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Vol.40 No.4
JournalLetter

Journal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2016

Theoretical Investigation on Electronic and Magnetic Structures of FeRh
発行（公社）日本磁気学会 〠101‒0052 東京都千代田区神田小川町2丁目8番地
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H. Takahashi, M. Araidai, S. Okada and K. Shiraishi…77

Magnetic Recording

Model Calculation Considering Recording Time Window for Heat-Assisted Magnetic Recording
T. Kobayashi and Y. Fujiwara…81

Hard and Soft Magnetic Materials

Simultaneous Magnetic and Chemical Imaging of Nd-Fe-B Thin Films by Means of XMCD-PEEM Technique
R. Goto, S. Okamoto, T. Ohkochi, N. Kikuchi, O. Kitakami, and T. Nakamura

Structure and Magnetic Properties for FePt Thin Films Prepared on MgAl2O4 and MgO Substrates

H. Iwama, M. Doi and T. Shima

…87
…91

Eﬀect of Si/Fe Composition, Substrate Temperature, and Substrate Orientation on the
Structure and Magnetic Properties of Fe-Si Alloy Film
T. Aida, T. Kawai, M. Ohtake, M. Futamoto, F. Kirino, and N. Inaba…95

Thin Films, Fine Particles, Multilayers, Superlattices

Preparation and Characterization of Bi Substituted Gadolinium Iron Garnet
BixGd3-xFe5O12 Films with x = 1 to 2.5 by Enhanced Metal Organic Decomposition Method

D. A. Wahid, J. Sato, M. Hosoda, and H. Shimizu…107

Power Magnetics

Demagnetization Analysis of Ferrite Magnet Using Two-line Approximation Based on Reluctance Network Analysis
D. Momma, Y. Yoshida, and K. Tajima…115

Power Magnetics

Improvement of Induction Motor Analysis Accuracy in Reluctance Network Analysis
T. Umesaka, K. Tajima, and Y. Yoshida…120

Biomagnetism / Medical Applications

Heat Generation of Core − Shell Particles Composed of Biodegradable Polymer and Iron Oxide
C. Oka, K. Ushimaru, N. Horiishi, T. Tsuge, and Y. Kitamoto

広告◇東英工業株式会社◇計測エンジニアリング株式会社◇ネオアーク株式会社

…126

40

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

4

2016

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Journal of the Magnetics Society of Japan
Vol. 40, No. 4
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Letter
Theoretical Investigation on Electronic and Magnetic Structures of FeRh
… …………………………………………………… H. Takahashi, M. Araidai, S. Okada and K. Shiraishi

77

Magnetic Recording
Model Calculation Considering Recording Time Window for Heat-Assisted Magnetic Recording………………………………………………………………………………… T. Kobayashi and Y. Fujiwara

81

Hard and Soft Magnetic Materials
Simultaneous Magnetic and Chemical Imaging of Nd-Fe-B Thin Films by Means of XMCD-PEEM
Technique……………………… R. Goto, S. Okamoto, T. Ohkochi, N. Kikuchi, O. Kitakami, and T. Nakamura
Structure and Magnetic Properties for FePt Thin Films Prepared on MgAl2O4 and MgO Substrates… ……………………………………………………………………………… H. Iwama, M. Doi and T. Shima
Effect of Si/Fe Composition, Substrate Temperature, and Substrate Orientation on the
Structure and Magnetic Properties of Fe-Si Alloy Film………………………………… T. Aida, T. Kawai, M. Ohtake, M. Futamoto, F. Kirino, and N. Inaba

95

Thin Films, Fine Particles, Multilayers, Superlattices
Preparation and Characterization of Bi Substituted Gadolinium Iron Garnet
BixGd3-xFe5O12 Films with x = 1 to 2.5 by Enhanced Metal Organic Decomposition Method… ………………………………………………………… D. A. Wahid, J. Sato, M. Hosoda, and H. Shimizu

107

Power Magnetics
Demagnetization Analysis of Ferrite Magnet Using Two-line Approximation Based on Reluctance
Network Analysis………………………………………………… D. Momma, Y. Yoshida, and K. Tajima

115

Power Magnetics
Improvement of Induction Motor Analysis Accuracy in Reluctance Network Analysis… …………………………………………………………………… T. Umesaka, K. Tajima, and Y. Yoshida

120

Biomagnetism / Medical Applications
Heat Generation of Core － Shell Particles Composed of Biodegradable Polymer and Iron Oxide… ………………………………………… C. Oka, K. Ushimaru, N. Horiishi, T. Tsuge, and Y. Kitamoto

126

Board of Directors of The Magnetics Society of Japan
President:
Vice President:
Director, General Affairs:
Director, Treasurer:
Director, Planning:
Director, Editing:Director, Public Information:
Director, Foreign Affairs:
Auditor:H. Fukunaga
Y. Honkura, K. Takanashi
Y. Takano, Y. Miyamoto
S. Sugimoto, K. Aoshima
C. Mitsumata, Y. Saito
H. Saotome, K. Kobayashi
M. Igarashi, H. Awano
A. Kikitsu, Y. Takemura
F. Kirino, Y. Suzuki

8791

INDEX
J. Magn. Soc. Jpn., 40, 77-80 (2016)<Letter>

Theoretical Investigation on Electronic and Magnetic Structures of FeRh
Hidekazu Takahashi, Masaaki Araidai*, Susumu Okada and Kenji Shiraishi*
Graduate School of Pure and Applied Sciences,University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan*Institute of Materials and Systems for Sustainability, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

In order to clarify the mechanism behind antiferromagnetic (AFM)-ferromagnetic (FM) phase transition, weinvestigate the electronic and magnetic structures of FeRh by using first principles calculations with the GGA + U
method. By choosing the appropriate values of the on-site Coulomb interaction (U) of Fe3d and Rh4d electrons, we
succeed in explaining the reported AFM-FM phase transition experiments for the first time by obtaining the totalenergy difference between the AFM and FM states (ΔE). Other physical quantities such as the density of states (DOS)are also consistent with experimental reports.
Key words: magnetic refrigeration, inverse magnetocaloric material, antiferromagnetic-ferromagnetic phasetransition, GGA + U method, on-site Coulomb interaction
1. Introduction
Room-temperature magnetic refrigeration technology
using magnetocaloric materials (MCMs) has recently
gained attention because it is expected to eliminate
refrigerants that are greenhouse gases and improve thesystemefficiency
ofrefrigerators.1)
Variousperformance-enhancing
MCMs
such
as
La(FexSi1-x)13Hy,2) MnFe(P,Si),3) and so on have beenfound so far. Inverse magnetocaloric materials (IMCMs)
such as FeRh4) and Mn2-xCrxSb5) have also been the focus
of attention because of the appearance of the ‘giant’
inverse magnetocaloric effect (IMCE) under a low
magnetic field. In particular, FeRh shows a first-orderantiferromagnetic (AFM)-ferromagnetic (FM) phasetransition at Ttr ≈ 320 ~ 370 K without a magnetic fieldand exhibits a giant adiabatic temperature change ΔTad(= 13 K) under 1.95 T. Recent studies suggest that ΔTad
can be increased up to 18 K per 1 T.6) The appearance of
new MCMs and IMCMs that are superior to FeRh is now
expected. It is quite important to understand the why
ΔTad is large in FeRh. Moreover, it is essential to clarify
the microscopic mechanism behind the AFM-FM phasetransition in order to develop new magnetocaloric
materials.
Since FeRh was discovered by Fallot in 1938,7)
various experiments8)-19) on its physical parameters havebeen performed, such as the difference between theminimum total energy of the FM state and that of the
AFM state (ΔE) related to Ttr.10)
Various theoretical investigations have also been
carried out. For example, Kittel proposed the exchange
inversion model.20) There have also been various theories
proposed. However, all of these currently remain thesubject of debate. Several investigations into electronic
and magnetic structures using various band-structure
calculation methods have been reported to date.21)-28) Weshould point out here that recent advanced
first-principles calculations26)-28) are not able toreproduce important physical quantities such as ΔE. In
particular, if ΔE calculations are inconsistent withexperiments, its mechanism as an IMCM cannot beclarified. Generally, in alloys containing 3d and 4dtransition metals, regard for electronic correlation is
known to be important. However, this is not consideredin all of the reported calculations, including Refs.
(26)-(28). Therefore, we treat this electronic correlation
as the on-site Coulomb interaction (U) and examine theeffect of U on various physical quantities, particularly
ΔE. In this paper, we investigate the electronic andmagnetic structures of FeRh and have succeeded in
reproducing
theAFM-FM
phasetransition
quantitatively for the first time.
2. Calculation Method
In FeRh, which is a CsCl crystal with a simple cubic
structure, the magnetic structures in the AFM and FM
states are shown in Fig. 1. In order to treat FeRh in both
the AFM and FM states, the crystal is considered aface-centered cubic structure with lattice constant a’= 2a,where a is the lattice constant in the case of a simple
cubic structure. The atomic positions of two Fe atoms
are (0.0, 0.0, 0.0) and (0.5a’, 0.5 a’, 0.5 a’). The atomic
positions of two Rh atoms are (0.25 a’, 0.25 a’, 0.25 a’)and (0.75 a’, 0.75 a’, 0.75 a’).

(a)

(b)

Fig. 1 Magnetic structure of (a) AFM and (b) FM
states of FeRh. The blue and violet circles
indicate Fe and Rh atoms, respectively. ↑ and ↓indicate the directions of the magnetic
moments.
The Vienna ab initio simulation package (VASP) 29),30)
with the projector augmented wave (PAW) method31),32)
was utilized for performing the first principles

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

77

INDEX

calculations. We used the Perdew-Burke-Ernzerhof
exchange-correlation functional33) with the Hubbard U
method (GGA + U)34) including U and the exchange
parameter (J ) for each atomic orbital in the materials,
as our GGA calculation results such as ΔE (= 31.5
meV/atom) and the magnitude relation of Fe magnetic
moment values between the AFM and FM states (3.12μB,
3.18μB) were inconsistent with experimental results. In
the calculations, the Dudarev approach, which is only
dependent on Ueff = U – J35), was adopted. The
magnitude of U and J for the Fe3d electron (UFe, JFe) andfor the Rh4d electron (URh, JRh) were set to (2.0 eV, 1.0eV) and (1.95 eV, 1.0 eV), respectively so that theobtained physical quantities of the Fe and Rh crystals(lattice constant, bulk modulus and density of states(DOS)) using these U and J were consistent with thereported experiments. The Methfessel-Paxton method36)
was adopted by choosing the width of the smearing Δσ =0.05 eV. A plane-wave basis set with an energy cutoff(Ecut) of 830 eV and an 11×11×11 Monkhorst-Pack kpoints mesh37) was used.38)
3. Results and Discussion
A comparison of the physical quantities obtained in
the present analysis by using the above GGA + U
calculation method and those reported in experiments isgiven in Table I. The calculation results are detailed asfollows. First, the relationship between the totalenergies of the AFM and FM states and the lattice
constant is investigated by choosing appropriatemagnitudes of UFe and URh to estimate ΔE. The obtained
results are shown in Fig. 2. As shown, the AFM state isstable when the lattice constant is small. With
increasing the lattice constant, the total energy of the
AFM state has a minimum at lattice constant (aAFM) (=2.99 Å) and the total energy difference between the AFM
and FM states becomes smaller. When the lattice
constant is increased further, the total energy of the FM
state has a minimum at lattice constant (aFM) (= 3.01 Å).
Finally, the FM state becomes stable. The obtained
values for aAFM and aFM are consistent with theexperiment (aAFM = 2.981 Å and aFM = 2.999 Å).9) It isnoted that the obtained value for ΔE (= 2.71 meV/atom)

Fig. 2 Total energy versus lattice constant. On the basisof the minimum of the AFM state, the closed
squares and the diamonds indicate the totalenergies of the AFM and the FM states,
respectively.

78

is consistent with the experimental value ΔE (= 2.80
meV/atom).10)
The other physical quantities that were obtained aredetailed as follows. The magnetic moments of the Fe andRh atoms (mFe, mRh) in the AFM and FM states areinvestigated. The obtained magnetic moments arealmost identical to those in the experiments.11) The
obtained mFe of the AFM state (= 3.31μB) becomes equal
to mFe of the FM state (= 3.31μB), which is slightly
different from the tendency obtained by the experiment(mFe of the AFM state > mFe of the FM state). In all of thereported calculations21)-28), the relationship whereby mFeof the AFM state < mFe of the FM state is satisfied.
However, in the present work, the magnitude relation of
the obtained mFe values between the AFM and FM
states is approaching that of the experiment.
The obtained relationship between the obtained
values of mFe and mRh of the AFM and FM states and thelattice constant is shown in Fig. 3. With increasing thelattice constant, (i) the change in mFe is much larger
than that in mRh, (ii) the change in mFe in the AFM stateis larger than that in the FM state, and (iii) themagnitude relation of mFe values between the AFM and
FM states is reversed near the observed lattice constant.

Fig. 3 mFe and mRh of the AFM and FM states versus
lattice constant.
The critical magnetic field at 0 K (Hc(0)) which canprovide us with useful information to understand the
IMCE of FeRh can be obtained by22)
Hc (0) = ΔE / (MFM –MAFM),(1)
where MFM and MAFM (= 0 μB) are the magnetization per
atom of the FM and AFM states, respectively. The
obtained Hc(0) (= 21.6 T) is consistent with theexperiments (= 21.2 T ~ 29.7 T).12),13),14)
The DOS and the partial density of states (PDOS) near
the Fermi level (EF) of the Fe and Rh atoms of the FM
and AFM states were investigated and are shown in Figs.
4(a)-(d) and Figs. 5(a)-(d), respectively. The distributionof DOS near EF of the FM state shown in Figs. 4(a) and(b) and of the AFM state shown in Figs. 4(c) and (d) aresimilar to the reported photoemission spectra.15),16) In
particular, the main peak positions of DOS near EF arearound –5.0 eV to –4.0 eV and around –3.0 eV to –2.0 eV.
Moreover, the obtained ratio of DOS at EF of the FM
state and that of the AFM state (D(EF)FM / D(EF)AFM) (=4.72) is also consistent with the experiments.17),18) The
reason the obtained value of D(EF)FM / D(EF)AFM is large

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEXnonmagnetic state becomes unstable and the FM state isenergetically advantageous. As a result, ΔE becomes
smaller compared with the GGA calculation result. From
Fig. 5(a) and (c), we can see that the Fe3d band in the
majority spin state for the AFM and FM states is almost
filled, while that in the minority spin state for the AFM
and FM states is inadequately filled. Similar results (notshown) were obtained by the GGA calculation. When themagnitude of UFe is increased to 2.0 eV, Fe3d band at EF
in the minority spin state moves to the upper energyside, which results in a decrease of the occupied Fe3d
PDOS in the minority spin state. This leads to anincrease of mFe in the AFM and FM states andimprovement of the magnitude relation of mFe values
between the AFM and FM states. From the above results,
the effect of U plays a crucial role in discussing the
AFM-FM phase transition.

is examined by using PDOSs, as shown in Figs. 5(a)-(d),respectively. PDOS at EF (PD(EF)) of a Fe atom of the
FM state for the minority spin state is much higher thanthat of the AFM state for the minority spin state, while
PD(EF) of an Fe atom for both the AFM and FM states
for the majority spin state is low and PD(EF) of an Rh
atom of both the AFM and FM states for the majority
spin and minority spin state are also low. Therefore,
D(EF)FM / D(EF)AFM becomes large due to the largechange in the contribution of Fe3d electrons to D(EF) in
the AFM-FM phase transition.
The effect of U on ΔE and mFe in the AFM and FM
states is investigated using PDOS. Comparing Fig. 5(b)with Fig. 5(d), magnetic states of Rh for the AFM and
FM states are nonmagnetic and FM states, respectively.
When the magnitude of URh is increased to 1.95 eV, theFig. 4 DOS near EF of (a) the FM state, (b) the FM state
for both the majority spin and the minority spinstates, (c) the AFM state, and (d) the AFM statefor each of the majority spin and the minority spinstates.

Fig. 5 PDOS near EF of (a) an Fe atom of the FM state,(b) an Rh atom of the FM state, (c) an Fe atom of
the AFM state and (d) an Rh atom of the AFM
state.

Table I Comparison of physical quantities obtained in the present analysis using the GGA+ U method andthose reported in experiments.
AFM

FM

Å

Å

meV

2.99

3.01

2.71

2.987
2.981

2.997
2.999

aAFM

present
work
Ref. (8)Ref. (9)Ref. (10)Ref. (11)Ref. (12)Ref. (13)Ref. (14)Ref. (17)Ref. (18)
Ref. (19)

ΔE

aFM

2.80

AFM

mFe

mRh

mFe

3.31

0

3.30

0

μB

μB

FM

μB

mRh

Hc(0)

μB

T

3.31

1.04

21.6

3.17

0.97

D(EF)FM /D(EF)AFM

γFM/
γAFMi)

4.72
2.41

23.4
29.7
21.2

3.75
5.95

AFM

FM

BAFMii)

BFMiii)

195.7

210.6

142±14133±20

142

158

GPa

GPa

i) Ratio of Sommerfeld coefficient γ of the FM state and that of the AFM state (γFM/γAFM),ii) Bulk modulus of the AFM state (BAFM), iii) Bulk modulus of the FM state (BFM)

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

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INDEX

The band structures of the AFM and FM states areinvestigated and are shown in Figs. 6(a)-(c), respectively.
The two band structures are considerably different. In
particular, in the FM state, the number of branches
crossing the Fermi surface in the minority spin state ishigher than that in the majority spin state. In the AFM
state, a hole pocket appears at the center of the Г point.

Fig. 6 Obtained band structures of (a) the FM state forthe majority spin state, (b) the FM state for theminority spin state, and (c) the AFM state.
4. Conclusion
In summary, the electronic and magnetic structures of
FeRh are investigated by using first principles
calculations including appropriately chosen values of U
for the Fe3d and Rh4d electrons, and we succeed in
explaining the reported AFM-FM phase transition
experiments for the first time by obtaining ΔE consistent
with the experimental reports, also for the first time.
Moreover, other obtained physical quantities are also
consistent with the experimental reports. We willattempt to clarify the mechanism behind the AFM-FM
phase transition by using the knowledge obtained in thepresent analysis.
Acknowledgements The authors are indebted tocolleagues on our team for advising us on computer
system support.
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38) ΔE obtained with Ecut 830 eV and an 11×11×11 mesh iscompared with that obtained with Ecut 680 eV and an
11×11×11 mesh. The difference in ΔE for the two conditions
is less than 0.01 meV. ΔE obtained with Ecut 830 eV and an
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830 eV and a 15×15×15 mesh. The difference in ΔE for thetwo conditions is about 0.1 meV.
Received Mar. 04, 2016; Accepted Apr. 23, 2016

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J. Magn. Soc. Jpn., 40, 81-86 (2016)<Paper>                
                                                                       
               
                                   
    
                            
                       
        
                                                  




                                                                
                 
                                       
              
                
                                                 
       
                                                      
                               
             





              
 


 
                        
                                                                           
               


Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

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INDEX                                                          
                                                                                
       
                                
          





                     
                           



                                
        
                                                        
      
                         
          
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                
      
                                        
                   
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          
    
      
               

      
             

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                                           
       

                         Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

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INDEX        
               

                                                                                                



     








                                                 
                





   

                           
     





                                                            

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                                                                                                 
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     
                                                                                                                                                
                             

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Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

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INDEX                  
                                                            
                                                                                                          

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                                                                                  
      
                         
              
                                                                          







                        





                                                                                           
                                                                                                                   

84                                                         
         
                          
       
        
          

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX             
          
                                                                     
                                                                      
        
                                                   
            
               

                                             Journal of the Magnetics Society of Japan Vol.40, No.4, 201685

INDEX                    
                    
           


               
        
              
                             
                                                                                                                      
               




       
                 
    

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Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX
J. Magn. Soc. Jpn., 40, 87-90 (2016)<Paper>

Simultaneous magnetic and chemical imaging of Nd-Fe-B thin films
by means of XMCD-PEEM technique
R. Goto1,*, S. Okamoto1, 2, T. Ohkochi3, N. Kikuchi1, O. Kitakami1, and T. Nakamura2, 3

1 Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University,

980-8577, Japan

2-1-1 Katahira, Aoba-ku, Sendai

1-2-1 Sengen,Tsukuba, Ibaraki 305-0047, Japan
3 Japan Synchrotron Radiation Research Institute/SPring-8, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan

2 Elements Strategy Initiative Center for Magnetic Materials (ESICMM), National Institute for Materials Science,

The coercivity mechanism of Nd-Fe-B thin film samples with and without Nd deposition was investigated bysimultaneous chemical and magnetic imaging by means of X-ray magnetic circular dichroism-photoemission
electron microscopy. The two Nd-Fe-B thin film samples exhibited almost the same surface morphology andmagnetic domain patterns, but their coercive fields were quite different, being 0.98 T for the sample with Nd
deposition and 0.55 T for sample without Nd deposition. The chemical distribution of Nd revealed that Nd
aggregates with the average size of 130 nm exist, and the density in the Nd-deposited sample is much higher thanthat in the not deposited one. A comparison of the magnetic and chemical contrast images implied that the Nd
aggregates act as domain wall pinning sites, indicating that the large coercivity difference in the Nd-Fe-B thinfilms would be attributable to the different density of wall pinning sites.
Key words: Neodymium-Iron-Boron magnets, thin films, magnetic reversal, X-ray magnetic circular dichroism,
photoelectron emission microscopy
1. Introduction
Nd-Fe-B magnets are a key material for highefficiency electric generators and motors. For theseapplications, numerous attempts have been made toenhance the coercivity while maintaining highsaturation magnetization. Although heavy rare earth(RE) elements such as Dy or Tb are usually added toincrease the coercivity of Nd-Fe-B magnets, these RE
elements degrade their saturation magnetization due
to antiferromagnetic coupling between 3d and 4f
magnetic moments. Moreover, the availability andprice of the heavy RE elements are currently serious
resource problems. Recently, the coercivity μ0Hc of
Nd-Fe-B sintered magnets has been successfullyenhanced to about 2 T even without addition of heavy
RE elements by various methods such as refinement of
the constituent crystal grains of the Nd2Fe14B phase 1)
and/or grain boundary diffusion of RE elements torestore magnetic anisotropy near the grain boundaries
or to suppress intergranular exchange coupling 2), 3).
However, the μ0Hc obtained by these techniques
remains much smaller than the anisotropy field of
μ0Hk = 7.5 T 4).
The large discrepancy between the μ0Hc and μ0Hk
observed in a wide variety of permanent magnets,
which is known as Brown’s paradox 5), is the subject ofa long-standing debate in magnetics. To solve thisproblem, a detailed analysis of the magnetization
reversal process is indispensable. So far it is widely
accepted that nucleation of reversed domains
dominates the magnetization reversal in Nd-Fe-B

magnets, judging from the initial and minor
magnetization curve behaviors 6). On the other hand,the angular dependence and c-axis dispersion
dependence of μ0Hc 7), 8) strongly suggest that domain
wall depinning is the dominant process in Nd-Fe-B
magnets.
Recently, we proposed a new approach to examine
the magnetization reversal process 9). At a finite
temperature, magnetization reversal proceeds under
the influence of thermal activation, which enables themagnetization to overcome a finite energy barrier
separating local energy minima. The energy barrier isa function of a magnetic field H, and its function form
depends on the magnetization reversal process. For
example, the energy barrier is a quadratic function of
H for coherent rotation and/or nucleation 10) and alinear function of H for weak pinning of a domain wall11). The energy barrier function can be determined
experimentally by analysis of magnetic viscosity
measurements. We applied this type of analysis to two
kinds of (001) oriented Nd-Fe-B thin film samples withand without a Nd overlayer which is preferentiallydiffused along the Nd-Fe-B grain boundaries during
the deposition 9). In spite of the large difference in theircoercivities, both of their barriers were found to belinear functions of H, suggesting that weak domain
wall pinning is dominant in both samples. It should be
stressed here that the above two Nd-Fe-B thin film
samples have almost the same structures, such as
c-axis orientation, grain size, and so on. In order tounderstand the reason for the large coercivity

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

87

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difference mentioned above, simultaneous magnetic
and chemical distribution imaging were performed on
the two Nd-Fe-B film samples by means of X-ray
magnetic circular dichroism-photoemission electron
microscopy (XMCD-PEEM).
2. Experiments
Nd-Fe-B thin films examined in the present study
are grown on MgO (001) substrates with the layer
structure of MgO/Mo(30 nm)/Nd(0.25 nm)/Nd-Fe-B(50nm)/Nd(tNd = 0, 1 nm)/Mo(10 nm). For brevity, the
Nd-Fe-B film samples with and without a Nd
deposition are denoted as Nd-Fe-B/Nd and Nd-Fe-B,
respectively. The composition of the Nd-Fe-B layer isadjusted to Nd12.8Fe78.7B8.5 in at% by controlling the
sputtering rates of Nd, Fe, and B. The substrate is
kept at Ts = 500oC during deposition of both Nd-Fe-B
and Nd. The detailed sample fabrication conditions andmagnetic and structural characterization methods aredescribed elsewhere 9). Since both Nd-Fe-B/Nd andNd-Fe-B are prepared under the same condition, they
have the same crystal structure with good c-axis
orientation. The surface morphologies and magnetic
domain structures were observed by atomic force
microscopy (AFM) and magnetic force microscopy(MFM),
respectively.
X-ray magnetic
circulardichroism-photoemission
electronmicroscopy(XMCD-PEEM) was performed with Nd M4, 5 and Fe L2,
3 edges at the BL25SU beamline of SPring-8. Soft
X-rays were incident on the sample at 30 degree withrespect to the sample plane, enabling us to detect
perpendicular component of the magnetizations. Prior
to the XMCD-PEEM experiment, the Mo capping
layers were etched ex situ down to about 5 nm
considering the very short probing depth of PEEM. The
samples were observed at room temperature without
application of a magnetic field.
3. Results and Discussions
Figures 1(a) and 1(b) show the perpendicularmagnetization curves of Nd-Fe-B and Nd-Fe-B/Nd,
respectively. While they both exhibit high remanence
ratios, their coercive fields are quite different, being
μ0Hc = 0.55 T for Nd-Fe-B and 0.98 T for Nd-Fe-B/Nd.
According to the AFM images in Figs. 1(c) and 1(d),both samples have a partially-connected island
structure with the mean size of 100±50 nm. Figures
1(e) and 1(f) show the MFM images of thermallydemagnetized Nd-Fe-B and Nd-Fe-B/Nd, respectively.
Their domain structures are very similar with theaverage size of 200 nm. This is roughly two times
larger than the grain size in Figs.1 (c) and 1(d),indicating that each Nd-Fe-B grain is more or lessexchange-coupled to neighboring grains. In spite of thevery similar micro- and domain-structures, the
Nd-Fe-B with and without Nd deposition exhibit quite

88

Fig. 1 (a) and (b) perpendicular magnetization
curves, (c) and (d) AFM images, and (e)and (f) MFM images of thermal
demagnetization states. (a), (c), and (e)show Nd-Fe-B, and (b), (d), and (f) show
Nd-Fe-B/Nd.
different coercivities.
In order to explore the reason for the difference, we
performed simultaneous chemical and magnetic
imaging by means of XMCD-PEEM. Figure 2 shows the
X-ray absorption spectra (XAS) of the Nd-Fe-B
obtained at the Fe L2, 3 and Nd M4, 5 edges. In addition
to the clear Fe and Nd absorption edges, a small
shoulder is observed at the slightly higher energy side
near the Fe L3 edge owing to oxidation of Fe. This
oxidation may be caused by partial over-etching of the
Mo capping layer. We believe this small amount ofoxidation does not affect the following discussion.
Figures 3(a) and 3(b) show the chemical contrast
maps of Nd for Nd-Fe-B and Nd-Fe-B/Nd, respectively,

Fig. 2 XAS spectra for (a) Fe L2, 3 and (b) Nd M4, 5
edges of Nd-Fe-B and Nd-FeB/Nd.

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INDEX

Fig. 3(a) and (b) chemical contrast images of Nd,(c) and (d) magnetic contrast images, and(e) and (f) contours of magnetic contrast
shown in (c) and (d) overlapped with Ndchemical images. The red-colored contrast
of contours corresponds to the Nd content
under themselves. (a), (c), and (e) show
Nd-Fe-B, and (b), (e), and (f) show
Nd-Fe-B/Nd.

which were displayed as the spatial distributions of thephotoemission intensities at the Nd M5-edge (978.5 eV)
normalized to those at a pre-absorption-edge (972.0 eV).
Since Nd is one of the main constituents of the samples,
Nd is distributed over the whole area of the samples,
as indicated by the blue-colored areas in Figs. 3(a) and3(b). In addition to this uniform Nd distribution, many
tiny Nd-rich aggregates with the size of 130 nm can beclearly observed as indicated by green areas in thesame figures. Obviously, the density of the Nd
aggregates in Nd-Fe-B/Nd is much higher than that in
Nd-Fe-B. According to cross-sectional transmission
electron microscopy (TEM) observation of the Nd-Fe-B
film prepared under the same conditions, Ndaggregates exist laterally beside the Nd-Fe-B particles
on the Mo buffer layer 12). Figures 3(c) and 3(d) show
XMCD-PEEM images of Nd-Fe-B and Nd-Fe-B/Nd,
respectively, which were taken to be the XMCD
amplitude defined as the difference of XMCD intensity
between the Fe L3 edge (707.6 eV) and Fe L2 edge
(720.8 eV) to highlight the very weak XMCD contrast.
In spite of this data processing, the XMCD contrast is
still very weak, probably due to the presence of the Mo
capping layer. However, XMCD contrasts reflecting themagnetic domain states can be clearly noted, and thepatterns are similar to the MFM images in Figs. 1(e)and 1(f). The average domain width of Nd-Fe-B in fig.

3(c) is about 200 nm, being comparable with the value
from MFM images in Fig. 1(e). For Nd-Fe-B/Nd,
however, the domain width roughly reaches 400 nm,
which is about 2 times larger than that from MFM in
Fig. 1(f). This discrepancy is probably brought about by
weak magnetic contrast in the XMCD measurements.
The contours of these XMCD contrasts are overlaid on
the chemical mapping of Nd in Figs. 3(e) and 3(f). Notethat the magnetic contours which correspond to
domain walls partially run across Nd aggregates as
indicated by the red-colored portions on the contours.
It suggests that Nd-rich aggregates act as pinning sitesof magnetic domain walls. This tendency is more
obvious in the Nd-Fe-B/Nd sample shown in Fig. 3(f).
Each magnetic contour overlaps multiple Nd
aggregates, and in some cases lies along the aggregates.
The above observation implies that Nd aggregates act
as pinning sites of magnetic domain walls. When amagnetic domain wall is pinned at multiple defects, Ndaggregates in this study, the effective pinning force inthe two-dimensional system as in the present study
may be proportional to the density of defects 13) if theso-called weak pinning process is dominant 14). Thus
based on the present experimental results, we atpresent consider that the larger coercivity for
Nd-Fe-B/Nd is due to higher density of pinning sites, inthis case Nd aggregates. This conclusion isqualitatively consistent with our previous report, inwhich we found that domain wall pinning was
dominant for both Nd-Fe-B and the Nd-Fe-B/Ndsamples 9).
4. Conclusion
To discuss the origin of the different coercive fields of
Nd-Fe-B thin film samples with and without Nddeposition, simultaneous observations of magnetic andchemical contrast images were carried out by the
XMCD-PEEM technique. These two Nd-Fe-B films
exhibit almost the same surface morphologies andmagnetic domain patterns, but their coercive fields arequite different. From the Nd chemical contrast imaging,it was found that a large number of Nd aggregateswith the average size of 130 nm exist, and the densityof the Nd aggregates for the Nd deposited sample ismuch higher than that for not deposited one. Although
the XMCD contrasts of these thin film samples werevery weak, patterns similar to the MFM images wereobtained. A comparison of the chemical and magnetic
contrast images implied that the Nd aggregates act aswall pinning sites. This result indicates that the large
difference in coercive fields of the Nd-Fe-B thin films
with and without Nd deposition is attributable to thedifferent density of wall pinning sites.
Acknowledgements This work was partially supportedby the Elements Strategy Initiative Center for

Journal of the Magnetics Society of Japan Vol.40, No.4, 201689

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Magnetic Materials from MEXT, the Management
Expenses
Grantsfor
National
Universities
Corporations from MEXT, and JSPS KAKENHI Grant
Number 24360261. The XMCD measurements were
performed with the approval of the Japan Synchrotron
Radiation Research Institute (JASRI) (Proposal No.
2014B1272).
References
1) Y. Une and M. Sagawa: J. Japan Inst. Met. 76, 12 (2012).
2) H. Nakamura, K. Hirota, T. Ohashi and T. Minowa: J. Phys.
D. Appl. Phys. 44 ,064003 (2011).
3) H. Sepehri-Amin, T. Ohkubo and K. Hono: Acta Mater.
61 ,1982 (2013).
4) R. Grössinger, X.K. Sun, R. Eibler, K.H.J. Buschow and H.R.
Kirchmayr: J. Magn. Magn. Mater. 58, 55 (1986).
5) W.F. Brown, Rev. Mod. Phys. 17, 15 (1945).
6) R. Skomski and J. M. D. Coey: Permanent Magnetism, p.175(Institute of Physics Publishing, Bristol and Phyiladelphia,
1981).
7) F. Cebollada, M. Rossignol, D. Givord, V. Villas-Boas and J.
González: Phys. Rev. B 52, 13511 (1995).

908) Y. Matsuura, J. Hoshijima, R. Ishii, J. Magn. Magn. Mater.
336, 88 (2013).
9) R. Goto, S. Okamoto, N. Kikuchi and O. Kitakami: J. Appl.
Phys. 117, 17B514 (2015).
10) E.C. Stoner and E.P. Wohlfarth: Philos. Trans. R. Soc. A
Math. Phys. Eng. Sci. 240, 599 (1948).
11) P. Gaunt: J. Appl. Phys. 59, 4129 (1986).
12) R. Goto, S. Okamoto, N. Kikuchi and O. Kitakami: in
preparation for submission13) See, for example, the very simple and classical Neel modelon domain wall pinning. (e.g. A. H. Morrish: The PhysicalPrinciples of Magnetism (Wiley-IEEE Press, 2001)).
14) According to our previous analysis on magnetic viscosity
measurements, the functional form of the energy barriersuggests the weak pinning/depinning process in conventional
NdFeB magnets.
Present address*Santoku Corporation, 4-14-34 Fukaekitamachi,
Higashinada-ku, Kobe, Hyogo 658-0013, Japan
Received Sep. 25, 2015; Revised Jan. 29, 2016; Accepted Apr.
11, 2016

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J. Magn. Soc. Jpn., 40, 91-94 (2016)

Structure and magnetic properties for FePt thin films
prepared on MgAl 2 O 4 and MgO substrates<Paper>H. Iwama, M. Doi and T. Shima

Graduate School of Engineering, Tohoku Gakuin University, Tagajo, 985-8537, Japan

In order to investigate the effect of lattice mismatch between FePt thin films and single crystal substrates on thetetragonality and the magnetization process, FePt thin films have been fabricated on MgAl2O4 (MAO) (100) and MgO(100) single crystalline substrates at a substrate temperature of 700 °C. The Fe concentration in the FePt films wasvaried from 45.0 to 50.8 at. %. In addition to the fundamental (002) peak, (001) and (003) superlattice peaks haveclearly been observed in the X-ray diffraction patterns for all the samples, indicating the formation of L10 orderedstructure. The magnetization measurements show that all the samples are perpendicularly magnetized. Large
coercivity (Hc) of 57.8 kOe and 54.4 kOe was observed for the films with Fe49.3Pt50.7 and Fe48.3Pt51.7 (at. %) depositedon MgO and MAO substrates, respectively. It was confirmed that good hard magnetic properties can be obtained for
the Fe49Pt51 (at. %) thin film.
Key words: L10 ordered FePt, hard magnetic material, thin film, MgO substrate, MgAl2O4 substrate
1. Introduction
The magnetization process of assemblies offerromagnetic nanoparticles with a large uniaxial
magnetocrystalline anisotropy is of great scientific andtechnological interest, since they are expected to be
applied in forthcoming magnetic devices such as highdensity magnetic recording media and high performancebiasing nano-magnets. It is well known that themagnetization process and the coercivity depend
strongly on the characteristic size and the morphologyof the assemblies of ferromagnetic particles. Since FePt
alloy shows high uniaxial magnetocrystalline anisotropy(Ku = 7.0×107 erg/cm3) [1], moderate saturation
magnetization and high corrosion resistance, several
studies have recently been done on L10 ordered [CuAu(I) type] FePt thin films [2–14] and nanoparticles [15,16] using conventional thin film preparation methods
and chemical syntheses. It is also thought to overcome
the instability of magnetization vectors caused bythermal fluctuation even in the nano-meter scaled
particles. However, magnetization process of FePt thinfilms has not been fully elucidated. The latticemismatch plays a crucial role in the growth of epitaxial
thin films. Generally, MgO single crystalline substrate
has been commonly used to induce the L10 ordered (001)texture of FePt films. Recently, low temperature
fabrication of epitaxial FePt thin films below 400 ºC
have been reported for MgAl2O4 [17] single crystalline
substrates. However, systematic investigations of theeffects of lattice mismatch on the structure andmagnetic properties of FePt films have rarely beenreported. Therefore, it would be worthwhile to study the
structure and magnetic properties of FePt films
prepared on different substrates. For this purpose, two
single crystal substrates MgO (NaCl-type) and MgAl2O4(Spinel-type) were chosen. The values of unstrained
lattice mismatch between a-axis of L10 FePt ordered

alloy and these substrates are 8.4 % for MgO [18] and3.8 % for MgAl2O4 [19].
In this study, in order to investigate the effect oflattice mismatch between FePt thin films and single
crystal substrates on the tetragonality and themagnetization process, FePt thin films have been
fabricated on MgAl2O4 (MAO) (100) and MgO (100)single crystalline substrates, their structure andmagnetic properties have been investigated.
2. Experimental procedure
All the samples were prepared using an ultrahighvacuum magnetron sputtering system (ULVAC, QAM4)
with co-deposition of Fe and Pt directly onto polishedsingle crystalline MgO (100) or MAO (100) substrates.
The lattice parameters of L10 ordered FePt alloy, MAO(100) substrate and MgO (100) substrate are aFePt =0.385 nm, cFePt = 0.371 nm (L10-Fe50Pt50 (at. %)) [20],aMAO = 0.404 nm [19] and aMgO = 0.420 nm [18]. The
targets were commercial products with purities higher
than 99.99 at% for Fe and 99.9 at% for Pt. The basepressure was under 8.5×10–7 Pa. High-purity argon of
0.2 Pa was introduced during sputtering. The substrates
were heated to Ts = 700 ºC during deposition. The
nominal thickness of FePt layer was fixed at 10 nm. The
compositions of the films were determined by anelectron probe X-ray microanalysis (EPMA) and X =45.0, 47.2, 48.3, 48.8, 49.3, 49.8 50.3 and 50.8 for
FeXPt100–X (at. %) are confirmed. The structural analysis
was performed by X-ray diffraction (XRD) with Cu Kα
radiation. The lattice constant of c-axis was obtained by
the out-of-plane XRD measurement, while the value ofa-axis was obtained by the in-plane XRD measurement.
The film morphology was observed by atomic force
microscopy (AFM, in tapping mode). The magnetic
properties were measured by a superconducting
quantum interference device (SQUID) magnetometer inthe field up to 70 kOe at room temperature (R. T.).

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Fig. 1.

XRD patterns for FePt thin films preparedon MgO (100) substrate. Inset show thein-plane XRD patterns for FePt thin films.
The Fe content X for FeXPt100–X films are
45.0 (a), 47.2 (b), 48.3 (c), 48.8 (d), 49.3 (e),49.8 (f), 50.3 (g) and 50.8 (at. %) (h).
3. Results and discussion

XRD patterns for FeXPt100–X films with various Fe
content prepared on MgO (100) substrate are shown in
Fig. 1. The Fe content was varied as follows: X = 45.0 (a),47.2 (b), 48.3 (c), 48.8 (d), 49.3 (e), 49.8 (f), 50.3 (g) and
50.8 (at. %) (h). In addition to a fundamental (002) peak,(001) and (003) superlattice peaks of the L10-FePt phasewere clearly observed for all the samples. The peak fromthe other plane of the L10 structure was not observed.
Therefore, it is confirmed that the c-axis of FePt layers
was aligned perpendicular to the film plane for the FePt
films. With increasing X, the peak position of the (001)plane shifts to a higher angle, suggesting that thelattice parameter of c-axis decreases due to the changeof the tetragonality of L10 ordered FePt phase. From theintegrated intensities of fundamental and superlattice
peaks extracted from numerical fitting, the degree of
long-range chemical order parameter S was evaluated.
The detailed procedure for the evaluation of S was
described in a previous letter [21]. The S shows the
maximum of 0.80±0.05 for Fe49.3Pt50.7 (at. %) (e).
Magnetization curves for the FeXPt100–X films
prepared on MgO (100) substrate are shown in Fig. 2.
All the measurements were preformed at R.T.. The solidand broken lines denote the magnetic fields applied in
the perpendicular direction to the film plane andin-plane directions, respectively. The magnetic easy
axes are perpendicular to the film plane for all thesamples, since the [001] axis of the tetragonal L10
ordered structure was perpendicular to the film plane as92

Fig. 2.

Magnetization curves for FePt thin films
prepared on MgO (100) substrate. The Fecontent X for FeXPt100–X films are 45.0 (a),47.2 (b), 48.3 (c), 48.8 (d), 49.3 (e), 49.8 (f),50.3 (g) and 50.8 (at. %) (h).

demonstrated in Fig. 1. Coercivity (Hc) of 38.4 kOe wasobtained for the film with X = 45.0 (at. %) (a). The
maximum Hc of 57.8 kOe was obtained for the film with
X = 49.3 (at. %) (e). With further increasing of Fe
content, Hc decreases slowly, but still keeps a quite
large value of 48 kOe for the film with X = 49.8 (at. %)(f). However, Hc decreased to 27.7 kOe for the film with
X = 50.8 (at. %) (h). The in-plane magnetization does not
saturate even at a magnetic field of 70 kOe, which is the
maximum magnetic field of the SQUID magnetometer,
indicating that they possess high uniaxial magnetic
anisotropy. A remarkable step in the initial
magnetization curve was observed for all samples. A
steep increase of the magnetization at low magnetic
field was observed. The fractional magnetization at low
magnetic field corresponds to the magnetic domain wall
displacement; in other words, particles larger than 200
nm (single domain size [22]) with multiple domain
structure are magnetized at low magnetic field.
However, it is to be magnetized at applied magnetic
field more then 10 kOe, because they contain single
domain particles. Hence, the magnetization process
governed by the magnetic domain wall displacement in
the multiple domain particles and the rotation of themagnetization in the single domain particles.
XRD patterns for FeXPt100–X films prepared on MAO(100) substrate are shown in Fig. 3. The Fe content wasvaried as follows: X = 45.0 (a), 47.2 (b), 48.3 (c), 48.8 (d),49.3 (e), 49.8 (f), 50.3 (g) and 50.8 (at. %) (h). Bothfundamental and superlattice peaks of the L10-FePt
phase were clearly observed for all the samples. The
unlabeled peaks were due to the MAO (100) substrate.

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Fig. 3.

XRD patterns for FePt thin films preparedon MgAl2O4 (100) substrate. Inset show thein-plane XRD patterns for FePt thin films.
The Fe content X for FeXPt100–X films are
45.0 (a), 47.2 (b), 48.3 (c), 48.8 (d), 49.3 (e),49.8 (f), 50.3 (g) and 50.8 (at. %) (h).

The peak from the other plane of the L10 structure was
not observed. It is also confirmed that c-axis of FePt
layers was successfully aligned perpendicular to thefilm plane for the films deposited on the MAO (100)substrate. This indicates that the highly (001) oriented
L10 structure was achieved for the FePt films, even withdifferent Fe content of the FePt layer. From theintegrated intensities of fundamental and superlattice
peaks extracted from numerical fitting, the degree of
long-range chemical order parameter S was evaluated.
The S shows the maximum of 0.74±0.05 for Fe48.3Pt51.7(at. %) (c). The clear four fold symmetry was also
confirmed in both of FePt thin films on MgO (100) andMAO (100) substrates by 2θχ/φ scan of XRD. As a result,the epitaxial growth of FePt thin films on MgO (100)and MAO (100) substrates were confirmed. From theAFM observation, island growth with the island size of
about 150 nm was observed in both the FePt thin films
on the MgO (100) and the MAO (100) substrates.
Magnetization curves for FePt films with various
Fe content prepared on MAO (100) substrate are shownin Fig. 4. The magnetic field was applied in theperpendicular (solid line) and in-plane (broken line)
directions to the film. The easy magnetization axis isaligned perpendicular to the film plane for all thesamples. The [001] axis of the tetragonal L10 orderedstructure was perpendicular to the film plane asdemonstrated in Fig. 3. Hc of 44.1 kOe was obtained forthe film with X = 45.0 (at. %) (a). The maximum Hc of
54.4 kOe was obtained for the film with X = 48.3 (at. %)(c). With further increasing Fe content, Hc decreases
slowly, but still keeps a quite large value of 52.1 kOe forFig. 4.

Magnetization curves for FePt thin films
prepared on MgAl2O4 (100) substrate. The Fecontent X for FeXPt100–X films are 45.0 (a),47.2 (b), 48.3 (c), 48.8 (d), 49.3 (e), 49.8 (f),50.3 (g) and 50.8 (at. %) (h).

the film with X = 49.8 (at. %) (f). However, Hc wasdecreased to 44.8 kOe and 30.8 kOe for the films with X= 50.3 (g) and 50.8 (at. %) (h), respectively. Similar to
the result observed in the initial magnetization curvesof the films deposited on MgO (100) substrate, themagnetization process for the FePt films deposited on
MAO (100) substrate is thought to a mixture of amagnetic domain displacement and a rotation of themagnetism.
The a-axis, c-axis, c/a and Hc for FePt thin films
deposited on MgO (100) and MAO (100) substrates withdifferent Fe content are summarized in Fig. 5. Solidcircles and solid triangles denote the data for the FePt
film deposited on MgO (100) substrate, while open
marks are denote the data for the films deposited on
MAO (100) substrate. Maximum value of a-axis was
obtained for both substrates at X = 47.1 (at. %).
However, a-axis was decreased with further increased of
Fe content. While monotonical increase was obtained forc/a more than X = 48 (at. %) and maximum. Hc was
obtained at X = 49 (at. %) for both films. From theseresults, it is confirmed that lattice spacing of a-axis isstrongly dependent on the composition rather than theone of c-axis. The reason why the FePt films depositedon MAO (100) substrates show large Hc at wide
composition region is thought to arise from a smalllattice mismatch between the substrate and the FePt
film. The more detail investigation of morphologicalanalysis will be necessary for the exact discussion of Hc.
4. Summary
The structure and magnetic properties of FePt films

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University.
References
1)
2)
3)
4)
5)
6)
7)
8)
9)

Fig. 5.

Effect of Fe content X on the lattice constantof a and c-axis, the tetragonality represented
by c/a and coercivity Hc for FeXPt100–X thinfilms prepared on MgO (100) and MgAl2O4(100) single crystalline substrates.

10)
11)
12)
13)

prepared on MgO (100) and MAO (100) substrates havebeen investigated. The FePt layer was epitaxially grownon MgO (100) and MAO (100) substrates. Large Hc of
57.8 kOe and 54.4 kOe was obtained for the films with
Fe49.3Pt50.7 and Fe48.3Pt51.7 (at. %) deposited on MgO(100) and MAO (100) substrates, respectively. It was
confirmed that good hard magnetic properties can beobtained for the Fe49Pt51 (at. %) thin film. Although,similar behavior of Hc dependence on the composition
was observed in FePt thin films on MgO (100) and MAO(100) substrates, large Hc can be obtained at wide
composition range of FeXPt100–X thin films, even at low
Fe content between 45.0 and 48.3 (at. %).

14)

Acknowledgements
This work was partially
supported by the Research Institute for Engineeringand Technology at Tohoku Gakuin University. This
work is a cooperative program of the Cooperative
Research and Development Center for Advanced
Materials, Institute for Materials Research, Tohoku

21)

94

15)
16)
17)
18)
19)
20)

22)

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S. Okamoto, and T. Shimatsu: J. Appl. Phys., 115,
17B712 (2014).
K. Wasa, M. Kitabatake, and H. Adachi: THIN FILM
MATERIALS TECHNOLOGY Sputtering of Compound
Materials, (2004) Springer Verlag, Heidelbrg-New York.
W. F. Gale, and T. C. Totemeler: Smithells Metals
Reference Book (2004) ELSEVIER, Oxford.
K. H. J. Buschow: Handbook of Magnetic materials 19,(2011) ELSEVIER, Amsterdam.
T. Shima, T. Moriguchi, S. Mitani, and K. Takanashi: Appl.
Phys. Lett., 80, 288 (2002).
T. Shima, K. Takanashi, G. Q. Li, and S. Ishio: Mater.
Trans., 44, 8, 1508 (2003).

Received Oct. 19, 2015; Accepted Mar. 24, 2016

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INDEX
J. Magn. Soc. Jpn., 40, 95-106 (2016)<Paper>Effect of Si/Fe Composition, Substrate Temperature, and Substrate Orientationon the Structure and Magnetic Properties of Fe-Si Alloy Film
Takuya Aida1, Tetsuroh Kawai1, Mitsuru Ohtake1,2, Masaaki Futamoto1,
Fumiyoshi Kirino3, and Nobuyuki Inaba4

Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
2Faculty of Engineering, Kogakuin University, 2655-1 Nakano, Hachioji, Tokyo 192-0015, Japan1

3Graduate School of Fine Arts, Tokyo University of the Arts, 12-8 Ueno-Koen, Taito-ku, Tokyo 110-8714, Japan
4Faculty of Engineering, Yamagata University, 4-3-16 Jyonan, Yonezawa, Yamagata 992-8510, Japan

Fe100–xSix (x = 0, 2, 6, 10 at. %) alloy films are prepared on MgO single-crystal substrates of (001), (110), and(111) orientations at temperatures ranging between room temperature and 600 °C by using a radio-frequency
magnetron sputtering system. The film growth behavior, the crystallographic properties, and the magnetic
properties are systematically investigated. Fe-Si(001) single-crystal films with bcc structure are formed on MgO(001)substrates. The Fe-Si films deposited on MgO(110) substrates consist of epitaxial bcc(211) bi-crystals whoseorientations are rotated around the film normal by 180° each other. Fe-Si films grow epitaxially on MgO(111)substrates with two types of bcc(110) variant whose crystallographic orientations are similar to the
Nishiyama-Wasserman and the Kurdjumov-Sachs relationships. The orientation dispersion of Fe-Si film decreases
with decreasing the Si composition, with increasing the substrate temperature, and with decreasing the index of thesubstrate crystallographic plane. The Fe-Si films deposited on MgO(001) and (110) show in-plane magnetic
anisotropies reflecting the magnetocrystalline anisotropies of bulk Fe-Si alloy crystals. The Fe-Si films deposited on
MgO(111) show nearly isotropic in-plane magnetic anisotropies that possibly come from the multiple variant
structure. The coercivity decreases with increasing the Si composition and with decreasing the substratetemperature.
Keywords: Fe100–xSix (x = 0 – 10 at. %) alloy, epitaxial thin film, MgO single-crystal substrate, soft magnetic property
1.

Introduction

Fe-Si alloy is a typical soft magnetic material andhas been used in transformers, motors, etc. It is known
that the crystallographic structure and the magnetic
properties change depending on the Si composition andthe processing temperature1,2). In particular, Fe – 3
wt. % Si (≈ Fe – 6 at. % Si) alloys are widely used in therelated industries because of excellent soft magnetic
properties with high permeability, high saturation
magnetization (Ms), and low coercivity (Hc). In suchapplications, grain-oriented or non-grain-oriented
silicon steel sheets are generally employed, where theoverall magnetic properties are influenced by the
structure consisting of crystal grains. Therefore,
understanding the magnetic properties of Fe-Si crystals
with different orientations is very important to further
improve the overall soft magnetic properties.
There are some reports on the investigations
concerning the relationships of Si/Fe composition andcrystallographic orientation with respect to themagnetic properties by using bulk Fe-Si single-crystal
materials3,4). However, it is not easy to prepare bulk
crystal samples systematically varying the Sicomposition or the crystallographic orientation. In
contrast, it seems possible to prepare thin film crystal
samples,where
thecomposition
andthecrystallographic orientation can be respectively
controlled by the target composition and the orientationof single-crystal substrate. In the present study,

Fe100–xSix (at. %, x = 0 – 10) alloy thin films areprepared on MgO single-crystal substrates of (001),(110). and (111) orientations at temperatures ranging
from room temperature (RT) to 600 °C. The influences offilm composition, substrate temperature, and substrateorientation on the detailed structure and the magnetic
properties are systematically investigated.
2.

Experimental Procedure

Fe100–xSix (x = 0, 2, 6, 10 at. %) alloy films of 40 nm
thickness were deposited on polished MgO substrates of(001), (110), and (111) orientations by using aradio-frequency (RF) magnetron sputtering systemequipped with a reflection high-energy electron
diffraction (RHEED) facility. The base pressures werelower than 4 × 10–7 Pa. Before film formation,
substrates were heated at 600 °C for 1 hour to obtainclean surfaces. The distance between a target andsubstrates was fixed at 150 mm. The Ar gas pressure
was kept constant at 0.67 Pa. The RF powers for Fe,
Fe98Si2, Fe94Si6, and Fe90Si10 targets were respectively
fixed at 52, 59, 54, and 54 W, where the deposition rates
were 0.02 nm/s. The substrate temperature was varied
in a range from RT to 600 °C.
The surface structure was studied by RHEED. The
resulting film structure was investigated by 2θ/ω-scanout-of-plane and 2θχ/φ-scan in-plane X-ray diffractions(XRDs) with Cu-Kα radiation (λ = 0.15418 nm). The
surface morphology was observed by atomic force

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

95

INDEX004

microscopy (AFM). The magnetization curves were
measured by vibrating sample magnetometry.
3.

Results and Discussion

3.1

A2(001)[110] || MgO(001)[100].
Fe-Si(001) single-crystal films with A2 structure are
obtained on the substrates, where the Fe-Si(001) lattice
is rotated around the film normal by 45° with respect tothe MgO(001) lattice. In this configuration, the latticemismatch slightly increases from –4.0% to –4.4% withincreasing the x value from 0 to 10 at. %, where thelattice constants of bulk MgO (a = 0.4217 nm8)), Fe (a =0.2866 nm6)), and Fe89.5Si10.5 (a = 0.2853 nm9)) crystals
are used.
Figures 2(a-1)–(d-1) and 3(a-1)–(d-1) show theout-of-plane and in-plane XRD patterns measured for
Fe-Si films. Here, the scatteringvector of in-plane XRD_
is parallel to MgO[11 0]. Out-of-plane A 2(002) andin-plane A2(200) fundamental reflections are recognized,
whereas out-of-plane D03(002) and in-plane D03(200)96

Δθ50 = 0.98 °
WL

(c-1)
Fe94Si6(c-2)

Δθ50 = 1.23 °(d-1)
Fe90Si10

20

30

(d-2)
40

50
60
2θ (deg.)

70

80 –4

0

ω (deg.)4

Fig. 2 (a-1)–(d-1) Out-of-plane XRD patterns measuredfor (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(001) substrates at 200 °C. (a-2)–(d-2)
Rocking curves measured by fixing the diffraction angleof 2θ at the peak angles of A2(002) reflections in thepatterns of (a-1)–(d-1), respectively. The intensity isshown in (a-1)–(d-1) logarithmic or (a-2)–(d-2) linear
scale.
A2
D03

200
200

400

_

Effect of Si/Fe composition
Figures 1(a)–(d) show the RHEED patterns
observed for Fe100–xSix alloy films with x = 0 – 10 at. %deposited on MgO(001) substrates at 200 °C. Clear
diffraction patterns are observed for all the investigatedcompositions. The Fe-Si films grow epitaxially on thesubstrates. bcc-based disordered A2 phase and ordered
D03 phase exist in Fe-rich region of the bulk Fe-Si
binary alloy phase diagram5). Diffraction patterns for
A2(001) and D03(001) surfaces were thus calculated byusing the lattice constants of bulk Fe (a = 0.2866 nm6))
and Fe3Si (a = 0.5653 nm7)), respectively. Figures 1(e)and (f) are the schematic diagrams of the simulated
patterns of A2(001) and D03(001) surfaces, respectively.
The observed RHEED patterns are corresponding to thepattern simulated for A2(001) surface. The epitaxial
orientation relationship is determined as(b-2)

MgO(220)

Fig. 1 RHEED patterns observed for (a) Fe, (b) Fe98Si2,(c) Fe94Si6, and (d) Fe90Si10 films prepared on MgO(001)substrates at 200 °C. [(e), (f)] Schematic diagrams of
RHEED patterns of (e) A2(001) and (f) D03(001)single-crystal surfaces simulated by using the lattice
constants of bulk (e) Fe (a = 0.2866 nm6)) and (f) Fe3Si (a= 0.5653 nm7)), respectively. The incident electron beam
is parallel to (a)–(d) MgO[100], (e) A2[110], or (f)D03[110]. The filled and open circles in (f) respectively
correspond to the fundamental and the superlatticereflections.

(a-2)

Δθ50 = 0.84°(b-1)
Fe98Si2

(a-1)
Fe
(b-1)
Fe98Si2Δθχ50 = 0.95°(c-2)Δθχ50 = 1.19°(d-1)
Fe90Si10
30

(a-2)

(b-2)

(c-1)
Fe94Si620

Δθχ50 = 0.72°

Δθχ50 = 0.81°

Kβ_ 006_
115_
_ 115
224
004
224

(a-1)
Fe

Kβ

(f) D03Δθ50 = 0.73°

WL(d) Fe90Si10

Intensity (arb. unit)(b) Fe98Si2

Intensity (arb. unit)

112 002 112

A2(002)

_

002
002

A2(200)

_

A2
D 03

Kβ

(e) A2 004

MgO(002)(c) Fe94Si6(a) Fe

(d-2)
40

50
60
2θχ (deg.)

70

80 –4

0

ϕ (deg.)4

Fig. 3 (a-1)–(d-1) In-plane XRD patterns measured for(a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(001) substrates at 200 °C. The
scattering vector is parallel to MgO[110]. (a-2)–(d-2)
Rocking curves measured by fixing the diffraction angleof 2θχ at the peak angles of A2(200) reflections in thepatterns of (a-1)–(d-1), respectively. The intensity isshown in (a-1)–(d-1) logarithmic or (a-2)–(d-2) linear
scale.
superlattice reflections are absent. The XRD confirms
the crystal structure and the epitaxial orientation
relationship determined by RHEED.
Figure 4(a) shows the Si composition dependencesof lattice constants, a and c, of Fe-Si film. The lattice
constants are calculated by using the relation of (a, c) =(2 d A 2(200) , 2 d A 2(002) ). The Fe-Si lattices are slightly

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

0

1

Si composition (wt. %)
2
3
4

5

2000

a

1000

(a)

0.288

c

0.287
0.286

–2000
2000

1

4
6
Si composition (at. %)

8

10

5

1.0
0.8
0.6

Δθ50
Δθχ50
0

2

4
6
Si composition (at. %)(b) Fe98Si2

1000

Si composition (wt. %)2
3
4

Magnetization (emu/cm3)

1.2

0
(b)

2

θH = 45º (A2[110])

–1000

Bulk

0

θH = 0º (A2[100])(a) Fe00.285

Orientation dispersion
Δθ50, Δθχ50 (deg.)

Lattice constant c, a (nm)

INDEX

8

0
–1000
–2000
2000

(c) Fe94Si6

1000
0

10

–1000

Fig. 4Compositional dependences of (a) lattice
constants of a and c and (b) orientation dispersion
values of Δθ50 and Δθχ50 of Fe-Si film prepared on
MgO(001) substrate at 200 °C. The lattice constants ofbulk Fe-Si crystals are cited from Ref. 9.

–2000
2000

(d) Fe90Si10

1000
0
–1000
–2000
–1000

–500

0
500
Applied field (Oe)1000

Fig. 5 Magnetization curves measured for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(001) substrates at 200 °C.
Si composition (wt. %)0 1 2 3 4 5
(a)

30
20

Si composition (wt. %)0 1 2 3 4 5
1.8(b)Saturation magnetization
MS (kemu/cm3)

Coercivity HC (Oe)deformed along the c-axis due to accommodation oflattice misfits of about –4%. With increasing the Sicomposition, a and c values are decreasing. The
out-of-plane and in-plane orientation dispersions (Δθ50,
Δθχ50) are respectively estimated as the full widths at
half maximum of rocking curves measured by fixing thediffraction angles of 2θ and 2θχ at the peak angles ofout-of-plane A2(002) and in-plane A2(200) reflections, as
shown in Figs. 2(a-2)–(d-2) and 3(a-2)–(d-2). Figure 4(b)shows the Si composition dependences of Δθ50 and Δθχ50.
With increasing the Si composition, Δθ50 and Δθχ50
values are increasing. These results indicate that Si
composition in Fe-Si film affects delicately the crystal
unit cell size and the crystallographic quality.
Figure 5 shows the magnetization curves, where
the rotation angle of θH shows the applied field direction
with respect to A2[100] in A2(001). These films areeasily magnetized when the magnetic field is appliedalong A2[100], while the magnetization curves
measured along A2[110] saturate at higher fields.
Therefore, the magnetic properties of these films arereflecting the magnetocrystalline anisotropy of bulk
Fe-Si crystal with A2 structure.
It is recognized that the magnetization curvemeasured along A2[110] saturates at a lower magnetic
field and the coercivity decreases with increasing the Sicomposition from 0 to 10 at. %. The magnetic property
will be explained by considering magnetocrystalline

1.7
1.6

10
0

0 2 4 6 8 10
Si composition (at. %)

1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 6 Compositional dependences of (a) Hc and (b) Ms
values of Fe-Si films prepared on MgO(001) substrate at
200 °C.
anisotropy energy. When the magnetization rotates in
A2(001), the magnetic free energy is expressed as

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

97

INDEX

400 °C

(a-3)

600 °C

Fe90Si10

(d-1)

0

1

Si composition (wt. %)
2
3
4

2000

5

(a)

0.288

a

0.286

1.2

2

0
(b)

1

0

2

4
6
Si composition (at. %)

8

–2000
2000

10

5

1.0

Δθ50
Δθχ50
4
6
Si composition (at. %)θH = 45º (A2[110])(b) Fe98Si2

1000

Si composition (wt. %)
2
3
4

0.8
0.6

θH = 0º (A2[100])

0
–1000

Bulk

0.285
0

(a) Fe

1000

c

0.287

Orientation dispersion
Δθ50, Δθχ50 (deg.)

Lattice constant c, a (nm)(c-3)
Magnetization (emu/cm3)

(c-2)

(b-3)

8

0
–1000
–2000
2000

(c) Fe94Si6

1000
0

10

–1000

Fig. 4Compositional dependences of (a) lattice
constants of a and c and (b) orientation dispersion
values of Δθ50 and Δθχ50 of Fe-Si film prepared on
MgO(001) substrate at 200 °C. The lattice constants ofbulk Fe-Si crystals are cited from Ref. 9.

–2000
2000

(d) Fe90Si10

1000

deformed along the c-axis due to accommodation oflattice misfits of about –4%. With increasing the Sicomposition, a and c values are decreasing. The
out-of-plane and in-plane orientation dispersions (Δθ50,
Δθχ50) are respectively estimated as the full widths at
half maximum of rocking curves measured by fixing thediffraction angles of 2θ and 2θχ at the peak angles ofout-of-plane A2(002) and in-plane A2(200) reflections, as
shown in Figs. 2(a-2)–(d-2) and 3(a-2)–(d-2). Figure 4(b)shows the Si composition dependences of Δθ50 and Δθχ50.
With increasing the Si composition, Δθ50 and Δθχ50
values are increasing. These results indicate that Si
composition in Fe-Si film affects delicately the crystal
unit cell size and the crystallographic quality.
Figure 5 shows the magnetization curves, where
the rotation angle of θH shows the applied field direction
with respect to A2[100] in A2(001). These films areeasily magnetized when the magnetic field is appliedalong A2[100], while the magnetization curves
measured along A2[110] saturate at higher fields.
Therefore, the magnetic properties of these films arereflecting the magnetocrystalline anisotropy of bulk
Fe-Si crystal with A2 structure.
It is recognized that the magnetization curvemeasured along A2[110] saturates at a lower magnetic
field and the coercivity decreases with increasing the Sicomposition from 0 to 10 at. %. The magnetic property
will be explained by considering magnetocrystalline

(d-2)

0
–1000
–2000
–1000

–500

0
500
Applied field (Oe)1000

Fig. 5 Magnetization curves measured for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(001) substrates at 200 °C.

Coercivity HC (Oe)Fe94Si6

(c-1)

(b-2)

Si composition (wt. %)0 1 2 3 4 5
(a)

30
20

Saturation magnetization
MS (kemu/cm3)

Fe98Si2(b-1)

Si composition (wt. %)0 1 2 3 4 5
(b)

1.8
1.7
1.6

10
0

0 2 4 6 8 10
Si composition (at. %)

1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 6 Compositional dependences of (a) Hc and (b) Ms
values of Fe-Si films prepared on MgO(001) substrate at
200 °C.
anisotropy energy. When the magnetization rotates in

A2(001), the magnetic free energy is expressed as(d-3)

Fig. 7 RHEED patterns observed for (a) Fe, (b) Fe98Si2,(c) Fe94Si6, and (d) Fe90Si10 films prepared on MgO(001)substrates at (a-1)–(d-1) RT, (a-2)–(d-2) 400 °C, and(a-3)–(d-3) 600 °C. The incident electron beam isparallel to MgO[100].

1⋅K1⋅ (1 – cos4θM ) ,(1)8
where K1 is the magnetic anisotropy energy and θM is
the direction of magnetization. For Fe and Fe-Si alloy,
K1 is positive. Then, Ea becomes minimum at θM = 0°,
90° and becomes maximum at θM = 45°. Therefore,
A2[100] is the easy magnetization axis and A2[110] is
the hard magnetization axis. This calculation is well
explaining the measured magnetization curves. Figure 6
shows the Si composition dependences of coercivity (Hc)and saturation magnetization (Ms). Here, Ms value isregarded as the magnetization of Fe-Si film measured at
5 kOe. With increasing the Si composition from 0 to 10
at. %, the Ms value decreases linearly by about 11 %,and the Hc value decreases from 24 to 16 Oe reflecting
the soft magnetic property of Fe-Si alloy.

Fe
Lattice constant c (nm)

(a-2)

0.288

Lattice constant a (nm)

RT

Fe

(a-1)

0.289

Fe98Si2

Fe94Si6

Fe90Si10
(a)

0.286
0.284
0.282
(b)

0.287
0.285
0.283

0

200
400
Substrate temperature (°C)

600

Fig. 8 Substrate temperature dependences of (a) c and(b) a values of Fe, Fe98Si2, Fe94Si6, and Fe90Si10 films
prepared on MgO(001) substrates.

Ea =

98

Fe94Si6

Fe90Si10

Orientation dispersion
Δθ50 (deg.)

Effect of substrate temperature
Figure 7 shows the RHEED patterns observed for
Fe-Si films with different Si compositions grown on
MgO(001) substrates at RT, 400, and 600 °C. Clear
diffraction patterns corresponding to A2(001) surface
are recognized for all the compositions, whereas any
patterns corresponding to D03(001) surface are notrecognized.
Figure 8 shows the substrate temperaturedependences on lattice constants, a, and c, of Fe-Si films
with different Si compositions. With increasing thesubstrate temperature, c value increases, while a value
decreases for all the Si compositions.
Figure 9 shows the substrate temperaturedependences on out-of-plane and in-plane orientation
dispersions, Δθ 50 and Δθχ 50 . With increasing thesubstrate temperature, the Δθ 50 and Δθχ 50 values
decreases for all the Si compositions. The

Fe98Si2(a)Orientation dispersionΔθχ50 (deg.)

3.2

Fe

(b)

1.4
1.1
0.8
0.5
0.2
1.4
1.1
0.8
0.5
0.2

0

200
400
Substrate temperature (°C)

600

Fig. 9 Substrate temperature dependences of (a) Δθ50
and (b) Δθχ50 of Fe, Fe98Si2, Fe94Si6, and Fe90Si10 films
prepared on MgO(001) substrates.
crystallographic quality of Fe-Si film is improving
possibly through relaxation of film stress caused bylattice mismatch with the substrate.
Figure 10 shows the AFM images observed for Fe-Si
films with different Si compositions deposited at
different temperatures. The films deposited at RT, 200,
and 400 °C have flat surfaces with the arithmeticalmean roughness (Ra) values less than 2 nm. On the

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INDEX

400 ºC(a-3)

600 ºC
(a-4)

(c-1)

RT

200 ºC(c-2)

400 ºC(c-3)

600 ºC(c-4)

Fe

Fe94Si6RT
200 ºC(a-1) 50 nm (a-2)

Ra:

0.2 nm2Ra:(nm) 0.5 nm
0

0

(b-2)

Ra:

1.6 nm

18
0

(b-3)

Ra:

9.8 nm

85
0

(b-4)

Ra:

0.1 nm3Ra:(nm) 0.1 nm
0

(d-1)

2

2

Ra:

0.1 nm

0

(d-2)

0

Ra:

7.3 nm

56
0

(d-4)

(d-3)

Fe98Si2

Fe90Si10

(b-1)

4

Ra:

0.2 nm3Ra:(nm) 0.2 nm
0

2
0

Ra:

0.2 nm30Ra:

8.3 nm72
0Ra:

0.2 nm4Ra:(nm) 0.2 nm
0

2

3

Ra:

0.3 nm00Ra:

8.7 nm72
0Fig. 10 AFM images observed for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on MgO(001)substrates at (a-1)–(d-1) RT, (a-2)–(d-2) 200 °C, (a-3)–(d-3) 400 °C, and (a-4)–(d-4) 600 °C.
A2[100]2000
1000

200 ºCRT

400 ºCA2[110]600 ºC

(a-1)

(a-2)

(a-3)

(a-4)

(b-1)

(b-2)

(b-3)

(b-4)

(c-1)

(c-2)

(c-3)

(c-4)

(d-1)

(d-2)

(d-3)

(d-4)

Fe

0

–2000
2000
0
–1000
–2000
2000
1000

Fe94Si6

Magnetization (emu/cm3)

1000

Fe98Si2

–1000

0

–2000
2000
1000

Fe90Si10

–1000

0
–1000
–2000
–2.5

0

2.5 –2.50

2.5 –2.5
Applied field (kOe)0

2.5 –2.5

0

2.5

Fig. 11 Magnetization curves measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(001) substrates at (a-1)–(d-1) RT, (a-2)–(d-2) 200 °C, (a-3)–(d-3) 400 °C, and (a-4)–(d-4) 600 °C.
contrary, the Ra values of films deposited at 600 °C are
greater than 7 nm, where large islands with faceted
faces are formed as shown in Figs. 10(a-4)–(d-4). It isconsidered that migrations of deposited atoms areenhanced at a higher substrate temperature. The
variation of surface roughness as a function of substratetemperature is similar in these Fe-Si films.
Figure 11 shows the magnetization curves of Fe-Si
films at different substrate temperatures. The films

deposited at RT, 200, and 400 °C show the magnetic
properties reflecting the magnetocrystalline anisotropyof bulk Fe-Si crystal with A2 structure. With increasing
the substrate temperature up to 600 °C, the differencein the curves measured along A2[110] and A2[100]becomes small. The films are almost magneticallyisotropic in in-plane measurements. The reason ispossibly due to the shape anisotropy caused by thesurface undulation as shown in Figs. 10(a-4)–(d-4).

Journal of the Magnetics Society of Japan Vol.40, No.4, 201699

INDEX

311A 311B

Fig. 12 RHEED patterns observed for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(110) substrates at 200 °C. [(e), (f)] Schematic
diagrams of RHEED patterns of (e) A2(211) and (f)D03(211) single-crystal surfaces simulated by using thelattice constants of bulk (e) Fe and (f) Fe3Si, respectively.
The incident electron beam is parallel to (a)–(d)MgO[001]. The filled and open circles in (f) respectively
correspond to the fundamental and the superlatticereflections. The reflections indicated by the gray circlesin (e) show that the A2(211) plane has a reconstructedsurface of p(3×1).

(a-2)

80

90 –4

0
ω (deg.)4

Fig. 13(a-1)–(d-1) Out-of-plane XRD patterns
measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d)Fe90Si10 films prepared on MgO(110) substrates at
200 °C. (a-2)–(d-2) Rocking curves measured by fixing
the diffraction angle of 2θ at the peak angles of A2(211)reflections in the patterns of (a-1)–(d-1), respectively.
The intensity is shown in (a-1)–(d-1) logarithmic or(a-2)–(d-2) linear scale.
3.3

Effect of substrate orientation
Figures 12(a)–(d) show the RHEED patterns
observed for Fe-Si films with different Si compositions
deposited on MgO(110) substrates at 200 °C. Clear
diffraction patterns corresponding to A2(211) surface
are recognized, whereas diffractions corresponding toD03(211) surface are not observed, where the schematic
diagrams of RHEED patterns from A2(211) and D03(211) are respectively shown in Figs. 12(e) and (f). The
A2(211) RHEED pattern consists of two reflections, as
shown by the spots A and B in the diagram of Fig. 12(e).

100

20

A2(011)+A2(011)Δθχ50 = 1.60

30

(d-2)
40

50
60
2θ (deg.)

70

80 –4

0

ϕ (deg.)Fig. 14 (a-1)–(d-1) In-plane XRD patterns measuredfor (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(110) substrates at 200 °C. The
scattering vector is parallel to MgO[001]. (a-2)–(d-2)
Rocking curves measured by fixing the _diffraction angle_of 2θχ at the peak angles of A2(0 1 1) + A2(01 1 )reflections in the patterns of (a-1)–(d-1), respectively.
The intensity is shown in (a-1)–(d-1) logarithmic or(a-2)–(d-2) linear scale.

Lattice spacing (nm)

(d-2)
60
70
2θ (deg.)

(c-2)

(d-1)
Fe90Si1001(a)

Si composition (wt. %)
2
3
4

5

dA2(211)

0.117
0.116
0.204

(b)

dA2(011)+A2(011)

0.203
0.202

Orientation dispersion
Δθ50, Δθχ50 (deg.)Δθ50 = 1.13°50

Δθχ50 =1.57(c-1)
Fe94Si6

0.118

(c-2)

(d-1)
Fe90Si10(b-2)

Δθ50 = 1.02°

Δθ50 = 1.09°(c-1)
Fe94Si640

Δθ50 = 0.94°

Δθχ50 =1.52(b-1)
Fe98Si2

(b-2)

(b-1)
Fe98Si230

A2(211)

WL

(a-1)
Fe

Kβ

422

MgO(220)

Intensity (arb. unit)

211

(a-1)
Fe

Δθχ50 = 1.40
(a-2)

_

A2
D03

MgO(002)

533A
422AB

Intensity (arb. unit)

200B

0

2

0

1

_

(f) D03022_(d) Fe90Si10

211AB

011

_

200A

(b) Fe98Si2

A2
D03

222A

_

(e) A2_(c) Fe94Si6(a) Fe4
6
Si composition (at. %)8

Si composition (wt. %)
2
3
4

10

5

(c)

1.5
1.3
1.1
0.9

Δθ50
Δθχ50
0

2

4
6
Si composition (at. %)810Compositional
dependences of (a) dA2(211), (b)_dA2(0 1 1)+A2(01 1 ), and (c) Δθ50 and Δθχ50 of Fe-Si film
Fig. _15

prepared on MgO(110) substrate at 200 °C.

The epitaxial orientation relationship is determinedfrom the RHEED observation as follows,

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

4

INDEX(type A)_
A2(211)[011] || MgO(110)[001].

(type B)The Fe-Si(211) films consist of two types of variant
whose orientations are rotated around the film normal
by 180° each other. In this configuration, the lattice
misfit value differs depending on the in-plane direction
at the Fe-Si/MgO interface. The lattice misfit value
Fe98Si2

Fe94Si6

Fe90Si10

(a-1)

(b-1)

(c-1)

(d-1)

(a-2)

(b-2)

(c-2)

(b-2)

(a-3)

(b-3)

(c-3)

(d-3)

(a-4)

(b-4)

(c-4)

(d-4)

(a-5)

(b-5)

(c-5)

(d-5)

(a-6)

(b-6)

(c-6)

(d-6)

(a-7)

(b-7)

(c-7)

(d-7)

_

1000

Fe

0

1000

_

–2000
2000

θH = 31° (A2[113])

–1000

0

–2000
2000
1000

θH = 41°

–1000

0

1000

θH = 45°

–2000
2000

0
–1000

1000

_

–2000
2000

θH = 51° (A2[102])

Magnetization (emu/cm3)

–1000

0
–1000

1000

__

–2000
2000

0
–1000

1000

__

–2000
2000

0
–1000
–2000
–1

0

1 –1

0

1 –1
Applied field (kOe)

0

1 –1

θH = 90° (A2[111]) θH = 68° (A2[213])

2000

along MgO[001] is about –4%. Although there exists a
fairly large mismatch of around –17% along MgO[110],
epitaxial growth of Fe-Si crystal is taking place. This
type of epitaxial growth where misfit dislocations are
introduced at the interface is reported for the Cr/MgO
system10,11). The mismatch is considered to be reduced
through introduction of misfit dislocations in the filmaround the Fe-Si/MgO interface.

θH = 0° (A2[011])_

A2(211)[011] || MgO(110)[001],

0

1

Fig. 16 Magnetization curves measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(110) substrates at 200 °C.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

101

INDEX

_

_

(131)
_ _

(011)

(100)

__

_

__

_

(102)
(213)

(111)
__

(113)

_ _

(102)
(213)
_

_

_

_

_

(c)

(011)

(131)
(120)
(231)
__

_

(111)

(113)

(211)

_

_

_

(001) (113)

(120)
(231)

(001)

_

__

(131) (010)

(010)

_

(011)

(213)
(102)

_

_

__

(211)

(111)

_

__

(131)

(100)

(011)

(231)
(120)

__

(b) Type B
(231)
(120)

_

(113)

(111)

_

(111)
__

(111)
_

(010)
(011)
_

41°

(011)
_

(010)

(100)

(001)

(211)
(100)

(001)

__

[111]

[011]

30
60
90
120
150
Angle from A2[011], θM (deg.)

180

[011]
20
_

15
10
5
0

_

Anisotropic energy (kJ/m3)

Fig. 17 Pole-figure maps showing the configurationsof A2{100} planes of (a) type A, (b) type B, and (c) type
A + B, where A2(211) is centered.
_

102

(213)
(102)

_

Fig. 18 Anisotropy energy in A2(211) as a function ofmagnetization direction. K1 is set to 47 kJ/m3.
Si composition (wt. %)0 1 2 3 4 5
(a)

30
20

Si composition (wt. %)0 1 2 3 4 5
1.8(b)Saturation magnetization
Ms (kemu/cm3)

Coercivity Hc (Oe)1⋅K ⋅ (4 – 8cos2θM + 7cos4θM ) .
(2)
12 1
Figure 18 shows the anisotropy energy, Ea, as afunction of θM calculated by using the equation (2). It isshown that the easy magnetization axis lies along θM =41̊ or 139̊ _and_ the first hard magnetization axis lies
along A2[111] and_ the second hard magnetization axis
lies along A2[011]. When the measured magnetization
curves shown in Figs. 16 are compared with thecalculation, it is noted that the angle-direction of easymagnetization axis is in agreement with the calculation
for all the compositions. However, the experimental
data shown in Fig. 16 show that the _first hardmagnetization axis lies parallel_ _ to A2[01 1 ] and thesecond one lies parallel to A2[111]. There is a differencein the order of magnetization hardness, suggesting that
there exists an additional influence from the film
detailed structure. The XRD data shown in Fig. 15(c)indicate that the dispersion in Fe-Si film sample varies
depending on the crystallographic orientation whichsuggests the presence of anisotropic film distortion.
Such kind of distortion may have affected themagnetocrystalline anisotropy.
Figure 19 shows the Si composition dependences of
Hc and Ms values of Fe-Si film deposited on MgO(110)substrate. With increasing the Si composition from 0 to
10 at. %, the Ms value decreases linearly by about 13 %,and the Hc value decreases from 28 to 19 Oe reflecting
the soft magnetic property of Fe-Si alloy.
Figures 20(a)–(d) show the RHEED patterns

Ea =(a) Type A_

Figures 13(a-1)–(d-1) show the out-of-plane XRD
patterns of Fe-Si films deposited on MgO(110)substrates. A2(211) reflections are recognized, whereas
D 0 3 (211) reflections are not recognized. Figures
14(a-1)–(d-1) show the in-plane XRD patterns. Only thereflections from A2 crystals and the MgO substrates
are recognized for these films. Figure 15 shows the Sicomposition dependences of lattice spacing, dA2(211) and__dA2(0 1 1)+A2(01 1 ), and orientation dispersion of Δθ50 andΔθχ50 of these films. With increasing the Si composition,__
the dA2(211) and dA2(0 1 1)+A2(01 1 ) values are slightly
decreasing, whereas the Δθ50 and Δθχ50 values are
increasing similar to the case of Fe-Si/MgO(001)system.
Figures 16(a)–(d) show the magnetization curves of
Fe-Si films deposited on MgO(110) substrates. Here, θH
is the direction of magnetic field applied _to the sample
expressed in angle measured from A2[011] direction in
the A2(211) film plane. These films are easily
magnetized when the magnetic field is applied alongaround θH = 45°, while the magnetization curves
measured along θH = 0° and 90° saturate at higher
fields. Figure 17 shows the pole-figure maps indicating
the distribution of low-index_ planes including A2{100}planes. The angle of A2[011] and in-plane component of
A2(010) is 41°. The magnetic free energy is written in
the following equation when the magnetization rotatesin (211) plane,

1.7
1.6

10
0

0 2 4 6 8 10
Si composition (at. %)

1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 19 Compositional dependences on (a) Hc and (b)Ms values of Fe-Si films prepared on MgO(110)substrates at 200 °C.
observed for Fe-Si films deposited on MgO(111)su bstrates at 200 ° C. Clear RHEED patterns
corresponding to A 2(110) texture [Fig. 20(e)] areobserved. These RHEED patterns consist of two

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

Fig. 20 RHEED patterns observed for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films prepared on
MgO(111) substrates at 200 °C. [(e), (f)] Schematic
diagrams of RHEED patterns of (e) A2(110) and (f)D03(110) single-crystal surfaces simulated by using thelattice constants of bulk (e) Fe and (f) Fe3Si,
respectively. The_ incident electron beam is_ parallel to(a)–(d) MgO[1 1 0],_ (e) A2[001] and A2[ 1 10], or (f)D03[001] and D03[110]. The filled and open circles in (f)respectively correspond to the fundamental and thesuperlattice reflections.
Type D–17%–22%

MgO[112]__orientationofreflections, as shown by the spots C and D in the spot
map of Fig 20(e). The epitaxial orientation relationshipis determined by RHEED as follows,_A2(110)[001] || MgO(111)[110],(type C)__A2(110)[111] || MgO(111)[110].
(type D)
When the atomic arrangement of MgO(111) surface
which shows six-fold symmetry with respect to theperpendicular direction is considered, the A2(110)crystals of types C and D are interpreted to beconsisting of three and six variants whose orientations
are rotated around the film normal by 120° and 60°
eachother,
respectively.
The
crystallographic
orientation relationships of types C and D are similar to
the Nishiyama-Wasserman (NW)12,13) and the
Kurdjumov-Sachs (KS)14) relationships, respectively. In
these configurations, as shown_ in Fig. 21, large lattice_mismatches along MgO[11 2 ], –22%, and MgO[1 1 0],–17%, are involved at the A2(110)type C/MgO(111) andtheA2(110)type
interfaces.
The
D/MgO(111)crystallographic orientation relationships observed in
the present study is similar to those reported for the
Fe-based alloy films with bcc(110) orientation formedon MgO(111) substrates15,16).

MgO(222)

(c-2)

(d-1)
Fe90Si10

(d-2)

50

Δθ50 = 2.40°

6070
2θ (deg.)

80

90 –4

0

ω (deg.)4

Fig. 22(a-1)–(d-1) Out-of-plane XRD patterns
measured for (a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d)Fe90Si10 films prepared on MgO(111) substrates at
200 °C. (a-2)–(d-2) Rocking curves measured by fixing
the diffraction angle of 2θ at the peak angles of A2(110)reflections in the patterns of (a-1)–(d-1), respectively.
The intensity is shown in (a-1)–(d-1) logarithmic or(a-2)–(d-2) linear scale.

MgO

relationships

Δθ50 = 2.31°(c-1)
Fe94Si6

002

110

004

220

(a-1)
Fe

_

Epitaxial
Fig. 21Fe-Si(110) || MgO(111).

[110]

(b-2)

_

[111]

40

A2
D03

Fe-Si
_

–4%

30

Intensity (arb. unit)

Type C

Δθ50 = 2.10°(b-1)
Fe98Si2

(a-2)
Fe

(b-1)
Fe98Si2(b-2)
Fe98Si2(c-1)
Fe94Si6(c-2)
Fe94Si6(d-1)
Fe90Si10(d-2)
Fe90Si10

20

30
40
50
2θχ (deg.)

A2(002)442KS

Δθ50 = 1.73°(a-2)

MgO(022)

442KS

260NW
_

620NW 440

(a-1)
Fe

A2(110)(f) D03 660

A2(110)_(d) Fe90Si10

130NW

110
220

MgO(111)121KS

Intensity (arb. unit)

211KS

A2
D03

_

_

231KS

310NW 220(b) Fe98Si2

240NW

321KS

_

(e) A2 330(c) Fe94Si6(a) Fe

60

40

50
60
70
2θχ (deg.)

80

Fig. 23 (a)–(d) In-plane XRD patterns measured for(a) Fe, (b) Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films
prepared on MgO(111) substrates at 200 °C. _The
scattering vector is _parallel to (a-1)–(d-1) MgO[112] or(a-2)–(d-2) MgO[1 1 0]. The intensity is shown inlogarithmic scale.

Figures 22(a-1)–(d-1) and 23(a-1)–(d-2) show theout-of-plane and in-plane XRD patterns of Fe-Si films
deposited on MgO(111) substrates, respectively.
Reflections from A2 crystals are recognized, whereas
Reflections from D03 are not recognized.
Figure 24 shows the Si composition dependences oflattice constants, Δθ50, and Δθχ50. The lattice constants
are calculated by using the relation of

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

103

1

Si composition (wt. %)
2
3
4

2000

5

Bulk

0.286

c

1

4
6
Si composition (at. %)

8

10

5

4.0
3.0

Δθ50

2.0
1.0

Δθχ50
0

2

4
6
Si composition (at. %)810

Fig. 24 Compositional dependences of (a) a and c and(b) Δθ50 and Δθχ50 of Fe-Si films prepared on MgO(111)substrate at 200 °C.
_

a = (dA2(110)2 + dA2(110)2)1/2,(3)

c = 2dA2(002).

(4)

The Fe-Si lattices are slightly deformed along the c-axis
in accommodation of lattice misfits of about –4%. With
increasing the Si composition, the a value is decreasing,while the c value does not change much. The Δθ50 andΔθχ50 values are increasing with increasing the Sicomposition.
Figure 25 shows the magnetization curves. Here,θH is the direction of magnetic field applied to thesample expressed in angle measured from A2[001]direction in the A2(110) film plane. The magnetic freeenergy is written in the following equation when themagnetization rotates in (110) plane,
Ea =1⋅K ⋅ (7 – 4cos2θM – 3cos4θM ) .
32 1

(4)

Figure 26 shows the anisotropy energy, E a , as afunction of θM calculated by using the equation (4). It isshown that the easy magnetization axis lies along
A 2[001]. Indeed, it was reported that Fe(110)single-crystal films were easily magnetized when themagnetic field was applied along the Fe[001]direction17). However, the films prepared in the present
study show nearly isotropic in-plane magnetic
anisotropies. This is possibly because that the films
prepared in the present study are not single-crystals
but epitaxial thin films consisting of three and six
variants whose orientations are rotated around the film
normal by 120° and 60° each other (Fig. 21). In this104(b) Fe98Si2

1000

Si composition (wt. %)2
3
4

Magnetization (emu/cm3)

0
(b)

2

–2000
2000

0
–1000
–2000
2000

(c) Fe94Si6

1000
0
–1000
–2000
2000

(d) Fe90Si10

1000
0
–1000
–2000
–1000

–500

0
500
Applied field (Oe)1000

Fig. 25 Magnetization curves measured for (a) Fe, (b)Fe98Si2, (c) Fe94Si6, and (d) Fe90Si10 films grown on
MgO(111) substrates at 200 °C.

Anisotropic energy (kJ/m3)

Orientation dispersion
Δθ50, Δθχ50 (deg.)

–1000

a

0.284

5.0

0

[001]
20

_

0.285

0

θH = 90º (A2[110])

1000

0.287

0.283

θH = 0º (A2[001])(a) Fe

[110]

[001]

30
60
90
120
150
Angle from A2[001], θM (deg.)

180

_

0
0.288
(a)

_

Lattice constant c, a (nm)

INDEX

15
10
5
0

Fig. 26 Anisotropy energy in A2(110) as a function ofmagnetization direction. K1 is set to 47 kJ/m3.

case, the in-plane magnetic property of epitaxial thinfilm will be influenced by the distribution of variant

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

Si composition (wt. %)0 1 2 3 4 5
40
(a)
30
20
10
0

0 2 4 6 8 10
Si composition (at. %)Si composition (wt. %)0 1 2 3 4 5
1.8(b)Saturation magnetization
Ms (kemu/cm3)

Coercivity Hc (Oe)

INDEX

1.7
1.6
1.5
1.4

0 2 4 6 8 10
Si composition (at. %)Fig. 27 Compositional dependences on (a) Hc and (b)Ms values of Fe-Si films prepared on MgO(111)substrates at 200 °C.
crystals. The almost isotropic in-plane magnetic
anisotropies observed for the epitaxial thin films are
due to the complex variant structure.
Figure 27 shows the compositional dependences of
Hc and Ms values. With increasing the Si composition
from 0 to 10 at. %, the Ms value decreases linearly by
about 12 %, and the Hc value decreases from 34 to 19
Oe reflecting the soft magnetic property of Fe-Si alloy.
In the present study, Fe100–xSix (x = 0 – 10 at. %)epitaxial films are prepared on MgO single-crystal
substrates under similar experimental conditions. It isshown that single-crystal films of (001) orientation
grow on MgO(001), bi-crystalline epitaxial films with
(211) orientation grow on MgO(110), and epitaxial films
consisting of two types of (110) variant grow on
MgO(111) substrates. Although they are epitaxial thinfilm crystals, differences in quality and magnetic
properties are noted between these samples. For
example when the Δθ50 value, out-of-plane dispersion
which is a measure of crystallographic quality, iscompared between the samples prepared at 200 °C,
lower values are observed in the order of samples
prepared on MgO(001) < MgO(110) < MgO(111) for theinvestigated compositional range. The Δθ50 value isincreasing with increasing the Si composition for allcases. Similar tendency is also noted in the variation ofΔθχ50, in-plane dispersion, between these samples (Figs.
4(b), 15(c), 24(b)). The results indicate that the
crystallographic quality slightly degrades when
deposited on an MgO single crystal with higher index
plane.
Differences in coercivity are also noted between theepitaxial thin films. In-plane coercivity decreases withincreasing the Si content for the epitaxial Fe-Si films
grown on three kinds of crystallographic planes of MgO
single-crystal substrates (Figs. 6(a), 19(a), 27(a)). Whenthe coercivity is compared, lower values are observed in
the order of samples prepared on MgO(001) < MgO(110)< MgO(111) for the compositional range of x = 0 – 10
at. %. The low coercivities of Fe-Si(001) epitaxial films
are considered to be due to the high crystallographic
quality of single-crystal with low dispersion.
In the present study, Fe-Si single crystal films ofA2(100)orientation are obtained on MgO(100)substrate. The Fe-Si films prepared on MgO(110)substrate are epitaxial films of A2(211) orientation with
bi-crystalline structure, whereas the films formed on
MgO(111) are epitaxial films of A2(110) consisting ofvariants. By using these epitaxial thin films, it ispossible to investigate the magnetic properties such as
magnetostriction18), damping constant, etc. in relation
to the crystallographic orientation of Fe-Si magnetic
material. The thin film growth technique can beapplicable to the preparation of Fe-Si single-crystal
films, for example, with A2(110) by changing thesubstrate to GaAs(110) crystal19).

4.

Conclusion

Fe-Si alloy thin films are deposited on MgO
single-crystal substrates of (001), (110), and (111)orientations at temperatures ranging between RT and
600 °C by varying the Si composition, x, from 0 to 10
at. %. The effects of composition and substrateorientation on the structure and the magnetic
properties are investigated. Fe-Si(001) single-crystal
films are formed on MgO(001) substrates. Fe-Si films
epitaxially grown on MgO(110) substrates consist of
two (211) variants whose orientations are rotatedaround the film normal by 180° each other. Fe-Si(110)films grow epitaxially on MgO(111) substrates with
two-type
variants,
Nishiyama-Wasserman
andKurdjumov-Sachs relationships. The orientation
dispersion of Fe-Si film decreases with decreasing the
Si composition, with increasing the substratetemperature, and with decreasing the index of
substrate crystallographic plane. The magnetic
properties of films prepared on MgO(001) and (110) arereflecting the magnetocrystalline anisotropy of bulk
Fe-Si crystal with A2 structure. The Fe-Si epitaxial
films prepared on MgO(111) show almost isotropic
in-plane magnetic anisotropies which are related withthe multiple variant structure.
Acknowledgments A part of this work was supported
by JSPS KAKENHI Grant Numbers 25420294 and26820117 and Chuo University Grant for Special
Research.
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Received Nov. 30, 2015;

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

Accepted Mar. 30, 2016

INDEX
J. Magn. Soc. Jpn., 40, 107-114 (2016)<Paper>Preparation and Characterization of Bi substituted gadolinium iron garnet
BixGd3-xFe5O12 films with x = 1 to 2.5 by Enhanced Metal Organic
Decomposition method
D. A. Wahid, J. Sato, M. Hosoda, and H. Shimizu

Department of Electronic and Information Engineering, Tokyo University of Agriculture and Technology , 2-24-16 Naka-cho,

Koganei-shi, Tokyo 184-8588, Japan

Bismuth substituted gadolinium iron garnet thin films (Bi xGd3-xFe5O12) were prepared with x = 1, 2, and 2.5 onglass substrates by enhanced metal organic decomposition (EMOD) method. We mixed the solution containing Fe2O3,
Bi2O3 and Gd2O3 carboxylates so that we could obtain desired Bi content x. X-ray diffraction (XRD), opticaltransmittance / reflectivity, and Faraday rotation (FR) were measured for characterizations in order to examine theirdependence on annealing temperatures and different amount of Bismuth substitution ( x). When BixGd3-xFe5O12 thinfilms were directly prepared on glass substrates, Bi 2O3 phase were observed by XRD measurements and withincreasing Bi content x from 1 to 2, the FR increased from 1.2 to 5.8 deg./μm at the wavelength of 530 nm. FR of
Bi2.5Gd0.5Fe5O12 thin films prepared directly on glass substrates were smaller (0.35 deg./μm) than those with x = 2.
When Bi2.5Gd0.5Fe5O12 thin films were prepared with annealing temperature of 620oC with Gd3Fe5O12 buffer layer on
glass substrates, the films showed garnet crystal structure and FR, which is comparable with that of Bi2.5Gd0.5Fe5O12
thin films prepared on (111) (GdCa)3(GaMgZr)5O12 (SGGG) single crystal substrates. These results demonstratethat BixGd3-xFe5O12 thin films can be prepared on glass substrates with controlled Bi content and that FR as high asthat prepared on the SGGG substrate can be obtained by the EMOD method.
Key words: magnetic garnet, enhanced metal organic decomposition method, Faraday effect.

1. Introduction

metal organic decomposition (MOD) method is a

Bismuth substituted rare-earth iron garnets have aconsiderable interest owing to their large magneto optic
effect. Large FR with high transparency in the visible tonear infrared range1) are key properties which made themagnetic

garnetmaterials

suitableforvariousapplications for magneto-optical device elements such as
in magnetoplasmonic structure2), optical isolators3),
circulators4,5), and magnet photonic crystals (MPCs)
used

in

magneto-optic

spatiallight

modulators(MOSLM)6-9).
Bismuthsubstituted

gadolinium

iron

garnet(Bi:GdIG) is a ferrimagnetic material and shows
perpendicular magnetic anisotropy, which is one of themost desirable materials for magneto optical devices
owing to its high optical transmittance and extremely
high magneto optical activity in the visible and nearinfrared regions 10,11) , which enable this material to havehigh frequency application. FR can be controlled by Bi
substitution of Gd. Therefore, it is very important tocontrol the amount of Bi substitution in order to control
and increase the FR. There are several methods toprepare the bismuth substituted rare-earth iron garnet
thin films such as a laser ablation12), a liquid phase
epitaxy13), RF magnetron sputtering14), etc. Among them,promising one to prepare magnetic garnet film, because
it is a simple fabrication method which is composed ofspin coating of the MOD solution and annealing, andguarantees high uniformity in chemical composition andpurity combined with chemical stability. It was reported
that BixGd3-xFe5O12, BixY3-xFe5O12, and BixY3-x(FeGa)5O12
thin films were prepared on gadolinium gallium garnet(GGG) 12-17) and glass substrates 18). We have prepared
Bi:GdIG thin films on GGG substrates by annealing
with and without O2 gas and investigated the crystal
growthprocessandmagnetic

anisotropy19).

Thefabrication of magnetic garnet such as Bi2.5Y0.5Fe5O12
films was reported by using Nd2Bi1Fe4Ga1O12 buffer
layers on glass substrate which was fabricated by the
MOD method, and FR of 13.8 deg./μm at = 520 nm wasreported for the Bi2.5Y0.5Fe5O12 films18). It is important toobtain BixGd3-xFe5O12 thin films having higher Bi
content x and FR.

However, it is reported that

preparation of BixGd3-xFe5O12 with high Bi content on
glass substrates is difficult12-17). Therefore, fabrication of
BixGd3-xFe5O12 thin films with various Bi content x andcharacterization of FR are important. In order toinvestigate the effect of changing the Bi content x on FR
of BixGd3-xFe5O12 thin films by increasing the Bi content

x systematically, we fabricated the BixGd3-xFe5O12 thin

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

107

INDEXfilms on glass substrates by the EMOD method.

samples were pre-annealed at 550°C for 10 min. The

Furthermore, we used the Gd3Fe5O12 buffer layer inthickness by single spin coating step is typically 20 - 30

order to fabricate the BixGd3-xFe5O12 thin films withhigher x of 2.5 showing larger FR by the EMOD method.

nm. The conditions for spin coating, drying, andpre-annealing were fixed. We changed the mixing ratioof the SYM-BI05 and SYM-GD01 solutions in order to

2. Experiments
We fabricated BixGd3-xFe5O12 thin films with x = 1, 2change the Bi substitution x in BixGd3-xFe5O12 thin films,

and changed the final-annealing temperature. The

and 2.5 at different annealing temperatures of 620°C,

thickness of the samples slightly changes with the spin

650°C and 700°C on 15 mm x 15 mm glass substrate,coating speed, time and viscosity of the solutions. Spinand BixGd3-xFe5O12 thin film with x = 2.5 on 12 mm x 12

coating, drying and pre-annealing were repeated for 11

mm SGGG (111) single crystal substrate and Gd3Fe5O12

times to obtain an appropriate thickness. Spin coating,buffer layer / glass substrate by the EMOD method. The

drying and pre-annealing, were repeated 6 times for the

EMOD liquids used in this experiment are SYM-FE05

BixGd3-xFe5O12 films on the Gd3Fe5O12 buffer layer / glass

containing Fe2O3 carboxylates, SYM-BI05 containing

substrate.

Bi2O3 carboxylates, and SYM-GD01 containing Gd2O3

SGGG (111) single crystal substrate for a reference

carboxylates by Kojundo Chemical Laboratory so thatsamplewe could obtain BixGd3-xFe5O12 thin films with desired

BixGd3-xFe5O12 films prepared by pre-annealing process

Bi content x. Kojundo Chemical Laboratory Ltd provides

their own MOD solutions, as well as EMOD solutions

Also, we prepared a BixGd3-xFe5O12 film on

tocompare

the

FR.

The

amorphous

were then annealed at 620, 650 and 700 °C for 2 hours
for crystallization (final annealing). The pressure during

developed by Symetrix corporation of the United States

the annealing was atmospheric pressure. Bi:GdIG thin

and Kojundo Chemical Laboratory Ltd20). The MOD

films prepared in this study were characterized by x-ray

solution contains 2 – 3 kinds

diffraction

transmittance,

opticalreflectivity, and FR spectra. All the measurement wasdone at room temperature. We measured the XRD from

as

and

optical

Fe2O3

such

Gd2O3,(XRD),

carboxylates in acetic ester to prepare BixGd3-xFe5O12

carboxylates

Bi2O3,of metal oxides

thin films. In case of preparation of BixGd3-xFe5O12 thin

the central part of the samples. The diameter d of thefilms by the MOD method, Bi content x is fixed. On the

x-ray

other hand, the EMOD solution contains one metal oxide

measurement

beam

is

about

0.4

results ofmm.

Therefore,

the XRD show

theaveragecarboxylate in xylene and can be mixed with othercrystallinity of the samples over d = 0.4 mm. We

EMOD solutions containing other metal oxide. Therefore

estimated the thickness of the samples from the optical

it is possible to prepare the BixGd3-xFe5O12 thin films inreflectivity spectra, and discussed the relationshipany proportion of Bi content x, which enables greater

degree offreedomandmore precise control ofcomposition in order to prepare BixGd3-xFe5O12 thin films.
When we prepare the BixGd3-xFe5O12 thin films withdifferent Bi content x by the EMOD method, the EMOD
of

Fe2O3

carboxylate(productname

SYM-FE05),

Bi2O3

carboxylate(productnamesolutions

SYM-BI05), and Gd2O3 carboxylate (product name
SYM-GD05), are mixed and combined for different Bi
content x, which is advantage compared with the MOD

method. The selected components were mixed in the

between XRD and FR spectra.

3. Results and Discussion
Figure 1 shows the optical reflectivity spectra(wavelength  = 250 - 2600 nm) of the BixGd3-xFe5O12
samples annealed at 620, 650 and 700 °C, with the Bi

content x = 0, 1, 2 and 2.5 on glass substrates. The
incident direction of the light was normal to the sample.
In order to estimate the thickness of the BixGd3-xFe5O12
films, we fitted the measured optical reflectivity spectra
to reproduce the experimental results by the calculated
We calculated the reflectivity

desired stoichiometric ratio of BixGd3-xFe5O12 withreflectivity spectra.

solution was then filtered by advantec filter paper. The

BixGd3-xFe5O12 films by interfaces between air / film (af)different value of x = 1, 2 and 2.5 and stirred well. The
solution was spin-coated in 2 steps process of 500 rpm
for 10 s and 2000 rpm for 20 s, followed by drying on a

hot plate at 120°C for 10 min and the solvent areevaporated. In order to decompose the organic materials

spectra by considering the multiple reflection inside theand film / glass substrate (fs). We assumed that the film
thickness is uniform and the glass substrate is
non-absorbing and incoherent material. The reflectivity

R is calculated by the following formula (1) 21,22).

and obtain the amorphous metal oxide films, the108

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

R(1)

where Rafs, is the reflectivity within the interface
between air (a), film (f), and the interface between film(f) and substrate (s), Rsfa is the reflectivity within theinterface between substrate (s), film (f), and theinterface between film (f) and air (a), and Tafs is thetransmission within the interface between air (a), film (f),and the interface between film (f) and substrate (s). Rafs,

Rsfa and Tafs include the effect of multiple reflections

inside the film and can be expressed by the following
formulas (2), (3) and (4). They are related to the film
thickness d, wavelength , and refractive index n - ik of
the film. Since the refractive index has wavelength
dependence, we divided the optical reflectivity spectra totwo regions ( < 1000 nm and  > 1000 nm), and changed
the refractive index and thickness to reproduce theexperimentally obtained optical transmission spectra23).
In the final stage of the fitting, the films thickness d is
obtained.

(2)

(3)

(4)

The simulated reflectivity spectra showed by thedotted lines in figure 1. The thicknesses were estimatedto 170 - 210 nm for the samples with x = 1, 200 - 260 nm

for the samples with x = 2, and 330 - 360 nm for the

samples with x = 2.5. The viscosity of the solution wasincreased with increasing the Bi content x.

Therefore

the film thickness increased with increasing the Bi
content x.

Figure 2 shows the XRD spectra of the fabricatedsamples on glass substrates.

The XRD spectra ofsamples shows some peaks associated with (420) planeof BixGd3-xFe5O12, (104) plane of Fe2O3, (112) plane of
Gd2O3, (008) plane of -Bi2O3, (200) plane of BiO3, (222)plane of -Fe2O3, and (130) plane of -Fe2O3 phases.

Fig. 1 Optical reflectivity spectra (solid lines) of the
BixGd3-xFe5O12 samples annealed at 620, 650 and

700 °C, with bismuth content x = 0, 1, 2 and 2.5 onglass substrates. The fitted spectra are shown bydashed lines.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

109

INDEXbaa)

BixGd3-xFe5O12 420

e)

BiO3

b)

Fe2O3 104f)β-Fe2O3 222

c)

Gd2O3 112g)

ε-Fe2O3 130d)ε-Bi2O3 008

u)Unknown phase(Bi:GdIG / glass sub)x = 1, 620°C(Bi:GdIG / glass sub)x = 1,

650°C(Bi:GdIG / glass sub)x = 1,

700°C(Bi:GdIG / glass sub)x = 2,

620°C(Bi:GdIG / glass sub)x = 2,

650°C(Bi:GdIG / glass sub)x = 2,

700°C(Bi:GdIG / glass sub)x = 2.5 , 620°C(Bi:GdIG / glass sub)x = 2.5, 650°C(Bi:GdIG / glass sub)x = 2.5, 700°C

200

ab
b

a

u

c
a
u
c
Intensity (count)

a

b

d
u

a

u

d
u

d

g

e
a

b

a

u

b

e
b

d
u

u

a

a

b

g

f
(GdIG buffer layer / glass sub)

u
a

x= 0,

650°C

f
(Bi:GdIG / GdIG buffer layer/glass sub),x = 2.5, 620°C

10

20

30

40

50

60

70

2θ (deg)
Fig. 2 X-ray diffraction spectra of the BixGd3-xFe5O12 thin films on glass substrates at annealing temperature of620, 650 and 700 °C with Bismuth doped x = 0, 1, 2 and 2.5 on glass substrates and Bi2.5:GdIG on GdIG buffer
layer/glass substrate.

110

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

20

30

40

50

BiGdIG 888
SGGG 888

SGGG 666

SGGG 222

Intensity (count)
10

BiGdIG 444
SGGG 444

INDEX

60
70
2θ (deg)

80

90

100

110

120

Fig. 3 X-ray diffraction spectra of the Bi2.5Gd0.5Fe5O12 thin film on SGGG (111) single crystal substrate at theannealing temperature of 620°C.

Please note that the vertical axis is in logarithmic scale.
When the Bi2O3, Gd2O3 and Fe2O3 carboxylates are
mixed with a ratio of 1 : 2 : 5, and the annealing
temperature of 620 – 700 oC directly prepared on theglass substrates, the diffraction signal from Fe2O3 islarger than that from BixGd3-xFe5O12. When the Bi2O3,
Gd2O3 and Fe2O3 carboxylates are mixed with a ratio of
2 : 1 : 5 and the annealing temperature of 620 – 650 oC
directly prepared on the glass substrates, the diffraction
signal from Gd2O3 is larger than that from BixGd3xFe5O12. When the annealing temperature is 700 oC, thediffraction signal from Bi2O3 is increased. When the
Bi2O3, Gd2O3 and Fe2O3 carboxylates are mixed with aratio of 2.5 : 0.5 : 5 and the annealing temperature of620 – 700 oC directly prepared on glass substrates, thediffraction signals from Bi2O3 and -Bi2O3 are much
more dominant than that from BixGd3-xFe5O12. The
diffraction peak associated with BixGd3-xFe5O12 were theweakest with x = 2.5 among all the samples without the

Gd3Fe5O12 buffer layer. With increasing the final
annealing temperature, the diffraction peak associatedwith ε-Bi2O3 increased. From the XRD spectra of thesamples, it is difficult to fabricate Bi:GdIG thin films

with high Bi content x = 2.5 directly on glass substrate.
In order to solve this problem, we fabricated agadolinium

iron

garnet(GdIG)

thin

film

with

composition of (Gd2O3:Fe2O3 = 3:5) as a buffer layer for
preparation of BixGd3-xFe5O12 thin films with higher Bi
content x of 2.5, with the thickness of 150 nm on theFig. 4 Optical transmittance spectra of the Bi:GdIG
samples annealed at 620, 650 and 700 °C, with thebismuth content of a) x = 2.5 on glass, GdIG buffer
layer / glass and SGGG (111) single crystal
substrates, b) x = 1 and 2 on glass substrates.

glass substrate at final annealing temperature of 650°C
by the EMOD method.

When the Gd2O3 and Fe2O3

carboxylates are mixed with a ratio of 3 : 5, thediffraction signals from Gd3Fe5O12, and -Fe2O3 aredominant.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

111

INDEX

Fig. 6 Faraday rotation spectra of the Bi2.5Gd0.5Fe5O12
samples annealed at 620°C with the bismuth content

x = 2.5 on gadolinium iron garnet buffer layer / glass
sub and SGGG (111) single crystal substrates.
phases such as ε-Bi2O3, BiO3 and Gd2O3 are suppressed.
The diffraction peak associated with β-Fe2O3 at theright side of the Bi:GdIG diffraction peak is associatedwith the Gd3Fe5O12 buffer layer. From figure 2, it was
confirmed that the Bi2.5Gd0.5-Fe5O12 thin film having
garnet crystal structure was prepared with the buffer
layer on glass substrate by the EMOD method.
Figure 3 shows the XRD spectra of Bi2.5Gd0.5Fe5O12
prepared by the EMOD method on (111) SGGG single
crystal substrate.
Fig. 5 Faraday rotation spectra of the BixGd3-xFe5O12
samples with different annealing temperatures and

444 and 888 diffraction peaks areclearly observed and other peaks associated withpolycrystalline or impurity phases were not observed.

bismuth content(a) x = 1, (b) x = 2 and (c) x = 2.5.

The lattice constant a was calculated to 1.2587 nm. It

Then we tried to fabricate a Bi2.5Gd0.5Fe5O12 thin film

samples prepared by liquid phase epitaxy (LPE) wason the GdIG buffer layer / glass substrate. The final
annealing temperature for Bi2.5Gd0.5Fe5O12 thin film
was set at 620°C instead of the annealing temperatureof 650°C shown in figure 2. This is because when the
final annealing temperature of the Bi2.5Gd0.5Fe5O12 film
is the same or higher than the final annealing
temperature for the GdIG buffer layer/glass sub., thepart of crystal structure of the GdIG buffer layer can be
destroyed25).

Therefore, we set the final annealing

temperature at 620°C for the Bi2.5Gd0.5Fe5O12 film on
the GdIG buffer layer/glass sub.
When the Bi2O3, Gd2O3 and Fe2O3 carboxylates are
mixed with a ratio of 2.5 : 0.5 : 5 and the annealing
temperature of 620 oC with the Gd3Fe5O12 buffer layer
on glass substrate, the diffraction signal from BixGd3xFe5O12 is the most dominant and the formation of other112

was reported that the lattice constant of Bi 2.5Gd0.5Fe5O121.259nm24),

andcomparable

to

that

of

our

Bi2.5Gd0.5Fe5O12 thins films on (111) SGGG substrate.
By comparing the lattice constant of two materials andthe results of figure 3, we estimated the composition of
our single crystal film to Bi2.5Gd0.5Fe5O12 by the EMOD
method.

Also the diffraction peaks associated with

Bi2O3, Gd2O3, Fe2O3, GdIG

andBiGdIG ofthepolycrystalline samples on the glass substrates wereconfirmed by comparing the lattice spacing d measured
by the XRD to the powder diffraction files
international

centerfor

diffraction

data

of

(ICDD).

Therefore, we estimated the fabricated crystal structureby the EMOD method to the garnet structure.
Figure 4 shows the optical transmittance spectra of
the BixGd3-xFe5O12 thin films on the glass substrates
with / without Gd3Fe5O12 buffer layer and on (111)

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEXSGGG single crystal substrate. The Bi2.5Gd0.5Fe5O12 on
the Gd3Fe5O12 buffer / glass sub has high transparency
in visible and near infrared region, higher than theBi2.5Gd0.5Fe5O12 film on (111) SGGG substrate.
Figure 5 shows the FR spectra of the fabricated
BixGd3-xFe5O12 thin films crystallized at 620, 650, and

700 °C with x = 1, 2 and 2.5 on glass substrates. The
magnetic field of 1 T was applied perpendicular to thesamples in order to fully magnetize the samples.
The samples with the annealing temperature of
650°C show larger FR (negative) than the other samples

with x = 1, 2, and 2.5 annealed at 620 and 700 °C.
Therefore the annealing temperature of 650°C is the
optimum condition for crystallization of the BiGdIG thinfilms on the glass substrate by the EMOD method. The

4. Conclusion

We have prepared BixGd3-xFe5O12 thin films on glass
substrates, with and without Gd3Fe5O12 buffer layer
prepared on glass substrates and (111) SGGG single
crystalsubstrate

by

the

EMOD

method.

Wecharacterized the XRD, FR and optical transmittancespectra of the samples.

The FR shows that theannealing temperature of 650 °C is the optimum
condition for crystallization of BixGd3-xFe5O12 on theglass

substrate.

From

the

XRD

spectra,theBi2.5Gd0.5Fe5O12 samples on the Gd3Fe5O12 buffer layershows that the Bi:GdIG thin films were successfully
fabricated on the glass substrates without forming Bi2O3
and Gd2O3 phases, which are observed in samples
without Gd3Fe5O12 buffer layer.

Furthermore, larger

FR of Bi:GdIG increased with increasing x to 2, andFaraday rotation (27.9 deg./μm at  = 533 nm) was

Figure 6 shows the FR spectra of the Bi2.5Gd0.5Fe5O12than that without Gd3Fe5O12 buffer layer, and thedecreased in the sample with high Bi content of x = 2.5.

thin films on the GdIG buffer layer / glass substrate and
SGGG (111) single crystal substrate. Bi2.5Gd0.5Fe5O12
thin film on the GdIG buffer layer / glass substrate
showed 27.5 deg./μm at the wavelength of 533 nm, whichis 8 times larger than that without the GdIG buffer layer.
This is because the sample with the GdIG buffer layer
showedthelargestdiffraction

signalfrom

the

BixGd3-xFe5O12 and garnet structure, and the samples
without garnet structure including other phases such as
Bi2O3 and Gd2O3 showing little FR,as shown in figure 2.
Maximum FR (negative) angle of the Bi2.5Gd0.5Fe5O12
thin films on SGGG substrate is 32.5 deg./μm at the
wavelength of 533 nm. The maximum FR of theBi2.5Gd0.5Fe5O12 thin films on the GdIG buffer layer /glass substrate is comparable with that on (111) SGGG
single crystal substrate. The FR of Bi2.5Gd0.5Fe5O12 thinfilms on the Gd3Fe5O12 buffer layer / on glass substrate(27.5 deg./m at  = 533 nm) is 3 time larger than that of
the reported Bi1.4Gd1.6Fe5O12

sample (9.3 deg./m at

= 520 nm.), which was fabricated by sintering, hotpress and annealing method26). Also it was reported that
Bi2.5Gd0.5Fe5O12 films on Nd2Bi1Fe4Ga1O12 buffer layers
on a glass substrate which was fabricated by the MOD
method had FR of 13.8 deg./m at  = 520 nm, which ishalf of the FR of our Bi2.5Gd0.5Fe5O12 thin films on the
Gd3Fe5O12 buffer layer / on glass substrate 18). Therefore,
our samples fabricated by the EMOD method showed 2 3 times larger FR compared with that of previously
reported BixGd3-xFe5O12 samples.

obtained on the sample with the Gd3Fe5O12 buffer layer
Faraday rotation is comparable with that prepared on
SGGG (111) single crystal substrate.

It is important tosuppress the formation of the Bi2O3 and Gd2O3 phases by
the Gd3Fe5O12 buffer layer in order to prepare

BixGd3-xFe5O12 thin films having higher Bi content x andFR, from the XRD spectra and measurement of the
Faraday rotation.

These findings are important torealize BixGd3-xFe5O12 thin films having large Faraday
rotation for future applications to MOSLMs and opticalisolators on the glass substrates.

Acknowledgements

This

work

was

partially

supported by JSPS KAKENHI (Grant Number 24656010
and 15K13942) and Support Center for Advanced
Telecommunications
Foundation.

(SCAT)

Technology

Research,

The authors would like to thank Prof. T.

Sameshima for the guidance of the optical reflectivity
measurement.

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20) http://www.kojundo.co.jp/English/Guide/material/csd.html
21) D. Pekker, and L. Pekker: Thin Solid Films., 425, 203(2003).
22) M. M. Gader: Euro. Intl. J. Sci. Technol., 2, 214 (2013).
23) R. Kitamura, L. Pilon, and M. Jonasz: Appl. Opt., 46, 8118
(2007).
24) P. Hansen, K. Witter, and W. Tolksdorf: Phys. Rev., 27,4375 (1983).
25) M. Hosoda, J. Sato, D. A. Wahid, H. Shimizu: Proc. the 63rd .
spring meeting of Japan Society of Applied Physics.,
20a-S621-2, Tokyo, (2016).
26) H. Takeuchi: Jpn. J. Appl. Phys., 14, 1903 (1975).
Received Jan. 27, 2016; Accepted May. 12, 2016

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX
J. Magn. Soc. Jpn., 40, 115-119 (2016)<Paper>Demagnetization Analysis of Ferrite Magnet
Using Two-line Approximation Based on Reluctance Network Analysis
D. Momma, Y. Yoshida*, and K. Tajima

Department of Cooperative Major in Life Cycle Design Engineering, Akita Univ., 1-1, Tegata Gakuen-machi, Akita 010–5802,*Department of Electrical and Electronic Engineering,

Japan䢢Akita Univ., 1-1, Tegata Gakuen-machi, Akita 010–5802, Japan

This study presents a method for determining the demagnetization characteristics of ferrite magnets based on
reluctance network analysis (RNA). First, an RNA model for determining the operating points of a magnet
considering demagnetization using a two-straight-line approximation of the demagnetization curve is discussed.
Then, using the proposed model, demagnetization characteristics are determined. Experimental results demonstrate
the validity of the proposed method.
Key words: reluctance network analysis, ferrite magnet, demagnetization analysis, two line approximation
1. Introduction
Permanent magnet (PM) motors based on powerfulrare-earth magnets are widely used in various
applications because of their high-performance
characteristics. However, rare-earth magnets may besubject to price rises as the production of such metals isconcentrated in a single country. Therefore, thedevelopment of highly PM motors without rare-earthmagnets is required.
Although the maximum magnetic energy product offerrite magnets is one tenth that of rare-earth magnets1), high-efficiency ferrite magnet motors have beenreported 2). Ferrite magnets in motors are exposed to alarge reverse magnetic field to obtain performanceequivalent to that of rare-earth magnet motors.
Therefore, ferrite magnets are at a risk ofdemagnetization because of their low coercive force.
Thus, it is necessary to consider the demagnetization of
ferrite magnets for ferrite magnet motor design.
Reluctance network analysis (RNA) is a useful
method to save calculation time in the estimation of thecharacteristics of PM motors, as reported in previous
studies 3)-6). However, a demagnetization analysis
method using RNA has not yet been proposed.
Because demagnetization analysis using finite
element analysis (FEA) has been previously discussed7)-8), this method is now applied to RNA. This study
presents an RNA model for determining the operating
points of ferrite magnets; this model uses a two-line
approximation of the demagnetization curve. To verify
the accuracy of the proposed model, the calculated
results are compared to values obtained fromtwo-dimensional (2D) FEA and experimental results.
2. Derivation of the RNA Model
Fig. 1 shows the shape and specifications ofanalytical and experimental objects under consideration.
Exciting coils are wound around U-shaped cores. Ferrite
magnets with a thickness of 2 or 3 mm are sandwiched
between the cores. The number of winding turns of
exciting coils per leg is 80, and the stack length of thecores and ferrite magnets is 20 mm.
Fig. 2 illustrates the division of a 2D RNA model.
The RNA model is derived in a quarter region of theanalysis model shown in the figure, taking advantage ofthe analytical model’s symmetry. In the model, theelements around the air gap are divided with a size of
1.0 mm  1.0 mm. When the 3-mm-thick magnet is used,the element size of the magnet in the y-axis direction is
1.5 mm.
Each divided element is expressed in a 2D-unit
magnetic circuit. Fig. 3(a) shows the unit magnetic
circuit of the core and air region. In the figure, l is thelength of the element. The reluctance, Rm, in the unit
magnetic circuit is obtained from

Rm 

l

2s 0 l  ls ,(1)where  s is the relative permeability,  0 is thepermeability of vacuum, and ls is the stack length of themodel. The elements of a ferrite magnet can be expressedas the reluctance and magnetomotive force (MMF), Fm,
shown in Fig. 3(b). The reluctance of a ferrite magnet,
24 mm

20 mm

20 mm

Core

35 mm
10 mm
Ferrite magnet(Y30BH)

2 mm
S
N

N
S

Exciting
coil

y

z

x

2 mm

Magnets with a thicknessof 2 mm or 3 mm

Fig. 1 Specifications of analytical and experimental
objects.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

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INDEX

Rmag, is expressed by

Rm ag l2r 0 l  ls ,(2)where r is the magnet’s recoil. By connecting all unit
magnetic circuits together, the RNA model is obtained.
Fig. 4 illustrates the demagnetization curve of aferrite magnet, which is approximated by two lines. In
the figure, Br, Br’, Hc, and Hc’ are the residual magnetic
flux density before demagnetization, residual magnetic
flux density after demagnetization, coercive force before
demagnetization,andcoercive
force
after
demagnetization, respectively. If there is nodemagnetization in a ferrite magnet element, Fm isgiven byBr l .

2r 0(3)

When an operating point of a ferrite magnet is changedby an external magnetic field and becomes less than theknee point, the MMF after demagnetization, Fm’, can be
expressed as

Fm ' 

Br ' l .
2r 0zx
Fig. 2 Division of the RNA model.

(4)

To obtain the residual magnetic flux density after
demagnetization (Br’), B–H and J–H characteristics,
where J = B–0H as shown in Fig. 5, are used 9). First,
the operating point without considering an external
magnetic field, plotted as point a in the figure, isdetermined by the derived RNA model. The magnetic
field at this time is diamagnetic, Hd. At the same time,
point b, where a perpendicular line from point aintersects with J–H characteristics, is determined Then,line l0 is given as a straight line passing through point b
and the origin. Next, the operating point considering an
external magnetic field, plotted as point c in the figure,is determined. The external magnetic field, Hex, iscalculated as the difference between the magnetic fieldat point c and Hd. The line, l0, is shifted toward thenegative direction by Hex without changing the slope toobtain line l1. The intersection of J–H characteristics
and line l1 is plotted as point d. When point d is lessthan the knee point of J–H characteristics, irreversible
demagnetization occurs. Br’ is determined as the point
where the vertical axis intersects the straight line,
which passes through point d and is parallel to J–Hcharacteristics before demagnetization.
3. Demagnetization Analysis of the Ferrite Magnets
Using the proposed RNA model, the demagnetizationof the ferrite magnets is determined with an exciting
current that produces an external magnetic field
opposed to the magnetization direction. Three cycles ofa sawtooth wave, shown in Fig. 6, are applied toexciting coils. The maximum value of the current is 4.0
A when the magnet thickness is 2 mm, and 5.5 A when
the thickness is 3 mm.
Fig. 7 illustrates the direction of the magnetic flux
flowing through the core. This direction is caused by the
116

y

l
l

Rm

(a) Core and air

l

Rmag
l

Fm
(b) Magnet
Fig. 3 Unit magnetic circuit.

Br

B  r 0 H  Br
 1.40 106 H  0.385
Knee point

Hc Hc’ Hcb

Br’Parallel lines

B  0.6 104 H  13.7

Flux density (T)

Fm 

0

Magnetic field (A/m)
Fig. 4 Demagnetization curve approximated by twolines.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

l1

Knee point( J-H )

l0

Hex

B
b

Br

Parallel lines

J-H characteristics( J = B － µ0 H ) dBr’a

B-H characteristics

approximated by two lines

c
Hex
Hex

Hd

0

H

Fig. 5 Calculation method for the residual magnetic
flux density after demagnetization.

Fig. 8 Mesh distribution of the 2D-FEA model.

4.0A or 5.5A

0.4
0.4

Br = 0.385 T

RNA

2D-FEA

0.35
0.35

0.3
0.3

Current (A)

0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1

Br’ = 0.283 T

0.05
0.05

Flux density (T)Knee point( B-H )

00−-0.050.05

Fig. 6 Waveform of exciting current.

-250000−250000-200000−200000-150000−150000-100000−100000

Magnetic field (A/m)-50000−5000000(a) Graph for the 2-mm-thick magnet.

i

Br = 0.385 T

RNA

mag

2D-FEA

−-0.1
0.1

0.4
0.4
0.35
0.35
0.3
0.3

0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1

Br’ = 0.284 T

0.05
0.05

Flux density (T)Time (s)00

NS
Element A B C

Fig. 7 Direction of magnetic flux and detection points.
winding current and is the inverse of the flux of theferrite magnet. In the figure, elements A, B, and C are
the detection points of demagnetization.
To compare the results from the RNA model withthose obtained using FEA, the same calculation as thatof RNA was performed using the JMAG-Designer
Ver.14.1 software. Fig. 8 shows the mesh distribution of
the 2D FEA model. The number of elements of the FEA
model is 3,429.
Fig. 9 shows the operating points of element B
determined by the RNA and 2D FEA models. It isobserved that the data obtained by the proposed RNAmodel almost agree with the corresponding 2D FEA−-0.050.05-250000−250000-200000−200000-150000−150000-100000−100000

Magnetic field (A/m)-50000−50000

00

−-0.1
0.1

(b) Graph for the 3-mm-thick magnet.
Fig. 9 Calculated operating points of element B.
calculation results. The residual flux density of themagnet before demagnetization, Br, is 0.385 T. The
calculated residual magnetic flux density after
demagnetization by RNA, Br’, is 0.283 T when themagnet thickness is 2 mm, and 0.284 T when it is 3
mm.
Table 1 shows a comparison between the
demagnetization factors calculated by RNA and 2D FEA
for the 2-mm-thick magnet, and Table 2 shows acomparison of the calculated demagnetization factors by
RNA and 2D FEA for the 3-mm-thick magnet In thetables, the demagnetization factor, Dfac, is defined as

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

117

INDEX

Table 1 Demagnetization factors for the 2-mm-thickmagnet.

10 mm

Element
A [%]

B [%]

C [%]

RNA

14.9

26.6

14.9

2D-FEA

14.2

30.4

14.6

Ferrite magnets

U-shaped cores

Table 2 Demagnetization factors for the 3-mm-thickmagnet.
Element
A [%]

B [%]

C [%]

RNA

12.7

26.3

12.7

2D-FEA

7.9

31.0

8.0

Exciting coils(a) Exposed view

Table 3 Interlinkage magnetic flux of ferrite magnets.
2 mm

Supporters

Cores

3 mm

before [Wb]after [Wb]before [Wb]after [Wb]RNA

0.02360.01820.03080.0239Exciting coil

2D-FEA

0.02360.01730.03080.0229Supporter

Ferritemagnetfollows:

 B '
D fac  1  r  100 .
 Br 

(5)yDemagnetization factor at the center of the magnet isgreater than that at either end. The calculated values
obtained from the proposed model almost agree withthose obtained from 2D FEA.
Table 3 shows a comparison of the interlinkage
magnetic flux of the ferrite magnets calculated via RNA
and 2D FEA. After demagnetization, the interlinkage
magnetic flux decreased by approximately 25 % for bothmagnet thickness.
The number of time steps of the proposed model and
2D FEA model is 64 for three cycles of the sawtoothwave. The calculation times of the proposed and 2D
FEA models are 17 s and 58 s, respectively.

(a)4. Comparison with Experimental Resultsx

To verify the calculation accuracy of the RNA model,
the calculated values were compared to the measured
ones. Fig. 10 shows a photograph of the experimental
apparatus; Fig. 10(a) is an exposed view. The
supporters are sandwiched between the cores to fix thepositions of the cores and magnets. Fig. 10(b) shows anassembled experimental setup. Fig. 11(a) shows theconditions of the experiment, and Fig. 11(b) shows thedetection point of the magnetic flux density of theferrite magnet. The magnetic flux density wasdetermined using a gauss meter (GM-301, Denshijiki
Kogyo); the average values of the surface magnetic flux
density were obtained from 10 measurements withmagnets of the same size.
Fig. 12 shows the comparison of the magnetic flux
density of the magnet surface before and after
demagnetization. The DC input current is 4.0 A whenthe magnet thickness is 2 mm and 5.5 A when it is 3
118

z

x

(b) Assembled setup.
Fig. 10 Photographs of the experimental apparatus.
(b)
Detection point
Gauss meter
probe

y

y

z

Ferrite magnet

10 mm

z

x

20 mm

Fig. 11 (a) Measurement setup. (b) Detection point of
the magnetic flux density.
mm. In the figure, the error bars denote the maximum
and minimum the measured values. It is concluded thatthe magnetic flux density determined by the proposed
RNA model almost agrees with the corresponding 2D
FEA calculated and measured values.
5. Conclusions
This study presented the demagnetization analysis
of a ferrite magnet based on RNA. In the proposedmodel, the demagnetization curve of the magnet wasapproximated by two lines to estimate the magnetic flux
density before and after demagnetization. The validityof the proposed RNA model has been demonstrated bycomparing the calculated results with 2D FEA
calculation results and experimental results.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

References

0.14

Flux density (T)

0.12
0.1

0.08
0.06
0.04

0.02
0

RNA

2D-FEAmeasured

before

after

0.120

0.08720.111

0.08120.119

0.0827Flux density (T)(a) Graph for the 2-mm-thick magnet.

0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

RNA
2D-FEAmeasured

before

after

0.156

0.114

0.151

0.110

0.155

1) M. Sagawa, M. Hamano, and M. Hirabayashi: Eikyujishaku−Zairyokagaku to Oyo− (in Japanese), p. 16 (Agune Gijutsu
Center, Tokyo, 2007).
2) M. Sanada, Y. Inoue, and S. Morimoto: IEEJ Trans. IA, 13,
12, 1401-1407 (2011).
3) K. Nakamura, K. Saito, and O. Ichinokura: IEEE Trans.
Magn., 39, 3250-3252 (2003).
4) K. Nakamura, M. Ishihara, and O. Ichinokura: 17th

International Conference on Electrical Machines (ICEM
2006), PSA1-16 (2006).
5) K. Nakamura and O. Ichinokura: 13th International PowerElectronics and Motion Control Conference (EPE-PEMC
2008), 441 (2008).

6) Y. Yoshida, K. Nakamura, O. Ichinokura, and K. Tajima:
IEEJ Journal IA, 3, 6, 422-427 (2014).
7) A. Yamagiwa, K. Aota, Y. Sanga, H. Takabayashi and M.
Natsumeda: IEE JAPAN, RM-03-41 (2003) [in Japanese].
8) Y. Osawa and A. Yamagiwa: IEEJ, RM-13-62 (2013) [inJapanese].
9) https://www.hitachi-metals.co.jp/products/auto/el/pdf/hg-a2-b.pdf (As of January 09, 2016) [in Japanese].
Received Oct. 20, 2015; Revised Jan. 10, 2016; Accepted Mar.
21, 2016

0.106(b) Graph for the 3-mm-thick magnet.
Fig. 12 Comparison of magnetic flux densities ofmagnets.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

119

INDEX
J. Magn. Soc. Jpn., 40, 120-125 (2016)<Paper>Improvement of induction motor analysis accuracy
in reluctance network analysis
Tomoyuki Umesaka*, Katsubumi Tajima*, and Yukihiro Yoshida***Cooperative Major in Life Cycle Design Engineering, Graduate School of Engineering and Resource Science, Akita Univ.,
1-1Tegatagakuen-machi, Akita 010–8502, Japan**Department

of Electrical and Electronic Engineering, Graduate School of Engineering and Resource Science, Akita Univ.,

1-1Tegatagakuen-machi, Akita 010–8502, Japan

In previous studies, we applied reluctance network analysis (RNA) to the dynamic analysis of the induction motor.
However, the accuracy of our analysis of the motor characteristics using the RNA model was not high because thedetailed magnetic flux distribution in the rotor was not taken into account. In this paper, we propose a 3D RNA modelthat considers the detailed magnetic flux distribution in the rotor and skew of the rotor bar. Using the proposed RNAmodel, the winding currents of the induction motor under no-load and locked rotor conditions can be calculated withhigher accuracy than with the previous RNA model.
Keywords: Induction motor, Reluctance network analysis, Analysis of dynamic characteristics, Squirrel cage rotor, Skew,
High-speed calculation

1. Introduction

2. Capacitor motor (single-phase induction motor)

In Japan, the proportion of thermal power to the total〈2･1〉 Structure and principles of the capacitor motor

amount of power used has become large since most of the

The basic circuit of the capacitor motor is shown innation’s nuclear power plants have ceased operation. The

Fig. 1, where Cr is a running capacitor, Cs is a starting

proportion of fossil energy to total energy in Japan was
about 90% as of in 2011, and most of the fossil fuels were
imported. It has been pointed out that the stable supplyof future power in Japan will not be easy (1) because thecapacitor, v is the applied voltage, and im and ia are themainwindingandauxiliary

winding

currents,

respectively.
By connecting Cr, the phase difference between the

power consumption of the world is increasing due toauxiliary and main winding currents is almost 90

population growth and economic growth in emerging

degrees. As a result, the rotating magnetic field isgenerated around the squirrel cage rotor, and the motor

countries.
Therefore, improving the efficiency of motors used ingenerates a driving torque.

various applications is strongly required. Of particularinterest are induction motors, which are used inextensive applications ranging from large industrial〈2･2〉Specifications of analysis object
The test motor is a capacitor start-type capacitor run
motor (SKD-DBKK8) made by Toshiba. Its specifications

equipment to compact household appliances.
aand dimensions are listed in Table 1. The main winding

motor

and auxiliary winding are both distributed windings.

characteristics of all potential materials and dimensions

Figure 2 and Table 2 show the arrangement and number

is required. The finite element method (FEM) hasof turns, respectively (2).

To

improvehigh-precision

theefficiency

calculation

of

such

methodofmotors,thecTherefore, in a previous work the authors appliedcvgreat deal of computing time and memory are required.

w

past, but for dynamic analysis of the induction motor, asgenerally been used for electromagnetic devices in the

reluctance network analysis (RNA) to the dynamic
analysis of the induction motor (2).
In the current work, we present an analysis of thew

accuracy improvement of the dynamic characteristics of
the induction motor based on RNA considering thedetailed magnetic flux distribution and skew of the rotor.

120

Fig. 1

Circuit configuration of a capacitor motor.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX3.
34 35 36 1 2 3
4
33

32
31
30
29
28
27
26
25
24
23
22

21 20 19 18 17 16

5

6

7
8
9
10
11
12
13
14
15

2-dimensional RNA model of capacitor motor〈3･1〉 Overview of Reluctance Network AnalysisTheauthors

previously

proposedamethodofreluctance network analysis (RNA) that is suitable fordynamic simulations of an orthogonal-core type variableinductor, the SR motor and IPM motor, because of its
simple modeling, high calculation accuracy, and ease of
coupled analysis. Moreover, in calculation based on RNA,
it is possible to use a general-purpose circuit simulation
program such as SPICE.

(a) Main windings

We explain the flow of construction of the RNA modelof the capacitor motor below.

34 35 36 1 2 3
33
4
32
5
31
6
30
7
29
8
28
9
27
10
26
11
25
12
24
13
23
14
22
15
21 20 19 18 17 16〈3･2〉RNA model of stator (3)The cross section of the capacitor motor is roughly
composed of a stator, a rotor, and the air gap, as shownin Fig. 3.
Because the stator has 36 slots in a circumferential
direction,

wedivide

it

into

36

parts

in

the

circumferential direction, as shown in Fig. 4. The
division of each part includes the surrounding space so
as to consider the linkage fluxes into multiple elements,(b) Auxiliary windings

as shown in Fig. 5. In the figure, each tooth is divided

Fig. 2

Arrangement of main windings.

intoTable 1

Specifications of specimen motor.

two

equal

parts

becausetheconcentrated

magnetomotive forces due to winding current are

Parameter
Frequency
Voltage
Current
OutputNumber of poles
Rated speed
Running capacitor
Starting capacitor
Number of stator slots
Internal diameter of stator
Outer diameter of stator
Gap width
Number of rotor slots
Outer diameter of rotor
Iron core length
Table 2

Value
50 Hz
100 V
12.6 A750 W
41440 rpm
40 mF
350 mF36
90.0 mm146.0 mm
0.3 mm44
89.4 mm93.0 mmarranged as shown in Fig.5. The divided elements can be
expressed by a unit two-dimensional magnetic circuit, asshown in Fig. 6.
StatorAir gaps

Rotor

Fig. 3

Cross section of a capacitor motor.

Number of turns of windings.

Main windings
Slot number
35-2,11-8,17-20,29-26
34-3,12-7,18-21,30-25
33-4,13-6,15-22,31-24
32-5,14-5,14-23,32-23

Turns
7
11
14
7

Auxiliary windings
Slot number
Turns
1-9,18-10,19-27,36-28
36
2-8,17-11,20-26,35-29
18
3-7,16-12,21-25,34-30
5Fig. 4

Division in the radial direction of stator.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

121

INDEX

The rotor has a chain structure consisting of end ringsAirand conductor bars. The magnetic flux  of the stator

Yokeflows to the rotor and the electromotive force e isgenerated by Faraday's law of electromagnetic inductionin the rotor to flow the eddy current i. In addition,Slotaccording to the law of Lenz, eddy current i acts to

Slotprevent the change of the magnetic flux flow, andgenerates a magnetomotive force in the opposite
direction of the magnetic flux. We obtained a chain
electrical circuit composed of 44 circuits (Fig. 9), where

Magnetomotive Forcefthe size of the conductor bar is Rbar = 1.14×10-4  thesize of the end ring is Rend = 4.54 × 10-6  and theresistivity is 75℃ of aluminum.

Teeth
Fig. 540
39
38

RNA model of the stator (1/36).

41

42

43 44 1

2 3

4

5

6

7

37
35

S

34

l

Rm

11

33

12

32

13

31

14

30

29
28
27

Fig. 7
Fig. 68
9
10

36

Magnetic circuit of element.

26

25 24

23 22 21

20

19

15
16
17
18

Division in the radial direction of the rotor.

Rotor bar

Reluctance Rm in this unit magnetic circuit can be

Magnetomotive force

represented by equation (1) with magnetic permeability

m, magnetic path length l [m], and sectional area S [m2]:

Rm 

l

mS

（1）

Rotor coreMagnetomotive force is proportional to the number of

Shaft

turns N and current i of the coil. The magnetomotive
force source is placed in consideration of the distributed

Fig. 8RNA model of the rotor (1/44).

winding of the main and auxiliary winding between
stator slots (2).
Rbar

〈3･3〉RNA model of the rotor (3)The rotor of the capacitor motor used in this paper isthe squirrel cage rotor. It has 44 slots in the

Rend

Rend


i

circumferential direction, so we divide the rotor into 44
parts in the circumferential direction, as shown in Fig. 7,

Rbar

where each part is represented as a magnetic circuit
network, as shown in Fig. 8. Therefore, by linking 44
circuits, we can derive the RNA model of the rotor.

122

Fig. 9

Electric circuit model of the rotor.

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX〈3･4〉Driving expression of the rotor (4)In an earlier work (5), we proposed an RNA model of the rotor
when the rotor is driving. This model consists of an electrical

4. 3-dimensional RNA model(5)〈4･1〉New RNA model of the rotor

circuit to evaluate the induced currents on the rotor bars and As described in <3.3>, the previous RNA model of theend rings and a magnetic circuit to express the MMFs

rotor in Fig. 8 is a reverse T-shaped simple magnetic

corresponding the induced currents on the rotor, as shown incircuit

that

did

not

considerthemagnetic

flux

Fig. 10. In the figure, there are eight stator slots and eight rotor

distribution of the core and skew of the rotor bars. To

slots .

improve the analysis accuracy of the motor, we have

The flux flowing into the first slot of the rotor r1 shown in Fig.
10 (a) is obtained by

distribution in the rotor and skew. We divide a part of 
4  
r1     s1  s 2  0 
     ,   (3)4  4  
where  is the rotating angle of the rotor. The magnetomotive
force generated by the induced current in the rotor electric circuit MMF1

the rotor shown in Fig. 8 into 19 elements corresponding
to the shape of the conductor bar and the iron core of therotor to make the new RNA model.
〈4･2〉 Driving expression of new RNA model
Here, we consider the magnetic flux r passing throughshown in Fig. 10 (b) is expressed by

4    4developed a new RNA model that represents the flux

 
 






 MMF
  1       ir1  
 ir 8 0      ,   (4)4

where ir1 and ir8 are the electric currents calculated by the electric circuit
model.

the rotor core. In the previous model (Fig. 8), all rpassed through the rotor core. In contrast, in the model

proposed here (Fig. 11), r flows in both the rotor core andthe conductor bar. In other words, r’ passes through therotor core between the conductor bars.

We calculate r’ on the rotating state as follows.

① Flux r can be given by using Fig. 10 (a): it flows from thestator to 1/44 of the rotor model (Fig. 11).

②  However, the magnetic flux r’ flowing between the
conductor bars is different from r. For this reason, we use
another RNA model to calculate r’ from r (Fig. 12).

③ To obtain a reaction field magnetomotive force ir in theelectric circuit model of the rotor using the r, we give theoriginal magnetic circuit MMF1–MMF44 with reference to Fig.
10. (b).

r(a) Fluxes flowing into the rotor.

ir 8

θ

ir1

MMF1

ir 2

Rotor
Rotor barbar

r’

Magnetomotive force
Rotor coreCore(b) MMFs acting on the stator
Fig. 10
stator.

Expression of coupling between the rotor and

Shaft
Shaft

Fig. 11

New RNA model of the rotor(1/44).

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

123

INDEXr1

rotor1

rotor2

r2

r3

rotor3

r2’

r1’

r3’

R’

・・・

Fig. 15

r44’

r43’

r44
Fig. 12rotor44

r43

S3-dimensional magnetic circuit of element.

5. Results and discussion

r42’
r42

rotor43l

 We examined the validity of the new RNA model of therotor42capacitor motor by using the OrCAD PSpice 16.6

Calculation circuit of r1’–r44’ fromr1–r44.

(Cadence Design Systems, Japan) as a solver for the
analysis〈4･3〉Consideration of skew

andaregular

PC(Intel®Core(TM)

i7-3770KCPU @ 3.5 GHz 3.5 GHz 16.0 GB RAM).

The conductor bars of the squirrel-cage rotor of the

Because the same flux distribution appears at every 180

induction motor are skewed as shown in Fig. 13. Because

degrees in the four-pole structure, we use a half model.

the 2-dimensional RNA model cannot express the skew, a With the stator and rotor core material, we assume a3-dimensional model is needed to consider the axial

non-oriented silicon steel sheet 50H600 (NIPPON

direction structure. In this paper, we constructed a

STEEL CORPORATION)

3-dimensionalrotor

permeability of 4000. The rotor conductor bars were thestructure of the axial direction to consider the skew ofsame relative permeability as air because their material

two slots. The rotor bar shape was approximated using a

is non-magnetic.

three-layer

RNA model

structureasrepresenting

shown

in

the

Fig.

14.

and a relative magnetic

The

In the case of applying the sinusoidal voltage of 50 Hz,

3-dimensional unit magnetic circuit used is shown in

the waveforms of the currents in the previous andFig. 15. For the laminated structure of the rotor core, theproposed model with locked rotor and under no-load are

reluctance R’ in the laminated direction was calculated

shown in Figs. 16 and 17. As we can see, the calculation

as a relative permeability of 25 using the methods ofaccuracy is improved. Moreover, from Fig. 17 shows thatreference 6.

the current pulsation occurring the previous model isreduced. This pulsation is thought to stem from errors in
the magnetic flux and the magnetomotive forces of the
Stator core

Stator slot

linear interpolation for use in driving expression, as

Air gap

described in <3.4>. However, by considering the detailed

Rotor bar

Shaft

Fig. 13magnetic flux distribution and the skew, we are able toreduce the magnitude of the pulsation.

The effective values Im, Ia obtained from these current

Rotor core

waveforms are shown in Tables 3 and 4. Calculation

Stator and rotor of capacitor motor.

errors of each winding current are compared with thecalculation results by the previous model. Results showthat they are greatly reduced. In particular, the2 slots
Layer 1

Layer 2

Rotor barLayer 3zr

Fig. 14

Rotor bar

calculation error of the main winding current of the
motor with locked rotor is reduced.

Figure 18 shows the change of Im, and Ia to slip s. As

we can see in figure, there is good agreement around thesynchronous speed. However, the error of the main
winding current is increased with the increase of slip s.
Twenty cycles of computation took about 30 minutes

Consideration of skew for the RNA model.

with the locked rotor, and about one hour in therotational state.

124

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

im

Current im ,ia (A)

20

ia

10

0
0.08
－10
-10

20

im (meas.)im (calc.)
ia (meas.)ia (calc.)

0.085

0.09

0.095

Current im ,ia (A)

30

0.1

－20
-20
－30
-30

Time t (s)

(a)
30

0
0.38
－10
-10

0.385

0.39

0.395

Im(prev.)Im(conv.)Im(prop.)Im(prop.)5

im (meas.)im (calc.)
ia (meas.)ia (calc.)ia

10

Im(meas.)Im(meas.)

im

10

0

im

20

Current im ,ia (A)Previous model

15

0

0.02

Fig. 18

0.4

Ia(meas.)Ia(meas.)Ia(prev.)Ia(conv.)ia
Slip s0.04

Ia(prop.)Ia(prop.)

0.06

Load characteristics of motor.

－20
-20
－30
-30

(b)
Fig. 16

6. Conclusions

Time t (s)Proposed model

Current waveforms of the motor with locked

rotor.

We proposed a 3D RNA model that considers thedetailed magnetic flux distribution in the rotor and skew
of the rotor bar. Experimental results showed that theCurrent im ,ia (A)

15
10
5

0
0.08
－10
-5

im (meas.)im (calc.)
ia (meas.)ia (calc.)imiacalculation accuracy of the winding currents under

0.085

0.09

0.095

no-load and locked rotor conditions are improved
compared with the previous RNA model. Also, thepulsation of winding current waveforms is reduced while

0.1

maintaining high-speed calculation. This is much-needed

－20
-10

progress in the high-precision characteristic calculation

－30
-15

Time t (s)(a)
Current im ,ia (A)

15
10

0
0.38
-5
－10

0.385

However, the calculation error of the main windingim (meas.)im (calc.)
ia (meas.)ia (calc.)

im

ia

5

of the induction motor.

Previous model

0.39

0.395

current of the motor with load became large in the low
speed area. Therefore, in our future work we intend to
improve the accuracy of the load characteristics of the

0.4

induction motor to apply the proposed method to

－20
-10

induction motor design.

－30
-15

Time t (s)(b)
Fig. 17

Proposed model

Current waveforms of the motor under no-load.

References(1)

Table 3 Im and Ia of the motor with locked rotor.
（Input voltage 25.6[Vrms]）
Im [Arms]
previous
Measurement

Ia [Arms]

proposedprevious

12.6

proposed
3.45

Calculation

18.1

14.4

2.68

4.11

Relative error

43.7%

14.3%

22.3%

19.1%

Table 4 Im and Ia of the motor under no-load.
（Input voltage 100[Vrms]）

Measurement
Calculation
Relative error

Im [Arms]
previous
proposed
7.35
6.45
6.99
12.2%
4.9%

Ia [Arms]
previous
proposed
2.57
2.66
2.56
3.5%
0.4%

Ministry of Economy, Trade and Industry Agency for Natural
Resources and Energy: “2013 fiscal year The annual report onenergy (Energy White Paper 2014)”，pp. 179–218 (2010).
(2) K. Tajima and T. Sato, J. Magn. Soc. Jpn., Vol. 34, No. 3, pp.
367–373 (2010).
(3) T. Miyaji, K. Tajima, T. Taniguchi and T. Sato, J. Magn. Soc.
Jpn., Vol. 27, No. 9, pp. 976–981 (2003).
(4) K. Tajima, M. Hattori, T. Miyaji, T. Sato, and Y. Sakamoto, J.
Magn. Soc. Jpn., Vol. 29, No. 6, pp. 680–685 (2005).
(5) T. Umesaka, K. Tajima, and Y. Yoshida, The papers of Technical
Meeting on Magnetics, IEE Jpn, MAG-15-116 (2015).
(6) S. Hayakawa, K. Nakamura, S. Akatsuka, T. Aoki, M.
Kawakami, T. Ohinata, K. Minazawa, and O. Ichinokura, J.
Magn. Soc. Jpn. 28, 425 (2004)

Received Nov. 16, 2015; Revised Feb. 29, 2016; Accepted Mar.
21, 2016

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

125

INDEX
J. Magn. Soc. Jpn., 40, 126-131 (2016)

Heat generation of coreshell particles composed of
biodegradable polymer and iron oxide<Paper>C. Oka, K. Ushimaru, N. Horiishi*, T. Tsuge, and Y. Kitamoto

Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku,

Yokohama 226-8503, Japan*Bengala Techno Lab., 1-19 Kodai, Miyamae-ku, Kawasaki 216-0007, Japan

A suspension of coreshell particles composed of a biodegradable polymer core and iron oxide nanoparticles(IONPs) exhibits higher heat generation under an alternating magnetic field compared with a suspension of IONPs
at the same IONP concentration. The improvement of the heat generation will be attributed to the change of thestrength of dipolar interactions between adjacent IONPs. The IONPs in the coreshell particles were relatively
isolated, in contrast with that in IONP suspension before the formation of the coreshell particles. Therefore, in thecoreshell particles, the dipolar interaction is reduced, and the heat-generating capability is increased. This
explanation is brought through investigating the influence of the agglomerate size of IONPs on the heat-generating
capability.
Key words: magnetic hyperthermia, coreshell particle, iron oxide nanoparticle, dipolar interaction, hydrodynamic
diameter, delta M plots
1. Introduction
Magnetic hyperthermia (thermotherapy), whichkills cancer cells by heat generated from magnetic
nanoparticles under alternating magnetic fields, is a
type of cancer treatment under study in clinical
trials1)4). In the magnetic hyperthermia, tumor tissues
are exclusively affected by selective accumulation of themagnetic nanoparticles, which are heat agents, in thetissues. Hence, the magnetic hyperthermia has been
attracting significant attentions as a more effective
treatment than conventional hyperthermia methods; alot of researchers have been investigating magnetic
nanoparticles and an apparatus generating themagnetic field for the treatment to improve theefficiency5)11).
In our previous study, a coreshell particle
composed of a core of a biodegradable polymer particle
and a shell of assembly of magnetic iron oxide
nanoparticles (IONPs) has been prepared as a
candidate for a drug carrier for magnetically guided
drug delivery system (MGDDS)12). It can loadhydrophobic drugs into its polymer core. We havealready confirmed that the coreshell particles werestrongly attracted to a NdFeB magnet, and will havemagnetic properties enough for MGDDS.
In the present study, heat generation of thecoreshell particles in the alternating magnetic field isinvestigated. The coreshell particle can act as a heat
agent for magnetic hyperthermia as well as a MGDDS
carrier because its structure includes magnetic
nanoparticles. Therefore, the coreshell particle isexpected to be a promising carrier having hybrid
function of a drug carrier and a heat agent. The heat
agent is an assembly of IONPs as a shell; the assembled
structure of the IONP-shell is controlled by the126

Fig. 1 Schematic illustration of coreshell particle
composed of biodegradable polymer and iron oxide
nanoparticles.
preparation conditions. The heat generation is induced
by relaxation losses of IONPs, which are Néel and
Brownian relaxation losses, and the relaxation
dynamics is greatly affected by their agglomerate state
due to dipolar interactions between IONPs13),14). To
discuss the heat-generating capability of the coreshellparticles in view of the agglomerate status in theirsuspension, the capability was compared with that of
IONP suspensions with various agglomerate sizes
manipulated by adding a flocculant and by changing
IONP concentrations.
2. Experimental
Two types of IONPs, whose sizes were 8 nm and 11
nm, were synthesized by a coprecipitation method using
FeCl2, FeCl3 and NaOH. Blocking temperatures of the
IONPs were about 240 K for the 8 nm IONPs, andhigher than room temperature for the 11 nm IONPs at
a powder state. Although the temperature of the 11 nm
IONPs indicates being ferromagnetic, both of the IONPs
seem to be superparamagnetic in these suspensions at
the room temperature. The coreshell particles wereprepared as reported in our previous report with the 8
nm IONPs12). To evaluate the heat-generating

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

capability, suspensions of the coreshell particles, the 8
nm IONPs, and the 11 nm IONPs were prepared at
IONP concentrations of 0.1, 0.3, 0.5, 1, 1.5, and 2.0 mg
Fe/mL. The IONP concentrations were determined by aconcentration of Fe in the suspension. The agglomerate
status, in particular, the size of the 11 nm IONPs was
manipulated by adding polyvinyl alcohol (PVA) as aflocculant to the IONP suspension.
The heating curves of the suspensions were measured
by a system with a coil generating the magnetic field ata frequency of 2 MHz and a field strength of 3.4 kA/mrms,
and temperature was measured with a fiber-optic
thermometer. Since the frequency is considerably high,
it is presumed that the Néel relaxation is dominantrather than the Brownian relaxation in the condition.
The heat-generating capability was evaluated by the
Box-Lucas equation15):

T(t) = T(0) + A(1  eBt)(1)where T is temperature, t is time, and A and B are
parameters related to the saturation temperature andthe curvature of the heating curve. At t = 0, the productAB represents an initial rate of temperature rise ΔT/Δt. The specific absorption rate (SAR) is proportional tothe product, expressed as

SAR = (ΔT / Δt ) (C / mFe)  AB

(2)

Table 1 Hydrodynamic diameter and the productAB of fitting parameters for suspensions of 8 nm
IONPs, and coreshell particles prepared using the
8 nm IONPs.

8 nm IONPs
Core-shell particles

Hydrodynamic
diameter( nm )79-

AB
per Fe mass
( K/(sg Fe))
37
64

Fig. 2 Heating curves of 0.3 mg Fe/mL ofsuspensions of 8 nm IONPs, and coreshell particles
prepared using the 8 nm IONPs.

where C is the heat capacity per unit mass of a
specimen and mFe is the Fe mass per unit mass of a
specimen. Therefore, the values of AB were calculated
from the heating curves of the suspensions of thecoreshell particles and the IONPs as a substitute for
SAR.
To elucidate the difference in magnetic interaction
between IONPs and the core-shell particles, zero-fieldcooled (ZFC) and field cooled (FC) magnetization,
isothermal remanent magnetization (IRM) and direct
current demagnetization (DCD) of the 8 nm IONPs andthe core-shell particles using the IONPs were measured.
The ZFC and FC measurements were conducted at 8.0
kA/m from 5 K to 320 K. The IRM and DCD were
measured at 5 K for delta M plots16). The IRM was
obtained by the following protocol; 1) starting from astate of zero remanence, 2) applying a field, and 3)
measuring magnetization (Mr) after decreasing the fieldto zero. For the DCD, the protocol was 1) saturating thespecimen in a positive field, 2) applying a negative field,
and 3) measuring magnetization (Md) after increasing
the field to zero. Mrs and Mds were obtained bychanging the applying field in each process. The
magnitude of the applying fields was from 12.0 kA/m to638 kA/m, and the field for the saturation was 798 kA/m.
The delta M (M) plots can be obtained by the following
equation16);M = Md  (1  2Mr)

(3)The M expresses the degree of a deviation from asystem without any magnetic interaction between
magnetic nanoparticles. Generally, negative M
represents dipolar-like (demagnetizing) interactions,and positive M indicates exchange-like (magnetizing)
interactions.
3. Results and discussion
The capability of a suspension of the coreshellparticles was superior to that of the 8 nm IONPs
prepared at the same IONP concentration, which was
0.3 mg Fe/mL. Figure 2 shows heating curves of thesuspensions, and Table 1 lists the product AB
calculated from the fitting parameters of these curves.
The product was approximately doubled by theformation of the coreshell particles. We speculated thisimprovement would be induced by the change of theagglomerate state of IONPs. Indeed, the agglomeratestate of IONPs in its suspension seemed considerably
different from that in the coreshell particles. In the
IONP suspension, IONPs agglomerate, resulting in theformation of a secondary particle; the hydrodynamic
diameter measured by dynamic laser scattering (DLS)
was 79 nm. On the other hand, the IONPs on thecoreshell particles relatively exist with a gap and theassembled size is equal to the size of the coreshellparticle as apparently observed in a TEM image of Fig.
3.

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INDEX

Therefore, we focus on agglomerate state, inparticular, on the agglomerate size of IONPs as aparameter to strongly influence the heat generation inorder to discuss the above-mentioned improvement of
the capability in the coreshell particles. The 11 nm
IONPs were employed for this experiment instead of the
8 nm IONPs to obtain larger amount of the heatgenerated from IONPs. The agglomerate size wasmanipulated by adding PVA. We selected ahydrodynamic diameter in the suspensions measured
by DLS as a parameter strongly correlated with theagglomerate size. Open circles in Fig. 4 represent thehydrodynamic diameter of the 11 nm IONPs at PVA
concentration of 0, 0.1, 0.2, 0.5, and 1.0 wt%. The
diameter was increased with the increase of PVA
concentration. The IONP concentration was 0.3 mg
Fe/mL.
Figure 5(a) shows heating curves of the IONP
suspensions with different concentrations of PVA. The
curves were changed by an amount of PVA. However, it
was found that the heat generation under thealternating magnetic field was observed even in PVA

aqueous solutions (aq.) without the IONPs as shown in
Fig. 5(b). The heating of the PVA aq. would be causedby an eddy current loss17),18). The temperature risedepends on the PVA concentration. Therefore, we drew
new curves subtracting the temperature rise of PVA aq.
from heating curves of IONP suspensions, so as toestimate the heat generation induced only by IONPs.
Figure 5(c) shows the recalculated curves, and filled
circles in Fig. 4 indicate the products AB of these
fitting parameters. The product was decreased with theFig. 3 TEM image of coreshell particle preparedusing 8 nm IONPs.

Fig. 4 Dependences of the product AB (filled
circles) and hydrodynamic diameter (open circles) of
11 nm IONPs on PVA concentration of the IONP
suspension.

128

Fig. 5 Heating curves of (a) IONP suspensions
prepared at different PVA concentrations, (b) PVA
aqueous solutions at different concentrations
without IONPs, and (c) curves recalculated bysubtracting (b) from (a).

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

INDEX

increase of the PVA concentration. This result suggeststhat the heat-generating capability is reduced by the
agglomeration.
To corroborate the results about the negative
influence of the agglomeration of IONPs on the heating
capability, the heating capability of IONP suspensions
with different IONP concentrations were evaluated. The
agglomerate size of IONPs can be regulated not only byadding the flocculant such as PVA but also by changing
the concentration of IONPs in the suspension based on
DLVO theory. Hence, the IONP suspensions wereprepared at different IONP concentrations. The
hydrodynamic diameter was increased with the increaseof the concentration as shown in Fig. 6 (open circles).
These heating curves after removing the heating effectof the solvent are shown in Fig. 7. The curves weredrawn by subtracting the heating of water, which is thesame as the result of 0 wt% PVA aq. in Fig. 5(b). The
product of the fitting parameters of the recalculated
curves is indicated in Fig. 6 (filled circles). The productdecreased exponentially with the IONP concentration.
The product AB is proportional to SAR. Therefore, thisresult indicates that the heat-generating capability of
IONPs is reduced by the agglomeration induced byincreasing the concentration of IONPs. The decrease ofSAR at high concentrations has also been demonstrated
in other papers13),19),20).
Figure 8 represents the relationship between thehydrodynamic diameter of IONPs and the product of thefitting parameters; the relationship was obtained fromthe dependences of the hydrodynamic diameter and the
product on the PVA concentration and IONP
concentration seen in Figs. 4 and 6. The productobviously exhibits a linear decrease against the increaseof the diameter, indicating the reduction of the heating
capability with the increase of the agglomerate size.
The tendency has also been reported by otherresearchers although the reason has been unclear21). In
addition, the relationship from the PVA-concentration
dependence (open circles) emerged above that from the
IONP-concentration dependence (filled circles). Because
the hydrodynamic diameter of IONPs with PVA wasevaluated to be larger than that without PVA due to theexistence of PVA, which was a hydrophilic polymer.
The reduction of the capability was probably related
to dipolar interactions between adjacent IONPs in the
agglomerate. Some researchers have reported that thedipolar interaction has a negative influence on SAR,
and three dimensional cluster of magnetic nanoparticles
exhibited the reduction of the heat generation22),23). We
speculate the reason why the interaction will become
greater with the increment of the agglomerate size of
IONPs in the following. One IONP in a larger
agglomerate interacts magnetically with more other
IONPs than that in a smaller agglomerate, resulting in
the increase of dipolar interactions. Therefore, the heatgeneration was reduced with the increase of theagglomerate size of IONPs leading to the increase of

Fig. 6 Dependences of the product AB (filled
circles) and hydrodynamic diameter (open circles) of
11 nm IONPs on IONP concentration of its
suspension.

Fig. 7 Heating curves of IONP suspensions ofdifferent IONP concentrations after removing theheating effect of the solvent, that is the curves
subtracting temperature rise of water.

Fig. 8 The product AB as a function ofhydrodynamic diameter of IONPs in its suspensionschanging PVA concentrations (open circles) and
IONP concentrations (filled circles).

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

129

INDEX

number of IONPs which one IONP interacted with.
We speculate that the improvement of theheat-generating capability by the formation of thecoreshell particles seen in Fig. 2 and Table 1 was
induced by a change of their agglomerate state of
IONPs. The IONPs were deposited on the biodegradable
polymer core with a gap between each IONP in thecoreshell particles. Whereas the assembly of IONPs isa two-dimensional cluster in the coreshell particles,
the agglomerate of IONPs is a three-dimensional
cluster in the IONP suspension, because the IONPs
spontaneously agglomerate in order to reduce surface
energy. The number of IONPs interacting with one
IONP in the coreshell particles is less than that in the
agglomerate of IONPs, which is the three-dimensional
cluster of IONPs. Thus, dipolar interactions in thecoreshell particles are weaker than in the agglomerateof IONPs, resulting in the improvement of theheat-generating capability. Figure 9 shows ZFC-FC
curves of the core-shell particles and the 8 nm IONPs. It
indicates that magnetic property of the core-shellparticles is obviously different from the 8 nm IONPs.

Fig. 9 ZFC (solid line)-FC (dotted line) curves ofcore-shell particles and 8 nm IONPs.

Fig. 10 Delta M plots for core-shell particles and 8
nm IONPs. Hc is coercivity at 5 K.

130

An energy barrier to magnetization reversal in the 8nm
IONPs seems to be larger in consequence of strong
agglomeration. Figure 10 exhibits delta M plotsobtained from IRM and DCD measurements16). The
magnitude of M represents the degree of the magnetic
interaction, and it is always zero in a system of
non-interacting particles according to the Wohlfarth
relationship. The maximum of the deviation from zeroin M was 0.33 for the core-shell particles, which was
smaller than 0.38 for the 8 nm IONPs. The magnetic
interaction, that is probably the dipolar interaction, wasrestrained by the formation of the shell assembly of the
IONPs.
4. Conclusion
The heat-generating capability of the coreshellparticles composed of the biodegradable polymer core
and the iron oxide nanoparticles was discussed in thepresent paper. The capability of the coreshell particles
was superior to that of the original IONPs used for theformation of the coreshell particles. The improvementby the formation of the coreshell particles wereexplained in view of the agglomerate state of magnetic
IONPs correlating to dipolar interaction. We
demonstrated that the heat-generating capability isinversely proportional to the hydrodynamic diameter, inother words, the agglomerate size of IONPs in thesuspension. The dependence on the agglomerate size isprobably explained by the number of IONPs interacting
in the agglomerate. Finally, we concluded the higher
capability of the coreshell particles was brought fromthe difference in the agglomerate state of IONPs
between the coreshell particles and the original IONP
suspension.
Acknowledgement The present work was partially
supported by Kobayashi International ScholarshipFoundation.
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30, 2016

Journal of the Magnetics Society of Japan Vol.40, No.4, 2016

131

INDEX

Editorial Committee Members・Paper Committee Members
H. Saotome and K. Kobayashi ((Chairperson), T. Kato, K. Koike and T. Taniyama (Secretary)
T. Daibou
Y. EndoH. GotoT. Hasegawa
N. Hirota
T. Ichihara
S. Ikeda
K. Iramina
K. Ishiyama
Y. Kanai
T. Kimura
S. Mizukami
H. Morise
T. Morita
T. Nagahama
M. NaoeT. Nishiuchi
T. OjiM. Oogane
T. Sasayama
T. SatoS. Seino
K. Sekiguchi
T. Shima
Y. Shiratsuchi
T. Yamamoto
K. Yamazaki
S. Yoshimura

S. Honda
H. Kikuchi
PHAM NAMHAIF. SatoT. Tanaka

N. Adachi
Y. Hirayama
K. KatoM. Ohtake
M. Takezawa

H. Hashino
H. KatoH. Naganuma
K. Tajima
H. Yuasa

K. Bessho
N. Inaba
A. Kikitsu
T. SatoT. Tanaka

M. DoiS. Inui
K. Miura
M. Sonehara
M. Tsunoda

T. DoiM. Kakikawa
E. Miyashita
T. Saito
S. Yabukami

A. Fujita
S. Kasai
T. Nakagawa
R. Sugita
K. Yamamoto

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優
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PHAM NAMHAI 西 内 武 司 長谷川 崇
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孝
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山本崇史
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哲
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藪上
信

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拓
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貴
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平山義幸

葛西伸哉
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加藤和夫
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別所和宏

金井
靖
清野智史
廣田憲之

菊池弘昭
関口康爾
本多周太

加藤宏朗
角田匡清
三浦健司

喜々津 哲
土井達也
宮下英一

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