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Vol.47 No.6
JournalJournal of the Magnetics Society of Japan
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2023

Thin Films, Fine Particles, Multilayers, Superlattices
Magneto-Optical Spectroscopy of Epitaxial CoxFe3-xO4 (001) Thin Films
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S. Wang, H. Onoda, J. Harbovsky, H. Yanagihara, J. Inoue, M. Veis, and T. Ishibashi

…137

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Journal of the Magnetics Society of Japan
Vol. 47, No. 6

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

CONTENTS
Thin Films, Fine Particles, Multilayers, Superlattices
Magneto-Optical Spectroscopy of Epitaxial CoxFe3-xO4 (001) Thin Films……… S. Wang, H. Onoda, J. Harbovsky, H. Yanagihara, J. Inoue, M. Veis, and T. Ishibashi

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
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J. Magn. Soc. Jpn., 47, 137-143 (2023)<Paper>M a g n e t o - o p t i c a l s p e c t r o s c o p y o f e p i t a x i a l C o xF e 3-xO 4 ( 0 0 1 ) t h i n f i l m s
S. Wang, H. Onoda*, J. Harbovsky**, H. Yanagihara*, J. Inoue*, M. Veis**, and T. Ishibashi

Department of Materials Science and Technology, Nagaoka Univ. of Tech., 1603-1 Kamitomioka, Nagaoka 940-2188, Japan

1-1-1 Tennodai, Tsukuba 305-0006, Japan
Prague 12116, Czech Republic* Department of Applied Physics, Univ. of Tsukuba,** Institute of Physics, Charles Univ.,

The magneto-optical (MO) spectra of spinel cobalt ferrite thin films with different distortions were measured in a
broad range of 0.59 – 3.54 eV. Instead of using the cation substitution method, we prepared cobalt ferrite thin films
with local distortion by using a RF magnetron sputtering method on an Mg2SnO4 buffer layer to induce epitaxial strain.
We derived the diagonal and off-diagonal elements of the dielectric tensor to investigate the influence of distortion on
the MO effect in the films. In the spectra of the off-diagonal dielectric elements, the transitions at 0.8, 1.8, and 2.0 eV,
which correspond to the optical transitions of tetrahedral (Co2+) and octahedral [Co2+], [Fe3+], were assigned to crystal
field (CF) transitions: (Co2+): 4A2 → 4T1(F), 4A2 → 4T1(P) and intervalence charge transfer (IVCT) transition: [Co2+]t2g→ [Fe3+]t2g, respectively. This result revealed that the Co ions were present in both the tetrahedral and octahedral
sites in the epitaxial CFO thin films. By comparing the relative amplitude of each MO transition of cobalt ferrite thinfilms with different distortions, we found that MO spectroscopy is a highly promising tool for evaluating local
distortions.
Keywords: magneto-optical spectroscopy, cobalt ferrite, thin films, dielectric tensor, magnetic anisotropy
1. Introducti on

Recently, it has been reported that a giant
perpendicular magnetic anisotropy (PMA) was induced
by a tetragonal distortion in epitaxially grown spinel
Co0.75Fe2.25O4 thin films 1)–5). A large PMA energy (Ku =1.47 MJ/m3) of Co0.75Fe2.25O4 thin films grown on a MgO(001) substrate was obtained undergoing 0.7% latticemismatch 2). Furthermore, a larger strain was introduced
into the Co0.75Fe2.25O4 thin film by introducing Mg2SnO4(MSO) buffer layers with 3.1% lattice mismatch 5),6),
resulting that a giant PMA energy of 6.1 MJ/m3 was
induced by a large epitaxial strain 6). This value is muchlarger than that of the Nd magnet, 4.9 MJ/m3 7).
Understanding the origin of the large magnetic
anisotropy (MA) energy is crucial for enhancing theperformance of permanent magnets.
The theory predicts that the MA energy of CoxFe3-xO4(CFO) is dependent on the distortion of the octahedral
structure in which Co2+ ions reside 8). To investigate thelocal structure of CFO and its impact on MA, various
methods have been utilized, including X-ray magnetic
circular dichroism (XMCD), X-ray magnetic linear
dichroism (XMLD) spectroscopy, and magneto-optical(MO) spectroscopy. The XMCD and XMLD spectra ofepitaxial CoxFe3-xO4 (x=0.2, 0.6) thin films, prepared bypulsed laser deposition method, revealed that thesubstantial MA energy originates from the large orbital
magnetic moments of distorted octahedron including
Co2+ (3d7), and no signals of tetrahedral Co2+ weredetected 9). In contrast, MO spectroscopy is a convenientmethod for studying the electronic structure of materials
Corresponding

author:T.

t_bashi@mst.nagaokaut.ac.jp).

Ishibashi(e-mail:without the use of a large facility for X-ray source.
Numerous studies on MO spectroscopy of spinel CFO
have been reported 10)–22). Unlike most spinel ferrites
such as Fe3O4, MgFe2O4, Li0.5Fe2.5O4 and NiFe2O4, theMO spectrum of spinel CFO features distinct transitions
in visible region and near-infrared region, due to Co ionsin tetrahedral and octahedral sites 15). As a result, theMO spectroscopy has a potential to be utilized to evaluate
the local structure of CFO thin films.
Previous studies on MO spectroscopy of ferrites haverevealed that the disturbed local symmetry can alter the
MO spectrum by the substitution of nonmagnetic cations
for Fe ions in spinel Fe3O4 22),23) and CoFe2O4 24)–26).
However, substituting other cations affect not only the
local symmetry but also the compositions resulting in achange in their magnetic properties, meaning that MO
spectra are influenced by more than one factor. In
contrast, our study focuses on the effect of distortion on
the MO spectroscopy of CFO thin films without changing
compositions. To solve these problems, we studied
Co0.75Fe2.25O4 thin films with different levels of distortion
by introducing an MSO buffer layer on MgO (001)substrate via RF magnetron sputtering. MO spectra ofepitaxial spinel-type CFO thin films over a wide energy
range (0.59 – 3.54 eV) have been measured for the firsttime. Dielectric tensor of Co0.75Fe2.25O4 thin films were
investigated. Finally, the relationship between local
strain and each optical transition was discussed.
2 . Di e l e c t r i c t e ns o r

The Faraday and Kerr spectra of magnetic thin films
are dependent on the incident angle and orientation ofmagnetization, and thus do not represent an intrinsic
response. In contrast, the dielectric tensor directlyreflects the electronic structure and the transition matrix

Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

137

INDEXof optical transitions. For a uniaxial anisotropy withmagnetization in the z-direction, the dielectric tensor has
the following form,
𝜀𝜀!! −𝜀𝜀!" 00 &,(1)
𝜀𝜀 = #𝜀𝜀!" 𝜀𝜀!!
0
0
𝜀𝜀##
$
$$
+ 𝑖𝑖𝜀𝜀!!
and the offwhere the diagonal element 𝜀𝜀!! = 𝜀𝜀!!
$$$diagonal element 𝜀𝜀!" = 𝜀𝜀!" + 𝑖𝑖𝜀𝜀!" .
The real and imaginary part of 𝜀𝜀!! and 𝜀𝜀!" can be
expressed in terms of refractive index 𝑛𝑛, the extinction
coefficient 𝜅𝜅 , Faraday rotation 𝜃𝜃% , and Faraday
ellipticity 𝜂𝜂% as follows 27),$(2)
= 𝑛𝑛& − 𝜅𝜅 & ,
𝜀𝜀!!
$$
(3)
𝜀𝜀!! = 2𝑛𝑛𝑛𝑛,
𝜆𝜆$(𝑛𝑛𝜂𝜂% − 𝜅𝜅𝜃𝜃% ),
(4)
=
𝜀𝜀!"
𝜋𝜋𝜋𝜋
𝜆𝜆
$$
(𝑛𝑛𝜃𝜃% + 𝜅𝜅𝜂𝜂% ),
(5)
𝜀𝜀!"
=
𝜋𝜋𝜋𝜋
where 𝜆𝜆 is a wavelength and 𝜁𝜁 is a thickness of asample.
From equations (4) and (5), we know that the offdiagonal elements relate to the magnetic properties, andthe off-diagonal elements can be determined bymeasuring the Faraday rotation and ellipticity.
In this study, we used the Lorentz functions todecompose the off-diagonal dielectric tensor elements toeach transition, where the diamagnetic andparamagnetic transitions were considered 28). The
expression of diamagnetic transition is described as,2(ω' − ω) ∗ 𝛤𝛤 − 𝑖𝑖((ω' − ω)& − 𝛤𝛤 & )(6)𝜀𝜀(𝜔𝜔) = 𝐴𝐴 ∙,
ω ∗ ((ω' − ω)& + 𝛤𝛤 & )&and the paramagnetic transition is expressed as,2𝜔𝜔' 𝛤𝛤 − 𝑖𝑖𝜔𝜔' (𝜔𝜔' & − 𝜔𝜔& + 𝛤𝛤 & )(7),𝜀𝜀(𝜔𝜔) = 𝐴𝐴 ∙(𝜔𝜔'& − 𝜔𝜔 & + 𝛤𝛤 & )& + 4𝜔𝜔 & 𝛤𝛤 &where 𝐴𝐴 is transition amplitude, 𝜔𝜔' is resonancefrequency, and 𝛤𝛤 is a half width at half maximum.

3 . Ex p e r i me n t s
3 . 1 S a mp l e p r e p a r a t i o n a n d c h a r a c t e r i z a t i o ns
We prepared two CFO samples, one of CFO thin films
grown on a MgO (001) substrate, and another CFO thinfilm grown on an MSO buffer layer on the MgO (001)substrate. CFO thin film with a thickness of 20 nm was
prepared on MgO (001) substrates as CFO/MgO by thereactive RF magnetron sputtering technique using CoFe
(1:3 atomic ratio) alloy targets. To change the distortionof CFO thin films, an MSO buffer layer of 7 nm thickness
were grown on single crystal MgO (001) substrates at 600ºC by the reactive RF magnetron sputtering using Mg
and Sn metal targets under 0.5 Pa pressure of Ar and O2
mix gas. Then the MSO film was post-annealed at 1000
ºC for 10 min in air. CFO thin film with a thickness of 20
nm was grown on the post-annealed MSO films and MgOsubstrate as CFO/MSO/MgO at 500 ºC using a CoFe (1:3
atomic ratio) metal alloy, under 0.5 Pa pressure of Ar andO2 mix gas.
Magnetization curves were measured by asuperconducting quantum interference device, SQUID-

138

VSM (Quantum Design, MPMS), at fields up to ± 9 T.
Thicknesses of CFO thin films were determined aspectroscopic ellipsometer (M-2000DI-YK, J.A.Woollam).
The crystallinity of prepared CFO thin films wascharacterized by the X-ray diffractometer (Rigaku,
SmartLab) using CuKa1 radiation (l = 0.154059 nm) for
out-of-plane measurements and CoKa1 radiation (l =0.178900 nm) for in-plane measurement monochromized
with a double Ge (220) monochromator.
3 . 2 Me a s u r e me n t s o f o p t i c a l a n d MO p r o p e r t i e s o f C F O
t h i n f i l ms
To investigate the complete dielectric tensor, we used
an ellipsometer to determine the diagonal element, andthe off-diagonal tensor were derived by spectroscopic
ellipsometry and MO spectroscopy. The optical properties
were measured by spectroscopic ellipsometry for anenergy range between 0.73 – 6.02 eV (206 – 1690 nm),
RC2 (J.A.Woollam). The diagonal dielectric elements
were fitted with the Tauc-Lorentz model using theCompleteEASE (J. A. Wollam Co., Inc.) software. MO
spectra ranging from 0.59 – 3.54 eV (350 – 2100 nm) were
measured by a multi-channel MO spectrometer 29).
The MO spectrometer used in this study was shown in
Fig. 1. All optical components of the MO spectrometer
were set on an ordinary optical table. The optical setup
includes a light source, a polarizer, a quarter-wave plate,an electromagnet (Max filed: ± 1.7 T), an analyzer, adetector, and three collimate lenses. A halogen lamp (ULH100L-3, TH4-100, Olympus Inc.) with a power of 100
W was used as a light source. A spatial filter was set infront of the light source, with a variable pinhole in the
focal point of the two N-BK7 plano-convex lenses L1 andL2 (Transmittance > 80% at 350 – 2100 nm). Two GlanThompson prisms with an extinction ratio of 1×105 wereused as a polarizer and an analyzer. Two types of
achromatic quarter-wave plates, SAQWP05M-700(Thorlabs Inc.) for 325 – 1100 nm and SAQWP05M-1700(Thorlabs Inc.) for 600 – 2700 nm, were used in themeasurement of ellipticity. Two types of multi-channel
spectrometers were used. The USB2000+VIS-NIR(Ocean Optics Inc., wavelength range: 350 – 1000 nm)
spectrometer with a 2048-element linear silicon CCD
array detector (ILX511B, Sony Inc.) was used for thevisible light, and the NIRQUEST512-2.5 (Ocean Optics

Fig. 1Illustration of MO multi-channel
spectrometer using Stokes parameter method.
*USB2000 + VIS-NIR, NIRQUEST512-2.5 (Ocean
Optics Inc.)

Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

INDEX

Inc., wavelength range: 900 – 2500 nm) with a 512element InGaAs linear array image sensor (G9208-512W,
Hamamatsu Photonics K.K.) was used for the nearinfrared light. The transmitted light from the analyzer
was focused by the collimation lens L3 into an opticalfiber connected to the multi-channel spectrometer. The
effective measurement range of the MO spectra isconsidered between 350 and 2100 nm (3.54 – 0.59 eV)
according to the above configurations.
In the process of MO measurement, the polarization
axis of the polarizer was fixed to the vertical plane as 0°
all the time, and the analyzer and the quarter wave-plate
are rotated by a stepping motor (DS102, Suruga Seiki).
The magnetic field was applied perpendicular to thesample up to 1.7 T by a double-yoked electromagnet.
To measure the Faraday rotation and Faraday
ellipticity spectra, we measured Stokes parameters,
defined by azimuth angle 𝜃𝜃 and ellipticity 𝜂𝜂 as
described by
𝑠𝑠'
1
𝑠𝑠(
cos 2𝜂𝜂 cos 2𝜃𝜃
(8)@𝑠𝑠 B = @ cos 2𝜂𝜂 sin 2𝜃𝜃 B .
&𝑠𝑠)sin 2𝜂𝜂
In this case, azimuth 𝜃𝜃 can be expressed as an equation,𝑠𝑠&1𝐼𝐼+,° − 𝐼𝐼(),°1(9)
M,𝜃𝜃 = tan*( L M = tan*( L𝑠𝑠(𝐼𝐼'° − 𝐼𝐼.'°22
where 𝐼𝐼'° , 𝐼𝐼+,° , 𝐼𝐼.'° , and 𝐼𝐼(),° are optical intensities
measured with the analyzer angles of 0º, 45º, 90º, and135º, respectively. For measuring the Faraday ellipticity
spectra, the analyzer is fixed to 0°, and the fast axis of
the quarter wave-plate is rotated to –45°, +45° with thepolarizer, corresponding to left-handed circularpolarization(LCP),
andright-handed
circularpolarization (RCP), respectively. Ellipticity 𝜂𝜂 can be
expressed by,𝑠𝑠)
1
𝐼𝐼/01 − 𝐼𝐼201
1
(10)
M,
𝜂𝜂 = sin*( L M = sin*( L𝑠𝑠'
𝐼𝐼/01 + 𝐼𝐼201
22
where 𝐼𝐼/01 and 𝐼𝐼201 are the intensities at the detector
obtained with polarization states of LCP, and RCP.
Using the above method and a multi-channel
spectrometer, Faraday rotation and Faraday ellipticity
spectra can be acquired within a mere 5 minutes. To
ensure accuracy, all Faraday spectra are averaged in
opposite magnetic field directions and calibrated 29),30),
effectively removing any offset due to the optical setup.
The measurement of Faraday rotation and ellipticity
spectra was conducted at room temperature.

Compared to the lattice constant of bulk CFO (a = 0.838nm), out-of-plane compressive strains of CFO thin films
in CFO/MgO and CFO/MSO/MgO were determined to be𝜀𝜀3 = −0.418% and 𝜀𝜀3 = −0.728%, while in-plane tensile
strains were 𝜀𝜀∥ = 0.537% and 𝜀𝜀∥ = 0.704% for
CFO/MgO and CFO/MSO/MgO, respectively. These
values are comparable to those reported previously 2),5).
The total distortions 𝜒𝜒 of CFO thin films were defined as𝜒𝜒 = 𝜀𝜀∥ − 𝜀𝜀3 6), 0.955% and 1.432% for CFO/MgO andCFO/MSO/MgO. These results indicated that both CFO
thin films are distorted by the lattice mismatch. The
larger distortion in CFO/MSO/MgO was induced by the
MSO buffer layer with larger lattice constant comparedto the MgO substrate. Additionally, Laue oscillation wasobserved in the XRD pattern for the CFO/MgO sample
shown in Fig. 2 (a), indicating excellent crystallinity anda smooth surface of CFO thin films. Postannealed MSO
layer was investigated by reflection high-energy electron
diffraction (RHEED) and cross-sectional transmission
electron microscopy (TEM) previously, indicating thatMSO layer is single crystal with a flat surface 6).
Fig. 3 shows magnetization curves of CFO thin films,
which were measured with magnetic fields applied
perpendiculartotheplane.
The
saturation
magnetization (Ms) was measured to be 395 kA/m forboth CFO/MgO and CFO/MSO/MgO thin films, which

4. Resul t s and di scussi on

X-ray diffraction (XRD) patterns of CFO/MgO andCFO/MSO/MgO measured in both in-plane and out-ofplane orientations are shown in Fig. 2. In Fig. 2 (a),diffraction peaks observed at 2q = 95.20° for CFO/MgO
and 95.59° for CFO/MSO/MgO correspond to the 008
diffractions of CFO with the spinel-type structure with c= 0.8345 and 0.8319 nm, respectively. In-plane lattice
constants of CFO thin films are determined from CFO(220) diffractions in Fig. 2 (b) to be a = 0.8425 nm for
CFO/MgO and a = 0.8439 nm for CFO/MSO/MgO.

Fig. 2 XRD patterns of CFO/MgO and CFO/MSO/
MgO. (a) Out-of-plane patterns in range of 85 – 100º,(b) In-plane patterns in range of 30 – 40º.

Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

139

INDEX$$
Table 1 Parameters used to fit diagonal elements 𝜀𝜀!!
of
CFO thin films on MgO and MSO/MgO. Lists are peak
position 𝜔𝜔' (eV), full width at half maximum 𝛤𝛤 (eV),amplitude 𝐴𝐴 of each oscillator (Osc.).

Sample
CFO/
MgO
CFO/
MSO/
MgO

Fig. 3 Out-of-plane hysteresis loop of CFO thinfilms prepared on MgO and MSO/MgO substrates,
measured by SQUID magnetometry.

Fig. 4 Diagonal elements of dielectric tensor of CFO
thin films on MgO and MSO/MgO.

was close to that of bulk CFO crystal, 425 kA/m 2). The
fact that the CFO thin films have Ms comparable to thatof bulk CFO crystal suggests that the distortion has not
significantly affected the saturation magnetization. On
the other hand, the CFO/MgO and CFO/MSO/MgO thinfilms exhibited different coercive fields of 5.94 A/m and12.63 A/m, respectively, depending on the distortion.
These characteristics of these CFO thin films used in thisstudy is consistent with previous reports 5),6).
$$$and 𝜀𝜀!!
The diagonal elements of dielectric tensor 𝜀𝜀!!
of CFO thin films are shown in Fig. 4. Five oscillators
were considered to fit the imaginary part of diagonal
elements of the dielectric tensor of these CFO thin films,
where the parameters used for the fitting are listed inTable 1. Thicknesses of the CFO thin films were
determined to be 25.27 ± 0.03 nm for CFO/MgO and 22.47± 0.09 nm for CFO/MSO/MgO, respectively. Thicknessesof the MSO buffer layer was determined to be 7.00 ± 0.39
nm. Postannealed MSO layer was also investigated,
resulting in a roughness of 1.05 nm, which indicates that

140

!!
"

Osc. 1

Osc. 2

Osc. 3

Osc. 4

Osc. 5

2.17

3.24

3.71

5.53

9.04

1.97

0.59

1.53

3.23

0.0001#15.509

1.495

9.403

21.694

11.468

2.25

3.21

3.69

5.51

7.78

"

1.96

0.64

1.50

3.28

0.41

16.327

1.933

9.038

21.613

3.859

!!
#

the MSO has a flat surface. The fitting was carried out
with small mean squared error (MSE) of 1.669 for
CFO/MgO and 2.025 for CFO/MSO/MgO. The real part of$of CFO thin films showed a broad
diagonal elements 𝜀𝜀!!
structure with two dominant peaks at 1.9 and 3.0 eV. The$$
showed that aimaginary part of diagonal elements 𝜀𝜀!!
$broad absorption from 1.3 eV. It was found that the 𝜀𝜀!!
of CFO/MgO is lower than that of CFO/MSO/MgO$$, the intensity of
between 0.73 and 3.1 eV. For 𝜀𝜀!!
CFO/MSO/MgO is larger than that of CFO/MgO between
1.5 – 4.5 eV. These differences can be attributed to theenhancement of optical absorption caused by theincreased distortion of CFO thin films.
Fig. 5 shows the Faraday rotation and ellipticity
spectra of the CFO thin films in range of 0.59 to 3.54 eV.
Faraday spectra of MgO (001) substrate and MSO buffer
layer measured under the same magnetic field weresubtracted from the measured spectra to eliminate theinfluence of the Faraday effect. As the applied magnetic
field cannot fully saturate both samples in thesemeasurements, the MO spectra with fully saturated were
estimated. Using the magnetic hysteresis loop, theestimated MO spectra were obtained by multiplying
coefficients of 1.53 and 2.16 for CFO/MgO andCFO/MSO/MgO, respectively, where those coefficientswere obtained by a ratio of a magnetization measured at
1.7 T and a saturation magnetization.
The Faraday spectra are in good agreement with thoseof the bulk spinel CoFe2O4 10),14). Both CFO thin films
exhibited a broad intense negative peak between 1.3 and2.8 eV and a narrow dispersion-type transition at 0.8 eV.
Although the transition energies did not change, theintensity of the rotation and ellipticity spectra increases
significantly in the CFO/MSO/MgO. To understand themicroscopic origin of the MO effect, we have derived theoff-diagonal elements 𝜀𝜀!" of the dielectric tensor using
equations (4) and (5).
Fig. 6 shows the spectra of real part and imaginary
part of 𝜀𝜀!" of the CFO thin films in the region between
0.73 and 3.54 eV. The structures of 𝜀𝜀!" of CFO thinfilms are in good agreement with the previous MO study
on bulk CFO crystals 10). To evaluate each opticaltransition, we fitted the real part of the off-diagonal$using equations (6) and (7).
dielectric tensor element 𝜀𝜀!"Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

INDEX

Fig. 5 Faraday rotation 𝜃𝜃5 and ellipticity 𝜂𝜂5spectra of CFO/MgO and CFO/MSO/MgO.

Fig. 6 Off-diagonal elements of dielectric tensor of
CFO thin films on CFO/MgO and CFO/MSO/MgO.

The assignment of MO transitions was based on previous
MO spectroscopic studies of CFO 10),15),22). The fitting
results are presented in Fig. 7. The fitting parameters,
including the transition amplitude A, peak position 𝜔𝜔'(eV), and half width at half maximum 𝛤𝛤 (eV), aresummarized in Table 2. Five MO transitions at 0.80, 1.32,
1.76, 2.05, and 2.50 eV were considered for both two CFO
thin films.
The MO spectra exhibited a diamagnetic transition
characterized by two peaks of opposite sign at 0.80 eV in
the low photon energy region, as well as a paramagnetictransition featuring a single negative peak at 1.76 eV.
These transitions are similar to those reported in Ref. 31),
where optical transitions were found at 0.86 and 1.98 eVcorresponded to two types of crystal-field (CF) transitionsof tetrahedral Co2+: 4A2 → 4T1(F) and 4A2 → 4T1(P) in Codoped ZnO single crystals. Therefore, we assigned the
diamagnetic transitions at 0.80 eV to the CF transitionof Co2+: 4A2 → 4T1(F), and the paramagnetic transition at
1.76 eV was assigned to the CF transition of Co2+: 4A2 →4T1(P). An intense broad paramagnetic transition at 2.05
eV is assigned to an IVCT transition: [Co2+]t2g → [Fe3+]t2g,
as identified by Peeters and Martens in polycrystalline
bulk CFO 13). A weak diamagnetic transition is observed

Fig. 7 Fitting to real part of off-diagonal dielectric
tensor elements of CFO thin films. (a) CFO/MgO, (b)CFO/MSO/MgO.

at 2.50 eV with two opposite peaks, consistent with apreviously reported transition at 2.6 eV in bulk spinel
Fe3O4 23), and assigned to an ISCT transition: (Fe3+)t2 →[Fe2+]t2g. Additionally, our fitting results obtained abroad paramagnetic transition at 1.32 eV with a positive
peak, which has not be previously discussed in CFO.
However, the exact assignment of this transition cannot
be confirmed in this study. It might be related to a CF
transition of tetrahedral Co3+: 5E → 5T2, as reported in(YGd)3(CoxFe5-x)O12 thin films at 0.95 eV 32),33), but
further investigation is needed to confirm this transitionin CFO.
The IVCT transition of [Co2+]t2g → [Fe3+]t2g and the CF
transitions of (Co2+): 4A2 → 4T1(F) and 4A2 → 4T1(P)associated with octahedral and tetrahedral sites wereobserved in both samples, as previously assigned. This
result suggests that Co2+ is not only present in theoctahedral site but also in the tetrahedral site. Previous
studies have indicated that the Co cations only exist in
the octahedral sites for epitaxial CFO thin films 6),9).
However, our finding demonstrates that the epitaxial
Co0.75Fe2.25O4 thin film is not a complete inverse-spinel
structure, despite having a lower Co composition than
CoFe2O4. Previous interpretations of the MA in epitaxial
CFO as originating solely from the large orbital magnetic

Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

141

INDEX

Table 2 Optical transitions of CFO thin films on CFO/MgO and CFO/MSO/MgO between 0.73 and 3.54 eV. Lists arepeak position 𝜔𝜔' (eV), half width at half maximum 𝛤𝛤 (eV), amplitude 𝐴𝐴, and assignment of each transition.
Tetrahedral and octahedral sites are denoted by ( ) and [ ], respectively.
Type
Assignment

CFO/MSO/MgO

CF

CF

IVCT

ISCT

(Co2+):(Co3+):(Co2+):[Co2+]t2g(Fe3+) t2

A2 → 4T1(P)→ [Fe3+]t2g→ [Fe2+]t2g

A2 → 4T1(F)

4

Shape
CFO/MgOCF

E → 5T2

5

dia

para

para

para

dia

0.80

1.32

1.76

2.05

2.50

0.11

0.35

0.10

0.35

0.18

#

0.00100.0342-0.0280-0.2550-0.0009

0.80

1.32

1.76

2.05

2.50

"

0.11

0.35

0.10

0.35

0.20

0.00190.0624-0.0473-0.4463-0.0020

!!
"

!!
#

moment of the octahedral Co2+ due to epitaxial strain 9),34),
ignoring the effect of tetrahedral Co2+. However, we havefound that Co2+ is also present in tetrahedral site inepitaxial CFO thin films, suggesting that the origin of
PMA in epitaxial CFO thin films needs to be re-evaluated.
Compared to the MO spectra of these two CFO thinfilms, we noticed a significant increase in the transition
amplitude of all MO transitions in CFO/MSO/MgO. The
IVCT transition [Co2+]t2g → [Fe3+]t2g amplitude increased
1.75 times from –0.2550 in CFO/MgO to –0.4463 in
CFO/MSO/MgO. Similarly, the transition amplitude of
the CF transition (Co2+): 4A2 → 4T1(F) at 0.86 eV
increased 1.90 times from –0.0010 in CFO/MgO to –0.0019 in CFO/MSO/MgO. We attribute the alteration of
the IVCT transition to the octahedral symmetry
perturbation caused by the epitaxial tensile strain. This
perturbation increases the distance between [Fe3+] and[Co2+] for adjacent octahedral sites along the a-axis. As
the oscillator strength of the IVCT transition is sensitive
to changes in the lattice, the longer lattice constant of the
CFO leads to a decrease in the transition amplitude of
the IVCT transition [Co2+]t2g → [Fe3+]t2g, as reported by
Fontijn et al.23).
Additionally, an increase in the CF transition (Co2+):
4A2 → 4T1(F) at 0.86 eV in CFO/MSO/MgO was observed,
with an amplitude 1.75 times higher than that oftetrahedral Co2+ in CFO/MgO. We considered that thisincrease is attributed to the perturbation of thetetrahedral symmetry caused by the epitaxial tensile
strain, which affects not only the octahedral symmetry
but also the trigonal symmetry of the tetrahedral
structure 23). Calculation results have shown that the Co
L23-edge absorption in the tetrahedral symmetry
increases with the increasing crystal field 35), which isconsistent with our results. Our findings suggest that the
distorted tetrahedral symmetry in CFO thin films
enhances the tetrahedral CF transitions.
Finally, we compared the intensity ratios of theoctahedral transition ([Co2+]t2g → [Fe3+]t2g) to the142

4tetrahedral transition ((Co2+): 4A2 → 4T1(F)) in CFO/MgO
and CFO/MSO/MgO. The ratio was found to be 1 : 0.34
for CFO/MgO and 1 : 0.37 for CFO/MSO/MgO. The slightdifference in ratio may be explained by the different
cation distributions caused by the distortion. Frisch etal.36) reported that the epitaxial tensile strain reduces
inversion, which shift Co from the octahedral site to thetetrahedral site. This shift results in an increase in thetetrahedral transition compared to the octahedraltransition. Therefore, the enhanced tetrahedraltransition intensity in CFO/MSO/MgO is consistent withthe cation distribution changes induced by epitaxial
tensile strain as reported by Frisch et al.36). However,further research is necessary to quantitative evaluate thecomposition of CFO.
5. Concl usi on

We investigated two types of high-quality spinel-type
CFO thin films prepared on MgO and MSO/MgO
substrates by the RF magnetron sputtering method,which had different strains of 0.955% and 1.432% ,respectively, induced by lattice mismatching. Dielectric
tensors of those CFO thin films were deduced from theoptical and Faraday spectra. By observing MOtransitions of tetrahedral (Co2+) and octahedral [Co2+] inboth samples, we revealed that Co ions are present inboth tetrahedral and octahedral sites in the epitaxial
CFO thin films. Furthermore, comparison of theamplitude of each transition indicated that the induced
tensile strain leads to an enhancement of MO transitionsin CFO thin films. Our results suggest that the MO
spectroscopy serves as a sensitive tool for qualitatively
investigating cation distribution in CFO thin films,
demonstrating the potential for qualitative evaluation of
local strain and laying the groundwork for future
quantitative analyses of local strain in CFO thin films.
Acknowledgements The authors acknowledge funding
from the Japan Science and Technology Agency (JST)Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

INDEX

under Collaborative Research Based on Industrial
Demand“High-Performance
Magnets:
TowardInnovative Development of Next-Generation Magnets”
under Grant JPMJSK1415. We also thank Prof. Asadaand Dr. Kimura for the measurement of the ellipsometryat the Center for Instrumental Analysis, Yamaguchi
University.
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Received May 14, 2023; Accepted Jul. 18, 2023

Journal of the Magnetics Society of Japan Vol.47, No.6, 2023

143

INDEX

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

K. Bessho
S. Honda
S. Muroga
Y. Shiota
S. Tamaru

M. DoiS. Isogami
M. NaoeS. Sugahara
S. Yoshimura

T. DoiT. Kawaguchi
T. Narita
I. Tagawa

T. Hasegawa
N. Kikuchi
Y. SatoK. Tajima

K. ItoA. Kuwahata
E. Shikoh
M. Toko
R. Hashimoto
K. Kobayashi
S. Seino
M. Takezawa

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

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

桑波田晃弘
田中哲郎
八尾
惇

小嶋隆幸
都甲
大
家形
諭

安達信泰
関野正樹
成田正敬

小林宏一郎
田島克文
別所和宏

菅原
聡
土井正晶
室賀
翔

清野智史
直江正幸
吉村
哲

磯上慎二
田倉哲也
白
怜士

川口昂彦
田河育也
橋本良介

菊池伸明
竹澤昌晃
長谷川 崇

佐藤佑樹
田丸慎吾
本多周太

塩田陽一
土井達也
槙
智仁

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