, epitaxial thin film, magnetostriction, rotating magnetic field
1.

Introduction

Magnetic thin films with large magnetostriction coefficients
have been studied for microelectromechanical-systemapplications such as actuators, sensors, and vibration energy
harvesting devices1–3). RFe2 (R: Tb, Sm, etc.) alloys show giant
magnetostriction cofficients4) of 10–3. However, high external
magnetic fields are required to show large magnetostriction,
since they have high magnetic anisotropies. Furthermore,
rare-earth free materials are desirable from the viewpoints ofcost and natural resource.
Fe-Co alloys with bcc structure are typical soft magnetic
materials and have recently attracted much attention as one ofmagnetostrictive
materials,
since
they
show
large
magnetostriction cofficients5–10) of 10–4. The magnetostriction
behavior varies depending on the crystallographic orientation.
Therefore in order to investigate the basic magnetostriction
properties, it is useful to prepare epitaxial thin films, since thecrystallographic orientation can be controlled by the substrateorientation. Fe-Co epitaxial films have been prepared on
single-crystal substrates of GaAs11–16), MgO17–23), MgAl2O422),
SrTiO322–24), Al2O323), etc. However, the magnetostriction has
not been investigated by employing Fe-Co epitaxial films,
though there exist reports on the magnetostriction ofpolycrystalline films8,9,25–31). In the present study, Fe100–xCox (x =0–50 at. %) films are prepared on MgO substrates of (001),(110), and (111) orientations. The influences of film orientationand composition on the magnetization and the magnetostriction
properties are systematically investigated.
2.

Experimental ProcedureAn ultra-high vacuum system consisting of two chambers

50

equipped with radio-frequency (RF) magnetron sputter
deposition and reflection high-energy electron diffraction(RHEED) facilities was employed. The base pressure ofdeposition chamber was lower than 4 × 10–7 Pa. MgO(001),
MgO(110), and Al2O3(0001) single-crystal substrates were used.
Before film formation, substrates were heated at 600 °C in thedeposition chamber to obtain clean surfaces, which wereconfirmed by RHEED (not shown here). MgO and Fe100–xCox
alloy (x = 0, 30, 50 at. %) targets of 3 inch diameter were
employed. The distance between target and substrate and the Ar
gas pressure were respectively fixed at 150 mm and 0.67 Pa. The
RF powers for MgO, Fe, Fe70Co30, and Fe50Co50 targets wererespectively adjusted to be 200, 50, 51, and 52 W. Under these
conditions, the deposition rate was 0.015 nm/s for MgO,
whereas it was 0.020 nm/s for the other materials. The substratetemperature during sputter deposition was kept constant at
300 °C.
Fe100–xCox films were formed on MgO(001) and MgO(110)substrates and MgO(111) underlayers hetero-epitaxially grownon Al2O3(0001) substrates. The crystallographic orientation
relationship between MgO underlayer and_ Al2O3 substrate_ wasdetermined by_ RHEED as MgO(111)[11 0] and (111)[1 10] ||Al2O3(0001)[1100]. The MgO underlayer consisted of two (111)variants whose orientations were rotated around the film normal
by 180° each other. The surface atomic arrangements of the twovariants are the same. Therefore,
only the crystallographic__
orientation of MgO(111)[11 0] || Al2O3(0001)[11 00] is usedbelow. The thicknesses of MgO(001), MgO(110), andMgO(111)/Al2O3(0001) substrates were respectively 0.30, 0.30,
and 0.43 mm, while that of Fe100–xCox film was fixed at 100 nm.
The crystallographic orientation relationship between film
and substrate was determined by RHEED. The resulting film

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

132

221

284

0.23

0.29

νFe (:= νFe100–xCox)

0.37

–0.05

0.18

0.23

Δl
ΔS · ts2 · Es · (1 + νf)=l
3 · L2 · tf · Ef · (1 – νs) ,(1)

where ΔS was the measured bending, L was the distance
between laser beam points (12.5 mm), t was the thickness, E wasthe Young’s modulus, ν was the Poisson’s ratio, and thesubscripts of f and s respectively referred to film and substrate.
The E and the ν values of single crystal vary depending on
the crystallographic direction, though E and ν are usually
defined in an isotropic elastic body. In the present study, E and ν
are respectively defined as σ/ε// and –ε⊥/ε//, where σ is theuniaxial stress applied along [g1 g2 g3], ε// is the strain occurredalong [g1 g2 g3], and ε⊥ is the strain occurred along the direction
perpendicular to [g1 g2 g3] in the film plane ([d1 d2 d3]⊥ [g 1 g 2 g 3 ] ⊥ out-of-plane direction). Based on the definitions,
E and ν of cubic single crystal are respectively expressed33,34) as

1
C11+C12=E(C11–C12)(C11+2C12)
+

ν = –

1
2
–
C44
C11–C12(γ12γ22+γ22γ32+γ32γ12)

(2)

,

–C12
(C11–C12)(C11+2C12)
+

1
1
–
2C44
C11–C12(γ12δ12+γ22δ22+γ32δ32)

C11+C12(C11–C12)(C11+2C12)
+

1
2
–
C44
C11–C12(γ12γ22+γ22γ32+γ32γ12)

–1

,

0.5
0

–0.5

structure was investigated by 2θ/ω-scan out-of-plane and2θχ/φ-scan in-plane X-ray diffractions (XRDs) with Cu-Kα
radiation (wave length: 0.15418 nm). The magnetization curves
were measured by vibrating sample magnetometry.
The magnetostriction was observed by using a cantilevermethod under a rotating magnetic field of 1.2 kOe. The bending
was measured by using a laser displacement meter fixed on a
vibration isolation table. The details of our measurement system
are reported in our previous paper32). The relative length change,Δl/l, was calculated from the following formula,(3)

where C11, C12, and C44 were the elastic stiffness values andAverage(ν = 0.34)

0

_

0.23

(b)

_

0.04

90
180
270
360
Angle from [001] (deg.)

_

νMgO

1

_

MgO
MgO_
MgO_
Crystal plane
MgO& direction (001)[110] (001)[100] (110)[001] (110)[110]
||
||
||
||
Fe
Fe
Fe_
Poisson’sFe _(001)[100] (001)[110] (211)[011] (211)[111]
ratio

0

_

Table 2 Poisson’s ratios of Fe and MgO single crystals.

0

[110]

EFe (:= EFe100–xCox) [GPa]Average(E = 217 GPa)

100

[110]

336

[001]

308

[001]

245

[110]

EMgO [GPa]

200

[110]

<111>

[001]

<110>

[001]

<100>

300 (a)_Crystal direction
Young’s modulus

Young’s modulus, E (GPa)Table 1 Young’s moduli of Fe and MgO single crystals.

Poisson’s ratio, ν

INDEX

90
180
270
360
Angle from [001] (deg.)

Fig. 1 In-plane (a) E and (b) ν distributions of Fe(110)single-crystal film.
(γ1, γ2, γ3) and (δ1, δ2, δ3) are respectively the cosines of anglesof [g 1 g 2 g 3 ] and [d 1 d 2 d 3 ] with respect to the three
crystallographic axes (a, b, c). Tables 1 and 2 summarize the E
and the ν values of MgO and Fe single crystals calculated withthe reported values of (C11, C12, C44)MgO = (286, 87, 148)35) and(C11, C12, C44)Fe = (237, 141, 116)36). Figures 1(a) and (b),respectively, show the in-plane E and ν distributions of Fe(110)single-crystal film. The E and the ν values of Fe(110) film withmultiple variants are respectively regarded as the averages of Fig.
1(a) (E = 217 GPa) and Fig. 1(b) (ν = 0.34). In the present study,
the E and the ν values of Fe crystal were used in the calculationof Δl/l for Fe-Co alloy films, since the elastic stiffness values of
Fe-Co alloys were unknown. For hexagonal Al2O3 crystal, thereported values37) of E = 407.5±62.5 GPa (345–470 GPa) and ν= 0.285±0.015 (0.27–0.30) were used.
3.

Results and Discussion

3.1

Film growth and structure
Figures 2(a)–(c) show the RHEED patterns observed forFe100–xCox films with different compositions formed on
MgO(001), MgO(110), and MgO(111)/Al2O3(0001) substrates,
respectively. Figures 2(d)–(f) illustrate the diffraction patterns
simulated for bcc(001) single-crystal, bcc(211) bi-crystal, andbcc(110) crystal with Nishiyama-Wasserman (NW)38,39) andKurdumov-Sachs (KS)40) variants, respectively. The details of
the simulations have been shown in our previous papers20–23).
The observed patterns of Figs. 2(a)–(c) are respectively inagreement with the simulated patterns of Figs. 2(d)–(f).
Therefore, Fe100–xCox(001) single-crystal, (211) bi-crystal, and(110) crystal films are respectively epitaxially grown on
MgO(001), MgO(110), MgO(111)/Al2O3(0001) substrates for all
the compositions of x = 0–50 at. %. The crystallographic
orientation relationships are determined as
Fe100–xCox(001)[110]bcc || MgO(001)[100],_
Fe100–xCox(211)[011_ ]bcc || MgO(110)[001],
Fe100–xCox(211)[011]bcc || MgO(110)[001],

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

(type A)
(type B)

51

INDEX

MgO(001)(a-1)

MgO(110)(b-1)

MgO(111)(c-1)

Fe70Co30

Fe50Co50

(a-2)

(a-3)

(d)

004
_

112
(b-2)

(b-3)

(e)

(c-3)

112

002

222A 211 222B 400A

022A 200B
(c-2)

_

Fe

(f) 420200A 022B
240NW1

330

NW1

_

211KS1310NW1

121KS1130NW1220

Fig. 2 (a)–(c) RHEED patterns observed for (a-1)–(c-1) Fe, (a-2)–(c-2) Fe70Co30, and (a-3)–(c-3) Fe50Co50 films formed on (a)MgO(001), (b) MgO(110), and (c) MgO(111)/Al2O3(0001) substrates. (d)–(f) Schematic diagrams of RHEED patterns simulated for(d) bcc(001) single-crystal, (e) bcc(211) bi-crystal, and (f) _bcc(110) multi-crystal with_NW _and KS variants. The _incident electron
beam is parallel to (a) MgO[100], (b) MgO[001], (c) MgO[110], (d) bcc[110], (e) bcc[011]+[011], or (f) bcc[001]+[111].
Figures 3(a-1)–(c-1) show the out-of-plane XRD patterns of
the Fe 100–x Co x epitaxial films with different orientations.
bcc(002), bcc(211), and bcc(110) reflections are observed for thefilms formed on MgO(001) , MgO(110) , and MgO(111)/Al2O3(0001) substrates, respectively. Figures 3(a-2)–(c-2) show
the in-plane XRD patterns of the epitaxial films formed on
MgO(001), MgO(110), and MgO(111)/Al2O3(0001) substrates_
measured by making the scatteringvector parallelto MgO[110],__
MgO[001], and MgO[11 0] (|| Al 2 O 3 [11 00]), respectively.
bcc(200) reflection is observed in the patterns_ of Fe100–xCox(001)single-crystal films [Fig. _3(a-2)]. bcc(011) reflection from theA-type variant and bcc(011) reflection from the B-type variant

20

100

40

60

80

Fe50Co50

0

20

40

60

Co content, x (at. %)

80

NW1–3
KS1–6

bcc(220)

Al2O3(000 12)
MgO
(222)

MgO
(111)

(c-2)

NW1

Fe

Fe

Fe70Co30

Fe70Co30

80100
Diffraction angle, 2θ or 2θχ (deg.)

0.155 (e)
0.145
0.135
0.125
d211 (Out-of-plane) d
211 (Bulk)
0.115d022_ (In-plane)d022_ (Bulk)
0.105
0.100

Fe70Co30
Fe50Co50

Fe50Co50

60

Fe

Al_2O3(2200)

bcc(022)A+(022)B

MgO
(004)
Kβ
WL

WL

40

NW1–3
KS1–6

bcc(211)A,B

Kβ
WL

Fe50Co50
bcc(011)A+(011)B

Fe70Co30

Fe

80

Fe

Fe70Co30

MgO
(002)

bcc(200)

MgO
(220)

60

(c-1)

Fe50Co50(b-2)

0.155 (d)d200 (Bulk)
0.145
0.135
d002 (Out-of-plane)
0.125d200 (In-plane)
0.115
0.105
0.100

0

MgO
(220)

MgO
(004)

bcc (002)

Fe

Fe70Co30

40
Lattice spacing (nm)(b-1)

Fe100–xCox(001)/MgO(111)

_
_

(a-1)

Fe100–xCox(001)/MgO(110)__Intensity (arb. unit)

MgO
(002)
Kβ
WL

(a-1)

_

In-plane XRD

Out-of-plane XRD

Fe100–xCox(001)/MgO(001)bcc(110)which are similar to the case of Fe100–xCox film growth bymolecular beam epitaxy20–23).

bcc(002)(type NW1)
(type NW2)
(type NW3)
(type KS1)
(type KS2)
(type KS3)
(type KS4)
(type KS5)
(type KS6)

Kβ
Kβ
WL

_
Fe100–xCox(110)[001]bcc || MgO(111)[110],_
Fe100–xCox(110)[001]bcc || MgO(111)[011_ ],Fe100–xCox(110)[001]_ bcc || MgO(111)[101],_
Fe100–xCox(110)[11_1]bcc || MgO(111)[11_0],Fe100–xCox(110)[11_1]bcc || MgO(111)[01_ 1],
Fe100–xCox(110)[111]||
MgO(111)[1
01],
bcc
_ _
_
Fe100–xCox(110)[1_11_]bcc || MgO(111)[11_0],Fe100–xCox(110)[1_11_]bcc || MgO(111)[01_ 1],
Fe100–xCox(110)[111]bcc || MgO(111)[101],

40

60

80

0.155 (f)d002 (In-plane)
0.145
0.135
0.125
0.115
d220 (Out-of-plane)
0.105
0.100

0

20

40

100

Fe50Co50d200 (Bulk)

d220 (Bulk)

60

80

Fig. 3 (a-1)–(c-1) Out-of-plane and (a-2)–(c-2) in-plane XRD patterns of Fe, Fe70Co30, and Fe50Co50 films formed on (a) MgO(001),_(b) MgO(110), and (c) MgO(111)/Al
substrates. The scattering vector of in-plane XRD is parallel to (a-2) MgO[110], (b-2)__
2O3(0001)
MgO[001], or (c-2) MgO[110] (|| Al2O3[1100]). The intensity is shown in logarithmic scale. (d)–(f) Compositional dependences ofout-of-plane and in-plane lattice spacings of Fe100–xCox films formed on (d) MgO(001), (e) MgO(110), and (f) MgO(111)/Al2O3(0001)
substrates.

52

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

1

–1
–1

__

_

1 [010]0.5

Magnetic field, H (kOe)

[110]

0.5

[110]

–0.5

0

[100]

[110]

1 [010]0.5

Magnetic field, H (kOe)

Normalized magnetization, M/Ms

Normalized magnetization, M/Ms_

00
:Mr/Ms

__

–0.5

[110]

[100]

_

–1
–1

[110]

1

0

_

[110]

[100]

[110]

1

[010]

Fe50Co50[110]

[110]

(c-2)
[110]
1

0

0.5
0
:Mr/Ms

[100]
[100]

–1
–1

__

0
:Mr/Ms

0.5

[110]

[110]

–0.5

0.5

0

Magnetic field, H (kOe)

1

[100]

[110]

_

_

[100]

[010]

Fe70Co30[100]Fe50Co50
(c-1)

_

1

0

1

_

_

[110]

(b-2)

_

[010]
[110]

Fe[100]Fe70Co30
(b-1)
_

1

(a-2)

_

Fe
(a-1)

Normalized magnetization, M/Ms

INDEX

1 [010][011]A,[011]B[215]A,[215]B2
1[111]A,0 kOe[111]B
: Hs
__

_
_ _

[251]A,[251]B

_

_
__

__

[215]A,[215]B__[111]A,[111]B[011]A,[011]B

_ _
_

__
_

_

_

_
_

_
_ _

_
_

__

_ _
_
_

__

_

_ _
_

__
_

_

_

__

_
_

__

_
_

_
_

__

__
_

_

Normalized magnetization, M/Ms

_

_
__

_ _
_

__
_

__

__

_

_
_

Normalized magnetization, M/Ms

_
_

__

[251]A,[251]B

(c-3)

_

1

[251]A,
1 [251]B[011]A,2[011]B_

0

Magnetic field, H (kOe)[215]A,[215]B2
1[111]A,0 kOe[111]B: Hs[011]A,[011]B__ __[215]A,[215]B[215]A,[215]B_____[111]A,[111]B[251]A,[251]B[011]A,[011]B–1__[251]A,[251]B[111]A,[111]B[111]A,[111]B(c-2)[215]A,[215]B1
0.5[111]A,0[111]B:Mr/Ms
_ _
_

_
_ _

__
_

[011]A,[011]B[111]A,[111]B

_
__

(b-3)

_
_ _

_
_ _

_
_ _

_

__

__

[215]A,[215]B1–1–2[251]A,[251]B

__
_

_
_ _

0.75
0 kOe
: Hs

[111]A,[111]B

0

Magnetic field, H (kOe)[251]A,
1 [251]B[011]A,2[011]B0[011]A,[011]B___[215]A,
1.5 [215]B_[011]A,[011]B–1[215]A,[215]B[251]A,[251]B

Fe50Co50[011]A,[011]B____[251]A,[251]B[011]A,[011]B

_

(a-3)

1.5

[111]A,[111]B

__

0.75

–1
–2

[111]A,[111]B

1_0

Magnetic field, H (kOe)[251]A,[251]B[251]A,[251]B[215]A,[215]B1
0.5[111]A,0[111]B:Mr/Ms

Fe50Co50

(c-1)

__

_

_

–1
–1.5 –0.75[215]A,[215]B__ _[011]A,[011]B0__[111]A,[111]B

Fe70Co30[011]A,[011]B_[111]A,[111]B[251]A,[251]B

(b-2)

_
_ _

Fe[251]A,[251]B

1[011]A,[011]B_0[251]A,[251]B

Fe70Co30

(b-1)

_

1

[011]A, (a-2)[011]B[215]A,[215]B1
0.5[111]A,0[111]B:Mr/Ms

_

Fe
(a-1)

Normalized magnetization, M/Ms

Fig. 4 (a-1)–(c-1) In-plane magnetization curves and (a-2)–(c-2) Mr/Ms distributions measured for (a) Fe, (b) Fe70Co30, and (c)Fe50Co50(001) single-crystal films formed on MgO(001) substrates. The applied magnetic field directions are shown by using the
crystallographic directions of Fe100–xCox film.

[251]A,[251]B_

Fig. 5 (a-1)–(c-1) In-plane magnetization curves and (a-2)–(c-2) Mr/Ms and (a-3)–(c-3) Hs distributions measured for (a) Fe, (b)Fe70Co30, and (c) Fe50Co50(211) bi-crystal films formed on MgO(110) substrates. The applied magnetic field directions are shown by
using the crystallographic directions of two Fe100–xCox(211) variants.
seem to be overlapped around 2θχ = 45° in the patterns ofFe100–xCox(211) bi-crystal films [Fig. 3(b-2)] by considering theepitaxial orientation relationships determined by RHEED.
bcc(002) reflection
from the NW1-type variant is recognized,_
whereas_ _ bcc(11 1) reflection from the KS1-type variant andbcc( 1 1 1 ) reflection from the KS4-type variant, which are
expected to appear around 2θχ = 55°, are absent in the patternsof Fe100–xCox(110) epitaxial films [Fig. 3(c-2)], because thebcc(hkl) reflections (h, k, l = ±1) are forbidden. The
out-of-plane and in-plane XRDs confirm the epitaxial
orientation relationships determined by RHEED. Figures
3(d)–(f) summarize the out-of-plane and in-plane latticespacings of Fe100–xCox films, which are estimated from the XRD
data. The lattice parameters of Fe100–xCox films agree with small
differences within ±0.7% with those of bulk Fe100–xCox crystal41),
which indicates that the lattice strains of Fe100–xCox films are
small.
3.2

Magnetic anisotropy
Figures 4(a-1) and (b-1) show two typical examples ofin-plane magnetization curves measured for the Fe and the
Fe70Co30(001) single-crystal films. The distributions ofnormalized remnant magnetization, Mr/Ms, are summarized in
Figs. 4(a-2) and (b-2). The applied magnetic field directions areshown by using the crystallographic directions of Fe100–xCox

film. The films show four-fold symmetric in-plane magnetic
anisotropies. The easy
directions are observed_ magnetization_
along [100], [010], [100], and [010] (blue solid lines in Figs.
4(a-2) and (b-2)), which is reflecting the magnetocrystalline
anisotropy of Fe100–xCox crystal with the easy magnetization
axes parallel to <100>6). Figure 4(c) shows the magnetization
property of the Fe50Co50(001) single-crystal film. Although afour-fold symmetry in in-plane magnetic anisotropy isrecognized,
magnetization
directions are parallel to_ the_easy__[110], [110], [1 1 0], and [11 0] (orange dotted lines in Fig.
4(c-2)), which are different with those observed for Fe and
Fe70Co30 films. It is known that the easy magnetization axes ofbulk Fe100–xCox crystal vary from <100> to <111> when the Cocontent increases beyond about 40 at. %6). Therefore, thein-plane magnetic anisotropy observed for Fe50Co50 film seems
to be reflecting the magnetocrystalline anisotropy of Fe100–xCox
crystal with the easy axes parallel to <111> and thedemagnetization field. The magnetic anisotropy ofFe100–xCox(001) film varies depending on the composition,
similar to the case of bulk crystal.
Figure 5(a-1) shows the hysteresis curves of the Fe(211)bi-crystal film. The distributions of Mr/Ms and saturation field(Hs) are respectively summarized in Figs. 5(a-2) and (a-3). The
applied field directions are shown by using the crystallographic
directions of two (211) variants. The Fe film shows a two-fold

Journal of the Magnetics Society of Japan Vol.43, No.3, 201953

INDEX_[100]B[211][001]A[010]B__[215]A[251]B_

Fig. 6 Pole-figure map of an bcc(211) bi-crystalline film
showing the angles of typical crystallographic directions.
3.3

Magnetostriction of (001) single-crystal films
The relative length change, Δl/l, of a cubic crystal caused
by magnetostriction8) is shown asΔl31
λ (α 2β 2 + α22β22 + α32β32 – )=
2 100 1 1
3l
+ 3λ111 (α1α2β1β2 + α2α3β2β3 + α3α1β3β1 ) ,(α1, α2, α3)(001) = (cosφ, sinφ, 0).

(β1, β2, β3)[001] = (1, 0, 0),

(6)

1 1
(β1, β2, β3)[110] = (0, 00, 00).
2 2

(7)

By substituting Eqs. (5)–(7) into (4), the relative length changes
measured along [100] and [110] under in-plane rotating

Normalized magnetization, M/Ms___

Normalized magnetization, M/Ms_

1 [112]

_

0.5

[211]

[121]

[101]

–0.5

0

0.5

Magnetic field, H (kOe)

__

_

0

–1
–1

_

–0.5

Magnetic field, H (kOe)

1 [011]

_

[121]

[101]

[110]

1 [112]

1 [011]
_

_

_

[211]

[110]

_

_

[110]

0
:Mr/Ms

[121]

_

[110]

0

_

_ _

__

0.5

(c-2)
[101]
1
[211]
0.5
[110]
0
:Mr/Ms
[112]

_

_

[121]

[011]

MgO[112]

__

[101]
1
[211]

(c-1)

__

_

_

_

_

_

_

_ _

__

_

_

_

_

_

__

1 [112]

–1
–1

_

_

0.5

Magnetic field, H (kOe)

[011]

[112]

_

[121]

[101]

[011]

MgO[112]

1

_

[211]

Fe50Co50
(b-2)

_

[110]

0
:Mr/Ms(5)

When the observation directions are parallel to [100] and [110],the (β1, β2, β3)[100] and the (β1, β2, β3)[110] values are respectively
expressed as

(b-1)

[110]

(4)

where λ100 and λ111 are the magnetostriction coefficients, (α1, α2,α3) and (β1, β2, β3) are respectively the cosines of the angles ofmagnetization and observation directions with respect to thethree crystallographic axes (a, b, c).
When the magnetization rotates in a (001) plane underin-plane rotating magnetic field as shown in Fig. 8(a), thecrystallographic direction of magnetization is shown as[cosφ sinφ 0], where φ is the angle of magnetization direction
with respect to [100]. The (α1, α2, α3) values are thus expressed
as

_

[110]

0

Type A
Type B[011]A [011]B_

0.5[111]B_[101]
1 [211]

1[111]A[100]A_ _Normalized magnetization, M/Ms

_

(a-2)

30

60

[111]B

Tilt angle(deg.)
0[001]A[111]A
__

[112]

[121]

0

[010]A_[011]

MgO[112]–0.5[215]B__–1–1[251]A

Fe70Co30

(a-1)

[110]

_ _

0

__

Fe

1

_

[011]A [011]B

symmetric in-plane magnetic anisotropy._ _The _ _easy
magnetization_ ___directions are observed along [251 ]A, [2 1 5]A,
[251]B, and [215]B (pink dotted lines in Figs. 5(a-2) and (a-3)),
which are respectively obtained by projecting [010]A, [001]A,[010]B, and [001]B on the (211) surface as shown in Fig. 6.
Therefore, the magnetic anisotropy is interpreted to bereflecting the magnetocrystalline anisotropy of Fe100–xCox
crystal with the easy axes parallel to <100> and thedemagnetization film, similar to the cases of Fe and
Fe70Co30(001) single-crystal films. Figure 5(c) shows themagnetic property of the Fe50Co50(211) film. A two-foldsymmetry in in-plane magnetic anisotropy is observed.
However,__the easy magnetization__ directions are parallel to[011 ] A +[011]B and [011]A+[011]B (blue solid lines in Figs.
5(c-2) and_ (c-3)).
__It is also_noted__that the Hs values measured
along [111]A+[111]B and [111]A+[111]B are not so high (orange
dotted lines in Fig. 5(c-3)), though the Mr/Ms values are low(orange dotted lines in Fig. 5(c-2)). Therefore,the__ _ film ismoderately
easilymagnetized
along
[1
11]
+[11
1 ] B andA___
[11 1 ] A +[1 11] B . _On_ the __contrary,themagnetization
curves_ ___measured along [251]A, [215]A, [251]B, and [215]B, which arerespectively obtained by projecting [010]A, [001]A, [010]B, and[001]B on the film plane, saturate at higher magnetic fields (pinkdotted lines in Fig. 5(c-3)). When the Co content increases up to
50 at. %, the easy and the hard magnetization axes arerespectively considered to be parallel to <111> and <100>6).
Therefore, the Fe50Co50(211) film shows the in-plane magnetic
anisotropy reflecting the magnetocrystalline anisotropy ofFe100–xCox crystal with the easy magnetization axes parallel to<111> and the demagnetization field. Figure 5(b) shows themagnetization property of the Fe70Co30(211) film. The Mr/Ms
and the Hs distributions of Fe70Co30 film are similar to those of
Fe50Co50 film. The result suggests that the Fe70Co30 film also
has easy magnetization axes parallel to <111>, though the easy
axes of bulk Fe70Co30 crystal are parallel to <100>6). The
threshold composition where the easy magnetization axeschange from <100> to <111> seems to be delicately influenced
by the film orientation.
Figure 7 shows the in-plane magnetic properties of the
Fe100–xCox(110) epitaxial films with NW and KS variants
formed on MgO(111)/Al2O3(0001) substrates. The films show
almost isotropic magnetization properties. Nine (110) variants
are coexisting in the (110) epitaxial films and the respective
magnetic anisotropies are overlapped. Therefore, isotropic
magnetization properties are considered to be observed.

Fig. 7 (a-1)–(c-1) In-plane magnetization curves and (a-2)–(c-2) Mr/Ms distributions measured for (a) Fe, (b) Fe70Co30, and (c)Fe50Co50(110) epitaxial films with NW and KS variants formed on MgO(111)/Al2O3(0001) substrates. The applied magnetic field
directions are shown by using the crystallographic directions of MgO underlayer.

54

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

INDEX

[110]

[110]

[110]

Relative length change, Δl/l[110](ϕ)[010]

Fe70Co30

Fe50×10–6(ΔS = 8 nm)

Relative length change, Δl/l[110](ϕ)

Fe50Co50

[110]

[110]

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

(d-2)

Fe

Fe70Co30

Fe50Co50

50×10–6(ΔS = 19 nm)

0

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

[110]

0

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

(d-1)

0

3
+ λ111
4
4

[110]

[010]

[100]

[100]

Ref. 5
Ref. 6
Ref. 7
Ref. 8
Ref. 42

Relative length change, Δl/l[100](ϕ)

λ 111

λ111

_

λ 100

100

(Co)

(c-2) λ111 < 0

3
λ
4 111

__

Present study

Ref. 5
Ref. 6
Ref. 7
Ref. 8
Ref. 42

4

–

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

0

20 40 60 80
Co content (at. %)

λ100

_

50

0

0

4

λ100

100

(Fe)

3
– λ111
4
4

λ100
[010]

150

–50

4

λ100

4

Present study

0

[100]

2

λ100

_

Magnetostriction constant,λ 100 ,λ111(b-2) λ100 < 0

λ
– 100

λ100

_

200

90
180
270
360
Rotation angle, ϕ (deg.)(c-1) λ111 > 0

3
λ
4 111

__

300 (e)
250

0

+

_

(×10–6)2_

M (// Hrot)[cosϕ sinϕ 0]

–

λ100
__

[110]

4

[010]

Δl / l[110]

ϕ

4

λ100

[100]

[010]

Δl / l[100][100]Relative length change, Δl/l[100](ϕ)

1

λ100

λ100

Fe100–xCox[001][110](b-1) λ100 > 0

(a)

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

Fig. 8 (a) Schematic diagram showing the magnetization and the observation directions with respect to the typical crystallographic
directions. (b) Δl/l[100](φ) and (c) Δl/l[110](φ) calculated for (001) single-crystal films with (b-1) λ100 > 0, (b-2) λ100 < 0, (c-1) λ111 > 0,and (c-2) λ111 < 0. (d-1) Δl/l[100](φ) and (d-2) Δl/l[110](φ) measured for Fe100–xCox(001) single-crystal films formed on MgO(001)substrates. (e) Compositional dependences of λ100 and λ111. The bulk values in (e) are cited from Refs. 5–8 and 42.
magnetic field, Δl/l[100](φ) and Δl/l[110](φ), are given as

3
1
Δl
(ϕ) =
λ cos 2ϕ + λ100 ,l[100]
4 100
4

(8)

3
1
Δl
(ϕ) =
λ sin 2ϕ + λ100 ,4 111
4l[110](9)which are respectively cosine and sine waves. It is noted that thephases of Δl/l[100](φ) and Δl/l[110](φ), respectively, reverse
depending on the signs of λ100 and λ111, as shown in Figs. 8(b)and (c). Furthermore, the λ100 and the λ111 values can be
estimated by using the following relations,λ100 =

43ΔlΔl(ϕ = 0º) –(ϕ = 45º) ,l[100]
l[100](10)

λ111 =

43ΔlΔl(ϕ = 45º) –(ϕ = 90º) .
l[110]
l[110](11)

Figure 8(d-1) shows the Δl/l[100](φ) measured for the
Fe100–xCox(001) single-crystal films with different compositions.
The phases of observed waves are in agreement with that of
calculated wave of Fig. 8(b-1). The λ100 value is thus positive forall the Fe100–xCox(001) films. Figure 8(d-2) shows the Δl/l[110](φ)
measured for the Fe100–xCox(001) films. The phases of waves

observed for Fe and Fe70Co30 films agree with that of calculated
wave of Fig. 8(c-2), whereas the phase of wave observed for
Fe50Co50 film is in agreement with that of wave of Fig. 8(c-1).
Therefore, the λ111 value is negative for the Fe and the Fe70Co30
films, while that is positive for the Fe50Co50 film.
Figure 8(e) shows the λ100 and the λ111 values plotted as afunction of Co content. The λ100 and the λ111 values increase withincreasing the Co content. The Fe70Co30 film shows a large λ100
value of +234×10–6 and a small λ111 value of –5×10–6. On thecontrary, a large λ100 value of +274×10–6 and a moderately large
λ111 value of +78×10–6 are observed for the Fe50Co50 film.
3.4

Magnetostriction of (211) bi-crystal films
When the magnetization rotates in a (211)A plane as shownin Fig. 9(a), the crystallographic direction of magnetization isshown as [–sinχ/ 3 cosχ/ 2 +sinχ/ 3 –cosχ/ 2 +sinχ/ 3 ], where_χ is the angle of magnetization direction with respect to [011]A(|| MgO[001]). The (α1, α2, α3)(211)A values are thus expressed as(α1, α2, α3)(211)A = (–sinχ cosχ sinχ cosχ sinχ
+
–
+
).
3 , 2
3 ,
2
3

(12)

_
When
the observation directions are parallel to [011 ]A and_[111]A, the (β1, β2, β3)[011_]A and the (β1, β2, β3)[1_11]A values arerespectively expressed as

Journal of the Magnetics Society of Japan Vol.43, No.3, 201955

INDEX

Relative length change, Δl/lMgO[001](χ)

50×10–6(ΔS = 15 nm)

0

90
180
270
360
Rotation angle, χ (deg.)[111]A,[111]B[011]A,[011]B[111]A,[111]B[011]A,[011]B[111]A,[111]B[011]A,[011]B[111]A,[111]B[011]A,[011]B

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

(d-2)

_

_

λ 111

Fe70Co30___

Ref. 5
Ref. 6
Ref. 7
Ref. 8
Ref. 420Fe50Co50
Fe

2

_
__

Ref. 5
Ref. 6
Ref. 7
Ref. 8
Ref. 42

100

(Co)

–

__
_

λ 100

20 40 60 80
Co content (at. %)

4

λ111
__
_

0

(Fe)

λ111

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

(d-1)

90
180
270
360
Rotation angle, χ (deg.)(c-2) λ111 > 0

λ111

_
__

–50

_
__

0

Present study

0

__
_

50

0

Relative length change, Δl/lMgO[110](χ)

3
λ
4 111

__
_

100

+

8

_
Relative length change, Δl/lMgO[110]
(χ)

_

4

+

λ111

[111]A,[111]B

8

λ100

150

[111]A,[111]B

2

λ100

λ111

_
__

(b-2) λ100+5λ111 < 0
λ
– 111

4

_
__

200

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

2

λ111

__
_

Present study0(c-1) λ111 < 0
λ
– 111

__
_

(e)

2

_
__

(×10–6)

λ
– 111

_
__

[0 1/ 2 –1/ 2]

8

__
_

M (// Hrot)cosχ sinχsinχ cosχ sinχ
[011]
–
+
–
+
3
2
3
2
3

+

[011]A,[011]B_90º

8[011]A,[011]B[111]

Crystallographic directionof Fe100–xCox(211) film

λ111

__
_

χ

Magnetostriction constant,λ 100 ,λ111

λ100(b-1) λ100+5λ111 > 0[111]A,[111]B_Δl / l[011]

250

3
λ
4 111

[011]A,[011]BΔl / l[111]Relative length change, Δl/lMgO[001](χ)[–1/ 3 1/ 3 1/ 3]

1

300

+

4

[111]A,[111]B

λ100

Fe100–xCox[211][011]A,[011]B(a)Fe

Fe50Co50
Fe70Co30

50×10–6(ΔS = 14 nm)

0

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

Fig. 9 (a) Schematic diagram showing the magnetization and the observation directions with respect to the typical crystallographic
directions. (b) Δl/lMgO[001](φ) and (c) Δl/lMgO[11_0](φ) calculated for (211) bi-crystal films with (b-1) λ100+5λ111 > 0, (b-2) λ100+5λ111 < 0,(c-1) λ111 < 0, and (c-2) λ111 > 0. (d-1) Δl/lMgO[001](φ) and (d-2) Δl/lMgO[11_0](φ) measured for Fe100–xCox(211) bi-crystal films formed on
MgO(110) substrates. (e) Compositional dependences of λ100 and λ111. The bulk values in (e) are cited from Refs. 5–8 and 42.

Δl
Δl
(χ) +
(χ)
l[111]Al[111]B=–31
λ cos 2χ + λ111,
4 111
4

Δl
Δl
(χ = 0º) –(χ = 45º)lMgO[001]
lMgO[001]

λ100 = 8

_

(18)

+

Therefore, when the magnetostriction
is measured _ along__
MgO[001] (|| Fe100–xCox[01 1 ]A+[0 1 1]B) and MgO[1 1 0] (||λ111 = –

__

56

(20)

which are shown in Figs. 9(b) and (c). Furthermore, the λ100 andthe λ111 values can be estimated by using the following
equations,

20
3

Δl
Δl
(χ = 90º) –(χ = 135º) ,lMgO[110]lMgO[110]

(21)

4
3

Δl
Δl
(χ = 90º) –(χ = 135º) .
lMgO[110]lMgO[110]

(22)

_

_

1
5
1
1
λ + λ cos 2χ +λ + λ , (17)8 100 8 111
8 100 8 111

Δl31(χ) = – λ111cos 2χ + λ111.
l[111]B
4
4

1
Δl
(χ) =
2
lMgO[110]

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

_

_

(16)

Since the Fe100–xCox(211) films consist of two types of variants,
A and B, it is necessary to take into account the Δl/l[01_1]B(χ) andthe Δ l/l[11__1]B(χ), which are respectively shown as follows,Δl(χ) =l[011]B1
51
1
λ + λ cos 2χ +λ + λ , (19)8 100 8 111
8 100 8 111

=

_

Δl
3
1
(χ) = – λ111cos 2χ + λ111.
l[111]A44ΔlΔl( χ) +( χ)
l[011]Al[011]B___
By substituting Eqs. (12)–(14) into (4), the Δl/l[011]A(χ) and the_Δl/l[111]A(χ) are respectively given as
Δl
1
5
1
1
λ + λ cos 2χ +λ + λ , (15)(χ) =l[011]A
8 100 8 111
8 100 8 111

1Δl( χ) =lMgO[001]
2

_

(14)

_

1 1 1
, 00, 0 ).
2 3 3

__

_

(β1, β2, β3)[111]A = (–

_

(13)

_

1
1
(β1, β2, β3)[011]A = (0, 00, – 00),
2
2

_
__
Fe100–xCox[ 1 11]A+[1 1 1 ]B), the averages of relative lengthchanges of types A and B variants, Δl/lMgO[001](χ) andΔl/l MgO[11_0] (χ), are respectively given as

INDEX_

Figure 9(d) shows the Δl/lMgO[001](χ) and the Δl/lMgO[110](χ)
measured for the Fe100–xCox(211) films. Figure 9(e) summarizes
the λ100 and the λ111 values. As the Co content increases, the λ100
and the λ111 values increase, similar to the case ofFe100–xCox(001) single-crystal film. The Fe50Co50(211) filmshows a large λ100 value of +236×10–6 and a moderately large
λ111 value of +97×10–6.

Fe100–xCox(110) epitaxial films prepared in the present study.
Therefore, the in-plane orientation can be regarded as being
random and the average of Δl/l(ψ) of each variant is expressed as

3.5

which is shown in Fig. 10(b). Although the relationship of λ100 >λ111, λ100 = λ111, or λ100 < λ111 can be determined by considering
the phase of observed wave, the values of λ100 and λ111 can not
be estimated in the case of the Fe100–xCox(110) epitaxial film.
The (λ100 – λ111) value is shown as

Δl
1
(ψ) =
l
2π
=

Magnetostriction of Fe100–xCox(110) epitaxial films with
NW and KS variants
When the magnetization rotates in a (110) plane as shownin Fig. 10(a), the crystallographic direction of magnetization isshown as [sinψ/ 2 –sinψ/ 2 cosψ]. Here, ψ is the angle ofmagnetization direction with respect to [001]. The (α1, α2, α3)values are thus expressed as(α1, α2, α3) = (sinψ/ 2 , –sinψ/ 2 , cosψ).

[sinω/ 2 –sinω/ 2 cosω]21
sin2ψsin2ω
λ100+ cos2ψcos2ω –2
3
3+ 3λ100sin2ψsin2ω
+ sinψcosψsinωcosω (25)
4

sin ω
sinω
–
cosω
2
2
_
Δl / l[110]ωψ M (// H ) [1/ 2 –1/ 2 0]
rot
[001]
sinψ
sinψ
–
cosψ
1

2

4

3
+ λ
16 16 111

λ100
8

+

3
λ
8 111

0

(27)

(b-2) λ100 < λ111

λ100

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

λ100
16

+

3
λ
16 111

λ100
4

0Fe70Co30

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

Present study
Ref. 5
Ref. 6
Ref. 7
Ref. 8
Ref. 42200
100
050×10–6(ΔS = 4 nm)

(d)

300

Fe50Co50

Fe

90
180
270
360
Rotation angle, ψ (deg.)(×10–6)

(c)

0

(26)

Δl
(ψ = 45º) .
l3–+ λ11188λ100______
Relative length change, Δl/l(ψ)2–(b-1) λ100 > λ111

λ100

Δl
(ψ = 0º)lλ100 –λ111

Fe100–xCox[110]______
Relative length change, Δl/l(ψ)

In order to characterize the magnetostriction of an epitaxial filmwith multi-variant structure, it is necessary to take into accountthe volume ratio of each variant and the respective relative
length changes. However, there are as many as 9 variants in the
(a)

16
3

______
Relative length change, Δl/l(ψ)=

dω[sinω/ 2 –sinω/ 2 cosω]______(24)

The Δl/l[sinω/ 2 –sinω/ 2 cosω] is thus given by substituting Eqs.
(23) and (24) into (4) as follows,Δl(ψ, ω)lΔl(ψ, ω)lFigure 10(c) shows the Δl/l(ψ) measured for the
Fe100–xCox(110) films. The phase of wave observed for Fe film isin agreement with that of calculated wave of Fig. 10(b-2),
whereas the phases of waves measured for Fe70Co30 and
Fe50Co50 films agree with that of wave of Fig. 10(b-1). The
result shows that the λ100 value is smaller than the λ111 value for
the Fe film, while the λ100 value is larger than the λ111 value for
the Fe70Co30 and the Fe50Co50 films. Figure 10(d) shows the(λ 100 – λ 111 ) values plotted as a function of Co content. As the
Co content increases, the (λ 100 – λ 111 ) value increases. The
Fe70Co30 and the Fe50Co50 films show large (λ100 – λ111) values,
indicating that large λ100 values are obtained.
Large λ100 values are obtained, even if Fe-Co films areprepared on MgO substrates with different orientations.
Therefore, well-defined epitaxial Fe-Co films have potentials toachieve large magnetostriction.

When the angle of in-plane observation direction with respect to[001] is shown as ω, the (β1, β2, β3) values are expressed as(β1, β2, β3) = (sinω/ 2 , –sinω/ 2 , cosω).

0

3
1
λ – λ111 cos2ψ +λ100 + 3λ111 ,16 10016λ100 – λ111 =

(23)

2π

–100

0

(Fe)

20 40 60 80
Co content (at. %)

100

(Co)

Fig. 10 (a) Schematic diagram showing the magnetization and the observation directions with respect to the typical crystallographic
directions. (b) Δl/l(ψ) calculated for (110) epitaxial multi-crystal films with (b-1) λ100 > λ111 and (b-2) λ100 < λ111. (c) Δl/l(ψ)
measured for Fe100–xCox(110) epitaxial multi-crystal films formed on MgO(111)/Al2O3(0001) substrates. (d) Compositional
dependences of (λ100–λ111). The bulk values in (d) are calculated by using λ100 and λ111 values in Refs. 5–8 and 42.
____________

Journal of the Magnetics Society of Japan Vol.43, No.3, 201957

INDEX

4.

Conclusion

Fe100–xCox (x = 0–50 at. %) alloy epitaxial films areprepared on MgO substrates with different orientations. The
magnetization and the magnetostriction properties arecharacterized. Fe100–xCox(001) single-crystal and (211) bi-crystal
films are respectively obtained on MgO(001) and (110)substrates, whereas Fe100–xCox(110) films with nine variants are
epitaxially grown on MgO(111) substrates. The (001)single-crystal and the (211) bi-crystal films, respectively, show
four- and two-fold symmetric in-plane magnetic anisotropies,
which are reflecting the magnetocrystalline anisotropy ofFe100–xCox crystal with the easy magnetization axes parallel to<100> or <111>. The easy magnetization directions varydepending on the film composition and orientation. On thecontrary, isotropic in-plane magnetization properties areobserved for the (110) epitaxial films due to an influence of thevariant structure. The magnetostriction behavior under rotating
magnetic field is studied. As the Co content increases, the λ100
and the λ111 values, respectively, increase from +10–5 to +10–4
and from –10–5 to +10–5 for both Fe100–xCox(001) single-crystal
and (211) bi-crystal films. Large λ100 values are also indicatedfor the Fe70Co30 and the Fe50Co50(110) epitaxial films. The
present study shows that it is possible to obtain large
magnetostriction of 10–4 by control of the film orientation andcomposition.
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Received Nov. 4, 2018; Revised Feb. 15, 2019; Accepted Feb. 27, 201958

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

INDEX
J. Magn. Soc. Jpn., 43, 59-63 (2019)<Paper>

Suppression of Jahn–Teller distortion by chemical pressure of SiO2 and local
structure analysis of CuFe2O4 nanoparticles
K. Fujiwara*, S. Kimura*, S. Miyano*, T. Ide*, and Y. Ichiyanagi*,***Department of Physics, Graduate School of Engineering, Yokohama National University, 79-5, Tokiwadai, Hodogaya, Yokohama, Kanagawa,
240-8501, Japan**
RCST, Graduate School of Science, Osaka University, 1-1, Machikaneyamacho, Toyonaka, Osaka, 560-0043, Japan

CuFe2O4 nanoparticles encapsulated by different amounts of amorphous SiO2 were prepared by a wet chemical method. These
nanoparticles were characterized by X-ray diffraction and X-ray absorption fine structure analysis and found to have either a tetragonal
or a cubic structure depending on the amount of SiO2. Magnetization measurements were performed for all samples using a SQUID
magnetometer. The tetragonal nanoparticles showed a smaller maximum magnetization (MS) and a larger coercive force (HC) than the
cubic nanoparticles.
Keywords: Extended X-ray absorption fine structure (EXAFS), Magnetic measurements, Iron oxide, Nano-particles,
Magnetization, Nanostructures
1. Introduction
Magnetic nanoparticles have long been of scientific andtechnological interest. Spinel-structured ferrite nanoparticles
with the formula MFe2O4 where M represents a divalent metal
ion are the most famous magnetic materials and have been usedin many industrial applications. The magnetic properties offerrite nanoparticles were drastically changed by varying the M2+
ions and their particle size, which suggests that there are many
possibilities for their application by the optimization of theirmagnetic properties1)–4). In recent years, ferrite nanoparticles
have also been investigated for biomedical applications such as
magnetic resonance imaging (MRI) enhancement, drug delivery,and heating agents for magnetic hyperthermia5)–11).
Copper ferrite (CuFe2O4) occurs in two structures: tetragonal
and cubic. In general, the tetragonal structure is more stable atroom temperature and transforms to the cubic structure whenheated above about 633–713 K 12) - 15). In CuFe2O4 bulk materials,
most of the Cu2+ ions occupy the octahedral B sites, meaningthat the cation distribution is inverse. Due to this distribution, theorbital overlap between Cu2+ and O2– is induced and theoctahedral B site distorts from the cubic structure to tetragonal
symmetry16), 17), which is known as the Jahn–Teller effect. Jahn–
Teller distortion only occurs at the B-site; therefore, thedistribution of Cu ions affects the structure. The magnetizationof CuFe2O4 is affected by this distortion; the cubic structure hasa higher magnetization than the tetragonal structure18).
Although CuFe2O4 nanoparticles can be synthesized by
combustion19), sol-gel20),21), co-precipitation22)–24), mechanicalmilling25), and solid-state reactions26), there are only a few
methods for obtaining size-controlled cubic Cu-ferrite because
its structure is greatly affected by the production conditions. For
example, the lattice structure is affected by various factors suchas lattice defects and heating and cooling speeds. Thesephenomena are probably caused by the small energy difference
between the Cu2+ ions that are present at the A-site and B-site27).
In our previous studies, we have shown that Cu-ferrite
nanoparticles could be obtained by a wet chemical method andthat particle diameter can be controlled28). Furthermore, it waspossible to encapsulate nanoparticles with amorphous SiO2 andthe structure of Cu-ferrite was affected by the state of the SiO2.
In the present work, we conducted a detailed study of the
CuFe2O4 nanoparticles encapsulated by varying amounts of SiO2.
The CuFe2O4 nanoparticles were synthesized by the wet
chemical method and their fine structure was studied by X-ray
diffraction (XRD), X-ray fluorescence (XRF) and X-ray

absorption fine structure (XAFS). The magnetic properties of thenanoparticles were also evaluated.
2. Experimental
CuFe2O4 nanoparticles surrounded by different amounts ofamorphous SiO2 were synthesized by a wet chemical method.
Aqueous solutions of CuCl2·2H2O, FeCl3·6H2O, Na2SiO3·9H2O,
and NaOH were mixed to obtain a precipitate by neutralization.
The mole ratio of the prepared reagent was Cu:Fe:Si = 1:2:n (n =0, 0.5, 2, 3, 4) and the amount of SiO2 was varied according to
the mole ratio of Na2SiO3·9H2O and NaOH concentration. The
obtained precipitates were washed three times with distilledwater and dried at about 350 K. The as-prepared samples werethen subjected to heat treatment in a furnace under air and at
annealing temperatures of ~1023 K, forming CuFe2O4 in nSiO2(n = 0, 0.5, 2, 3, 4) nanoparticles.
All of the prepared samples were examined by XRD (Cu-Kα, λ= 0.154 nm). The average particle sizes of these samples were
estimated by the Scherrer formula and crystallite size
distribution analysis software CSDA (RIGAKU). The lattice
constants were also calculated by Rietveld analysis using
RIETAN-FP software29). In addition, we performed XRF
analysis to examine their composition ratios.
X-ray absorption fine structure (XAFS) measurements were
performed to clarify the structures of the nanoparticles. The Cu–
K edge (8980.3 eV) and Fe–K edge (7,111.2 eV) XAFS spectra
were measured in the range of the X-ray absorption near-edge
structure (XANES) and the extended X-ray absorption finestructure (EXAFS) spectra were obtained using the transmission
method with a Si(111) monochromator at the BL-9C and
BL-12C station in the Photon Factory synchrotron radiation
facility, KEK, Japan. The cation distribution and atomic
distances of samples were analyzed using the fitting software
REX2000.
Magnetization measurements were performed using a SQUID
magnetometer (Quantum Design, MPMS). Magnetization curves
were measured at 5 K in the ±50 kOe applied magnetic field.
3. Results and Discussion
3.1 XRD analysis
Figure 1 shows the XRD patterns of CuFe2O4 in nSiO2 (n = 0,0.5, 2, 3, 4) nanoparticles annealed at 1023 K. All samples
showed a broad peak around 2θ = 23° that corresponded to

Journal of the Magnetics Society of Japan Vol.43, No.3, 201959

INDEX

amorphous SiO2. It was evident that these patterns were affectedby the amount of SiO2. The average particle diameters were
estimated from the broadening of the diffraction peaks using
Scherrer’s formula and CSDA and the estimated diameters of all
samples were controlled at around 12 nm. The particle diameters
were also confirmed by the TEM image (Figure 2). The samples
that were rich in SiO2 (n = 2, 3, 4) showed a single cubic spinel
phase (Fd3m). However, the samples without silica (n = 0) andinsufficient SiO2 (n = 0.5) showed multiphase patterns thatindicated both cubic and tetragonal spinel phases. Table 1 shows
the lattice constants calculated by Rietveld analysis. The axis
ratio of the n = 0 sample that showed tetragonal phase was c / a= 1.48.
By the SiO2 encapsulation, the lattice constants a and b wereincreased and the lattice structure became cubic. It wasconsidered that the distortion that was caused by different
lengths between Cu-O was suppressed by SiO2 coating. For the
cubic samples n = 2, 3, 4, the lattice constants showed almost thesame value, so the cubic lattice structure was unchanged by the
SiO2 amount. XRF measurements confirmed that thecomposition ratio of Cu:Fe maintained the preparation ratio. For
the SiO2, while the ratios were decreased from the preparation
ratio, the ratio was changed by n. These XRD patterns led to theconclusion that the crystal structures were affected by theamount of SiO2 and the CuFe2O4 nanoparticle’s structure
became cubic after encapsulation with sufficient SiO2, n≧2.
Owing to encapsulation by amorphous SiO2, CuFe2O4 wasproduced with a cubic spinel phase. It is plausible that theamorphous SiO2 layer suppresses the Jahn–Teller distortion
because of pressure from the encapsulated SiO2. Whendecreasing the amount of amorphous SiO2 by using a smallermole ratio n, the pressure was weakened, which promoted
distortion and formed the tetragonal phase.
3.2 XAFS analysis
To investigate the Jahn–Teller distortion and the effect of
encapsulation by amorphous SiO2 on Cu-ferrite nanoparticles,
we performed XAFS measurements and analyzed their finestructures. Using XAFS analysis, structural changes such as
cation distributions and atomic distances were observed30).

Table 1. The particle diameter and lattice constant values ascalculated using the XRD patterns.

SiO2 amount,
n
4
3
2

a/Å

b/Å

c/Å

c/a

8.36
8.35
8.35

8.36
8.35
8.35

8.36
8.35
8.35

1
1
1

0.5

－

－

－

-

0

5.84

5.84

8.64

1.48

Latticestructure
Cubic
Cubic
Cubic
Cubic and
Tetragonal
Tetragonal

Table 2. The composition ratios of CuFe2O4 in nSiO2 (n = 0,0.5, 2, 3, 4) nanoparticles measured by XRF. The ratios werenormalized to become CuαFeβO4 in γSiO2.

SiO2
amount n
4
3
2
0.5
0

Cu amount
α
1.03
1.07
0.96
1.00
0.98

Fe amount
β
1.97
1.93
2.04
2.00
2.02

Si amount
γ
1.65
1.54
0.98
0.31
0.00

Figure 3 shows the results of the Fourier transformation of the
k3-weighted Cu–K edge and Fe–K edge EXAFS spectra.
In Figure 3(a–d), the first peak at ~1.5 Å corresponds to the
distance between the metal ion and its nearest neighbor oxygen
atom (M–O). The second peak at ~2.6 Å represents the distance
between the two cations in the octahedral B sites (B–B). The
third peak at ~3.1 Å represents the distance between a cation in
an octahedral B site and a cation in a tetrahedral A site (B–A).
Figures 3(a) and (b) illustrate the Cu–K edge spectra of CuFe2O4
in nSiO2 (n = 0, 0.5, 4) nanoparticles; their particle diameter wascontrolled at around 12 nm. The XRD pattern of the n = 0
sample showed that it possessed a tetragonal spinel structure.
Therefore, it was expected that the Cu–O peaks at ~1.5 Å would
split into two peaks in the EXAFS spectra. However, the Cu–O

10

20

30

40

50

60

70

80
10

20

30

224

40

321

(f) Bulk

50

60

400

(c) n = 2112103(e) n = 0202
220(b) n = 3

211

422
511
440

220

(d) n = 0.5

101

Intensity / a.u.

111(a) n = 4

222
400

311

CuFe2O4 in nSiO2

7080

2 / degree

Figure 1. XRD patterns of CuFe2O4 in nSiO2 (n = 0, 0.5, 2,
3, 4) nanoparticles annealed at 1023 K. (a) n = 4, (b) n = 3, (c)n = 2, (d) n = 0.5 and (e) n = 0. (f) XRD pattern of the bulk
crystals of CuFe2O4.

60

Figure 2. TEM image of 12-nm CuFe2O4 in 4SiO2
nanoparticles.

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

INDEX

CuFe2O4 in nSiO2

Cu-O

0

1

Cu-K edge

n=4
n = 0.5
n=0
B-A

2

3

4

Interatomic distance, R / Å

5

0.5

6

B-B

n=4
n = 0.5
n=0

Cu-O

1.0

1.5

2.0

CuFe2O4 in nSiO2

㻌

Fe-O

0

1

2

3

4

3.5

5

Interatomic distance, R / Å

CuFe2O4 in nSiO2

㻌

n=4
n = 0.5
n=0

B-A

3.0

6

B-B

Fe-K edge

B-An=4n = 0.5 Fe-O
n=0

㻌

B-B

2.5

(b)

FT magnitude / a.u.

FT magnitude / a.u.

Fe-K edge

B-A

Interatomic distance, R / Å(a)㻌

CuFe2O4 in nSiO2

㻌

B-B

㻌

FT magnitude / a.u.

Cu-K edge㻌FT magnitude / a.u.

㻌

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Interatomic distance, R / Å

(c)

3.5

(d)

Figure 3. (a) Cu–K edge EXAFS spectra of CuFe2O4 in nSiO2 (n = 0, 0.5, 4) nanoparticles that were annealed at ~1023 K withparticle diameter controlled at approximately 12 nm. (b) Overlapped spectra image of graph (a). (c) Fe–K edge spectra of thenanoparticles in (a). (d) Overlapped spectra image of graph (c).
peaks were single for all samples and the peak intensity
weakened as the amount of SiO2 decreased. The EXAFS spectra
consisted of the superposition of sine waves with wavelengths
that correspond to the respective atomic distance where similar
wavelengths cancel each other out. The weak intensity Cu–O
peaks may be explained by the Jahn–Teller distortion effect inthis sample’s CuO6 octahedron. Figure 3(a) only showed the B–
B peak at ~2.6 Å and no peaks corresponded to the B–A bond at
3.1 Å in the n = 0 and 0.5 samples. However, for the n = 4
sample, there were small shoulders at 3.1 Å that corresponded to
the B–A bond. This result suggested that Cu2+ ions only became
distributed in the tetrahedral A site when n = 4, and this was a
typical feature of the cubic structure of Cu-ferrite nanoparticles.
Figures 3(c) and (d) show the Fe–K edge spectra of the
CuFe2O4 in nSiO2 (n = 0, 0.5, 4) samples. The B–B and B–A
peaks indicate that the Fe ions occupy both the tetrahedral A
sites and the octahedral B sites. Each sample exhibited nearly
equal intensities for the B–B and B–A peaks with the n = 0 and
0.5 samples. Therefore, the ratio of Fe ions in the tetrahedral A
sites and octahedral B sites would be 1:1. However, the n = 4

sample showed a higher B-B peak than B-A peak, whichindicated that the quantity of iron ions distributed in B-site wasincreased. This result showed good agreement with the result of
the Cu-K edge EXAFS spectra. Increasing the amount of Cu2+ions in the A-site squeezed Fe ions into the B-site. This indicatedthat the ion distribution was closely related to the lattice
structure. The distribution change in the metal ions produced the
cubic structure of Cu ferrite.
Based on these results, we assumed that the Cu ions occupied
Table 3. M-O length of CuFe2O4 in nSiO2 (n = 0, 0.5, 4)
nanoparticles obtained by EXAFS spectra.

SiO2 amount,
n
4

Cu-O
length / Å
1.49

Fe-O
length / Å
1.50

0.5

1.50

1.49

0

1.50

1.49

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

Latticestructure
Cubic
Cubic &
Tetragonal
Tetragonal

61

INDEX

the remaining octahedral B sites. Therefore, it was reasonable toexpect an inverse spinel structure in both samples. In the Fe–Kedge spectra, the atomic distance between the iron atoms in thesamples with tetragonal structures (n = 0, 0.5) were almost thesame as that of the cubic samples. However, more Fe ions weredispersed into the B site in the cubic samples. For the cubic
samples, the peak that corresponded to the Cu–O length became
stronger and there was a little B–A shoulder in the Cu-K edge
spectra. Table 3 shows the M-O length values for each metal ion
but does not directly indicate the distortion. We could consider
the particle diameter too small to detect the two Cu-O lengths forthe tetragonal structure. The peak intensities of Cu-O werechanged by n, which we think implied the lattice distortion. Fe
ions were more dispersed into the B site in the cubic samples.
Considering these experimental results, the distribution changeof the metal ions suppressed the Jahn–Teller distortion becausethat distortion by the Cu2+ ions only occurred in the octahedral
B-site. This can be explained based on the phenomenon that theamorphous SiO2 layer decreased the O2− content of the Cu-ferrite
nanoparticles, which created defects in the cation structure.
Therefore, the energy difference between the Cu2+ ions present at
the A- and B-sites decreased, so the Cu2+ ions could easily
occupy the A site and the lattice became cubic27). From theseresults, we concluded that the tetragonal structure was a result of
Jahn–Teller distortion in the CuO6 octahedral coordination andencapsulation by sufficient amorphous SiO2 suppressed this
distortion by causing lattice defects.
3.3 Magnetization measurements
Figure 4 shows the magnetization curves (M–H) of the
CuFe2O4 in nSiO2 (n = 0, 0.5, 2, 4) nanoparticles for which their
particle diameter was controlled to be approximately 12 nm. The
magnetization values of all samples were measured at 5 K in a
±50 kOe field. The magnetization values per unit M were
calculated by using the formula:
𝑀𝑀 =

𝑊𝑊
∗ 𝑚𝑚
𝑁𝑁A

where m is the measured magnetization data divided by the usedsample weight, W represents the molecular weight of CuFe2O4
including SiO2, and NA is Avogadro's constant. W was calculated

CuFe2O4 in nSiO2

T=5K
2.0

Magnetization, M / 

1.5
1.0

n=0
n = 0.5
n=2
n=4

0.0

0.02
0.01

-1.0

0.00

-1.5

-0.01

-2.0

-0.02
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-20

0References

20

40

Magnetic Field, H / kOe

60

Figure 4. Magnetization curves at 5 K of CuFe2O4 in nSiO2(n = 0, 0.5, 2, 4) nanoparticles with diameter controlled toaround 12 nm.

62

The SiO2 encapsulation effects were investigated for the
CuFe2O4 nanoparticles. The Cu ferrite encapsulated by different
amounts of amorphous SiO2 was synthesized using a wet
chemical method. XRD patterns showed that the structure of thenanoparticles was changed by the amount of added SiO2 andtheir particle diameters were controlled around 12 nm. EXAFS
analysis clarified that the encapsulation by amorphous SiO2
distributed Cu ions into the tetrahedral A-site and the structure
became cubic upon sufficient silica encapsulation. Magnetization
measurements showed that the cubic-structure sample had ahigher MS value than that of the sample with the tetragonal
structure. This result was caused by the change in the lattice
structure and the difference in Cu2+ ions distribution.

This study was partially supported by Precursory Research for
Embryonic Science and Technology at the Japan Science andTechnology Agency, JST-Mirai Program No. JPMJMI17D7, anda Grant-in-Aid for Science Research (No. 25286041) from theJapan Society for the Promotion of Science (JSPS).

-0.5

-40

4. Conclusions

Acknowledgments

0.5

-60

from the composition ratio obtained by XRF analysis. The
magnetization value M were expressed by μB unit. The saturation
magnetization (Ms) of the nanoparticles depends on various
amounts of SiO2: with n = 0, 0.5, 2, and 4, MS is 1.40, 1.50, 1.78
and 1.94 μB, respectively. These results show that the tetragonalspinel samples (n = 0, 0.5) have lower saturation magnetization
values than the cubic samples (n = 2, 4). Here, it was expectedthat the A–B distance (Fe–Cu distance) of the samples that
contain less SiO2 would become shorter than that of the cubic
samples because of Jahn–Teller distortion. Thus, different values
for the saturation magnetization in Fig. 4 suggest that theinteractions between the antiferro-coupling sites A and B changewith the A–B distance. This variation in the A–B distancedepends on the Cu–O distance caused by Jahn–Teller distortion.
The MS values differed between the cubic samples with n = 2
and 4. The distribution ratios were calculated using theirmagnetization values and composition ratio: the obtained results
were (Cu0.078Fe0.922)[Cu0.882Fe1.118]O4 for the n = 2 sample and(Cu0.133Fe0.867)[Cu0.897Fe1.103]O4 for the n = 4 sample. From theabove, we could confirm that the samples with sufficient silica (n≥ 2) gained a cubic structure and that the Cu2+ distribution waschanged by their structure. For the cubic samples n = 2 and 4, thelattice constant and their composition ratio of metal ions were
almost the same. The difference in the samples was only in theamount of SiO2. These results showed that the difference in MS
between the cubic samples with n = 2 and 4 was caused by theirdifferent distributions of metal ions. This implied that the Cu2+ions distribution was changed by the SiO2 amount for the cubic
samples.

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Received Oct. 26, 2018; Revised Dec. 24, 2018; Accepted Mar. 2,
2019

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INDEX
J. Magn. Soc. Jpn., 43, 64-69 (2019)<Paper>Integrated CMOS Switch Buck DC-DC Converter Fabricatedin Organic Interposer with Embedded Magnetic Core Inductor
T. Akiyama, S. Ishida, T. Shirasawa, T. Fukuoka, S. Hara, H. Yoshida,
M. Sonehara, T. Sato, and K. Miyaji

Spin Device Technology Center, Shinshu Univ., 4-17-1 Wakasato, Nagano 380-8553, Japan

In this paper, the development of a CMOS switch buck DC-DC converter fabricated in an organic interposerwith an embedded power inductor is described. The power inductor is fabricated by using a magnetic core made of an
Fe-based amorphous alloy powder-filler/epoxy composite sheet to form a fully closed magnetic circuit and isembedded in the organic interposer in a lamination process. The fabricated power inductor is located under a CMOS
control chip and has a of 3.5-mm-square footprint. The CMOS switch buck DC-DC converter runs at 20 MHz, andthe fabricated power inductor has an inductance of 150 nH and Q-factor of 38 at around 20 MHz. Furthermore, theinfluence of magnetic flux leakage from the embedded power inductor to a copper wiring pattern on the surface wasanalyzed in a simulation that utilized three-dimensional electromagnetic field analysis software (ANSYS; HFSS).
Based on the simulation result, the conduction losses of the inductor were calculated under the assumption of use ina synchronous buck converter operating with a 5-V input and 3.3-V 0.8-A output.
Keywords: power inductor, organic interposer, Fe-based amorphous alloy powder-filler/epoxy composite sheet,lamination process, DC-DC converter
1. Introduction
In recent years, power distribution losses between
power supply and the loads have increased due torequirement of low-voltage and high-current loads such
as LSIs. In order to reduce the power distribution loss,
the distributed power architecture with Point of Load
(POL) DC-DC converters has been widely used1),2).
However, development of the small power inductor isdesired because the POL DC-DC converter occupy
considerable footprint on the mother board3),4). The
package integrated power inductor has been studied5),6)
to make POL converter footprint smaller. INTEL has
developed package-integrated POL converter using
air-core solenoid inductor for their fourth-generationcore processor Haswell7). The air-core inductor can beeasily fabricated by only the metal process, but hasserious disadvantages such as low inductance value andundesired EMI noise due to widespread alternating
magnetic flux8). In order to reduce the footprint andreduce the EMI noise, it is expected to introduce amagnetic core in the inductor.
This paper describes the development of power
inductor using soft magnetic powder-filler/epoxy
composite sheets as a magnetic core. The embedded
power inductor in the organic interposer is made bylamination process. Furthermore, CMOS control
flip-chip IC and other Surface Mount Devices (SMD) are
mounted on the organic interposer by reflow soldering
at 180oC to fabricate 20 MHz switching buck DC-DC
converter. The simulation results focusing on theinfluence of leakage magnetic from the power inductor
to the surface wiring copper pattern at 20 MHz are also
described. Surface wiring copper pattern locates justabove the embedded power inductor and form a surface

64

layer of the organic interposer which CMOS control chipand SMDs are mounted.
2. Outline of organic interposer
Figure 1 shows a cross-section view of the power
inductor embedded in the organic interposer with 1.6
mm thick glass-fiber/epoxy center core and 50 m thickglass-filler/epoxy build-up layer. The glass-filler/epoxy
build-up layer is formed by thermal laminator in theorganic interposer fabrication process. In this work, themagnetic core power inductor embedded in the organicinterposer is based on the conventional lamination
process using soft magnetic powder-filler/epoxy build-up
sheet. The soft magnetic powder-filler/epoxy composite
sheet changed the glass-filler to soft magnetic
powder-filler. In this method, it is unnecessary tochange the conventional organic interposer fabrication
process but only changing the laminating condition of
the composite sheet9).
3. Fe-based amorphous alloy powder-filler/epoxy
composite sheet
The magnetic composite sheet consist of 2.56 mmedian diameter Fe-based amorphous alloy powder(Fe87.83Si6.59B2.54Cr2.53C0.51 (wt.%)) and epoxy resin.

Fig. 1

Cross-section of organic interposer.

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

INDEX

Figure 2 shows the static magnetization curve andcomplexpermeabilityofamorphousalloy
powder-filler/epoxy composite sheet measured using
VSM (Vibrating-sample magnetometer, Riken Denshi;
BHV-55), and RF Impedance/Material Analyzer(Hewlett-Packard; HP4291B) with coaxial waveguide.
The saturation magnetization of Fe-based amorphousalloy powder-filler/epoxy composite sheet is about 0.8 T.
A filling ratio of Fe-based amorphous alloy powder-fillerin the composite sheet is estimated at 64 vol.%. The
relative permeability ’ is about 9 at tens MHz. Also,
the imaginary part of the complex permeability ”
related to magnetic loss is small up to around tens MHz.
Furthermore, the coercivity of the amorphous
powder-filler/epoxy composite sheet measured using
coercivity meter (Denshijiki Industory; HC-1031) is 324
A/m (4 Oe).

Fig. 3 Cross-sectional view of power inductor withheight of about 70 m and Fe-based amorphous alloy
powder-filler/epoxy composite sheet.

4. Fabrication process of the power inductor
In the organic interposer, the Fe-based amorphousalloy powder-filler/epoxy composite sheet layer isformed by thermal lamination process. Since thecomposite sheet has a characteristic of thermoplastic
and becomes soft at high temperature, the composite
sheet is pressed and laminated to the FR-4 basesubstrate while it is heated at 150oC. By heating thecomposite sheet, it is possible to fill the composite
material between the thick film coil conductors having
large unevenness shown in Fig. 3 and can maintain theplanarization of the composite sheet surface10). The basesubstrate and the composite sheet is heated at 150oC,
then 190oC post curing is performed in a clean ovenafter the lamination.
The power inductor is embedded in the organicinterposer according to the fabrication procedure shownin Fig. 4. A copper spiral coil having a thickness of 70
m is fabricated by electroplating process using photo
resist lift-off process. The power inductor embedded in
the Fe-based amorphous alloy powder-filler/epoxy
composite sheet and forms a fully closed magnetic
circuit.

Fig. 4

Process for fabricating power inductor.

(a) Top view(a) M vs. H(b) ’ and ” vs. f
Fig. 2 (a) Static magnetization curve and (b) complex
permeability versus frequency of Fe-based amorphousalloy powder-filler/epoxy composite sheet.

(b) Cross-sectional viewFig. 5 Structure of power inductor consisting of 6-turn
70-m-thick copper spiral coil embedded in Fe-based
amorphous alloy powder-filler/epoxy composite sheet.

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INDEX

5. Power inductor using Fe-based amorphous alloy
powder/epoxy composite sheet
5.1 Power inductor structure
Figure 5 shows the structure of the power inductor. A
70 m thick electroplated copper 6-turn spiral coilwinding with 130/50 m line/space and 3.5 mm-squarefoot-print, has a DC coil resistance of 170 m5.2 Electrical characteristics of power inductor
Figure 6 shows the measurement result of theelectrical characteristics of the fabricated power
inductor using RF Impedance/Material Analyzer(Hewlett-Packard; HP4291B) and simulation result of
utilizing three-dimensional electromagnetic field
analysis software (ANSYS; HFSS). As shown in Fig. 6,
the inductance decrease slightly and equivalent series
resistance increase with increasing frequency. Since the
6-turn spiral coil has 130 m wide conductor lines, it isconsidered that skin effect and proximity effect in the
conductor width direction cause the inductance todecrease and equivalent series resistance to increase.
The fabricated power inductor has 150 nH at 20 MHz,
which was almost the same value as the simulation
result. Q-factor of fabricated power inductor was 38 at
20 MHz, which was 24% lower than the simulation
result. Since the inductance is almost the same as thesimulation result, the cause of the decrease in the
Q-factor is an increase in the equivalent series
resistance. The main reason for the increase inequivalent series resistance is presumed to be thecontact resistance between the spiral coil and the via
conductor and the parasitic resistance at the time of
measurement. Furthermore, the peak of the Q-factor
was about 40 MHz, it is necessary to change thestructure of the power inductor and the filling ratio of
Fe-based amorphous alloy powder of the composite
sheet for that the peak value becomes 20 MHz.
5.3 Organic interposer integrated CMOS switch buck
DC-DC converter
The surface wiring copper pattern formed just above
the embedded power inductor made by electroplatingprocess which is mount for CMOS control chip and SMD.
The appearance of the fabricated the organic interposer
integrated CMOS switch buck DC-DC converter isshown in Fig. 7. The footprint including the CMOS
control chip and SMD is 7.2 mm x 6.0 mm. The X-ray
photograph shows the power inductor is laid out under
CMOS control chip and SMD.
5.4 Influence of surface wiring pattern formed above
the power inductor
The eddy current is generated on the surface wiring
copper pattern due to the leakage magnetic flux fromthe embedded power inductor. The magnetic flux
generated by this eddy current has an opposite direction
to the main magnetic flux from the power inductor and66

decrease of the Q-factor of the power inductor. In thissection, the influence of leakage magnetic flux from theembedded power inductor to the surface wiring copper
pattern has been analyzed by simulation utilizing
three-dimensional
electromagnetic
field
analysis
software. A Simulation model is shown in Fig. 8. The
analysis condition is a sine wave with an effective valueof 1 A flow at 20 MHz.
Figure 9 shows the magnetic flux density distributionof the cross-section A-A’ of the power inductor (Fig. 8(b)).
From Fig. 9, It can be confirmed from the figure that theleakage magnetic flux is generated from the power
inductor to the surface wiring copper pattern.

(a) L vs. f(b) Rs vs. f(c) Q vs. f
Fig. 6 Measured and simulated (a) inductance L, (b)equivalent series resistance Rs, and (c) Q-factor versus
frequency f.

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

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Fig. 7 Photograph of fabricated CMOS switch buck
DC-DC converter.

Fig. 10 Eddy current generated on copper wiring
pattern on surface (top view, vector).

(a) top viewFig. 8view.

(b) cross view
Simulation model (a) top view and (b) crossFig. 9 Magnetic flux leakage from power inductor(cross view, contour).
Figure 10 shows the current density distribution of
the surface wiring copper pattern. The eddy current on
the surface wiring copper pattern is generated byleakage magnetic flux from the power inductor
embedded in the organic interposer. The eddy current
flows on the surface wiring copper pattern increase theequivalent series resistance of the power inductor.
Furthermore, the magnetic flux generated by the eddy
current decrease main magnetic flux from the power
inductor and its inductance value. It might be necessary
to increase the relative permeability of the composite
sheet and to increase the distance between the surface
wiring copper pattern and the power inductor in orderto the influence of the leakage magnetic flux.

Figure 11 shows the simulation result of frequency
characteristics of inductance L’, equivalent series
resistance Rs’, and Q ’-factor with and without thesurface wiring copper pattern. At 20 MHz, theinductance decreased by 14%, the Q ’-factor decreased
by 58% and the equivalent series resistance increases by
88% due to the influence of the surface wiring copper
pattern just above the embedded power inductor. The
main reason for lowing the Q ’-factor is the increase ofequivalent series resistance due to the eddy currents inthe surface wiring copper pattern caused by leakage
flux from the embedded power inductor. In case of thesurface wiring copper pattern just above the power
inductor, the equivalent series resistance becomes large,
so it is necessary to consider the inductor conduction
loss.
5.5 Inductor conduction loss
Figure 12 shows an equivalent circuit of thesynchronous buck DC-DC converter. Since capacitance
C in Fig. 12 is considered to besufficiently large, theinductor current waveform of the DC-DC converter
using ideal inductor is a triangular wave as shown in
Fig. 13. The inductor current increase/decrease linearly
during on/off of the high side switch S1. When the
inductor current is a triangular wave, the amplitude of
the ripple current is expressed by Eq. (1).

I R = V in D (1- D ) / 2 f L(1)The specification of the synchronous buck DC-DC
converter are listed in Table 1 and as follows, input
voltage; 5 V, load current; 0.8 A and constant on-duty
ratio D of high-side switch; 0.66. The effective value ofthe inductor current is expressed by Eq. (2).

Journal of the Magnetics Society of Japan Vol.43, No.3, 201967

INDEX

Fig. 13(a) L’ vs. f

Triangular current flowing in ideal inductor.

Table 1

Specifications of buck DC-DC converter
fabricated in organic interposer.
Item

Input voltage, Vin
Output voltage, Vout
Load current, IL
Table 2

5.0 V03.3 V00.80 AAC conduction loss of power inductor.
Item(b) Rs’ vs. f

Specification

PAC (w/o surface pattern)
PAC (w/ surface pattern)
I rms2 = (I L2 + I R2 / 3)

AC conduction loss
@ 20 MHz
3.90 mW
12.6 mW(2)

IL is a direct current superimposed current flowing in
the inductor, which is the output current of the DC-DC
converter. Therefore, the conduction loss P of theinductor in the operating state of the DC-DC converter
can be expressed by Eq. (3).
P = R (I L2 + I R2 / 3)
= R dc I out2 + R s I R2 / 3(c) Q ’ vs. f
Fig. 11 Simulated (a) inductance L’, (b) equivalent
series resistance Rs’, and (c) Q ’-factor versus frequency fwith and without copper wiring pattern on surface.

Fig. 12Equivalent circuit of synchronous buckconverter.

68

(3)

The conduction loss of the fabricated inductor is
calculated by using Eq. (3), the DC conduction loss is
108.8 mW and the AC conduction loss is 5.8 mW. The
AC conduction loss of power inductor with and without
surface wiring copper pattern are shown in Table 2.
Despite the increase in the AC conduction loss of thepower inductor due to the influence of the surface
wiring copper pattern, the DC conduction loss is muchlarger than the AC conduction loss. The large DC
resistance of the power inductor results in the decreaseof power conversion efficiency for CMOS switch buck
DC-DC converter. It is necessary to study the structureof the power inductor and increase the relative
permeability of the non-magnetic resin/soft magnetic
filler composite sheet to achieve low DC resistance.

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

INDEX

6. Conclusions

References

The CMOS switch buck DC-DC converter fabricatedin the organic interposer with an embedded amorphousalloy powder-filler/epoxy composite sheet core inductor
made by lamination process was developed andevaluated.
Thedeveloped
amorphousalloy
powder-filler/epoxy composite sheet core inductor has afootprint of 3.5 mm square, inductance of 150 nH, Q
factor of 38 at around 20 MHz. Although the Q-factor
decrease due to the influence of the surface wiring
copper pattern just above the embedded power inductor,
it did not lead to large increase of the inductor power
loss. The most important issue for power loss is thelarge DC resistance of the power inductor. The large DC
resistance of the power inductor decrease power
conversion efficiency of CMOS switch buck DC-DC
converter.
In the future work, authors will investigate the novel
structure and soft magnetic-filler/non-magnetic resin
composite sheet design to achieve low DC resistance andhigh Q-factor power inductor.

1) H. Kobayashi, F. Sato, K. Hagita, R. Takeda, M. Sonehara,
T. Sato, N. Matsushita, K. Kobayashi, H. Shimizu, T. Fujii,
K. Ishida, and T. Sakurai: J. Magn. Soc. Jpn. (in Japanese),37, 4. pp.314-319 (2013).
2) X. Zhou, P. L. Wong, P. Xu, F. C. Lee, and A. Q. Huang:
IEEE Trans. Pwr. Elec., 15, 6, pp.1172-1182 (2000).
3) S. Ji: Master of Sci Dissertation, Virginia Tech., (2013).
4) Y. Su: Ph.D. Dissertation, Virginia Tech., (2014).
5) K. Hagita, Y. Yazaki, Y. Kondo, M. Sonehara, T. Sato, T.
Fujii, K. Kobayashi, S. Nakazawa, H. Shimizu, T. Watanabe,
Y. Seino, N. Matsushita, Y. Yanagihara, T. Someya, H.
Fuketa, M. Takamiya, and T. Sakurai: J. Magn. Soc. Jpn.,
39, 2, pp.71-79 (2015).
6) J. Wibben, and R. Harjani: IEEE JSSC, 43, 4, pp.844-854(2008).
7) N. Kurd, M. Chowdhury, E. Burton, T. P. Thomas, C. Mozak,
B. Boswell, P. Mosalikanti, M. Neidengard, A. Deval, A.
Khanna, N. Chowdhury, R. Rajwar, T. M. Wilson, and R.
Kumar: IEEE JSSC, 50, 1, pp.49-58 (2015).
8) W. J. Lambert, M. J. Hill, K. Radhakrishnan, L. Wojewoda,
and A. E. Augustine: IEEE Trans. CPMT, 6, 1, pp.3-11(2016).
9) H. Yamaguchi, R. Oka, T. Akiyama, T. Sato, M. Sonehara,
and K. Miyaji: The Annual Meeting Record IEEJ 2017 (inJapanese), 2-118, (2017).
10)T. Akiyama, R. Oka, H. Yamaguchi, T. Sato and M.
Sonehara: The Paper of Technical Meeting on Magnetics and(inJapanese),
LinearDrives,IEE
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MAG-17-070/LD-17-038, pp.47-52 (2017).

Acknowledgments
This research was partially
supported by Semiconductor Technology Academic
Research Center (STARC), and JST-Mirai Program“Realization of a low carbon society through gamechanging technologies”, Japan.
Theauthors
thankResearcher
Toshitaka
Minamisawa, Shinshu University, for assisting theexperiment of power supply circuit.

Received Jan. 20, 2019; Revised Mar. 06, 2019; Accepted Mar.
15, 2019

Journal of the Magnetics Society of Japan Vol.43, No.3, 2019

69

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. SatoK. Sekiguchi
M. Sekino
T. Shima
M. Sonehara
T. Tanaka
S. YamadaK. Yamamoto
H. Yuasa
N. Adachi
S. Isogami
Y. Kota
T. Narita
M. Takezawa
S. Yoshimura

K. Bessho
K. KamataT. MakiD. Oyama
T. Takura

M. DoiH. KatoE. Miyashita
J. Ozeki
M. Tsunoda

T. DoiK. KatoT. Morita
T. Saito
S. Yabukami

Y. Kanai
K. Miura
T. Sasayama
Y. Shiratsuchi

T. Hasegawa
T. KodaS. Muroga
S. Seino
T. Yamamoto

N. Inaba
S. Kokado
H. Nakayama
K. Tajima
K. Yamazaki

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