In this study, various Fe-based thermoelectric full-Heusler thin films were fabricated on MgO substrates by a post-annealing process. It is clarified that crystal growth through the post-annealing process is prevented by both an initial crystallization and a lattice mismatch between the thin films and the substrate. One of the thermoelectric materials, namely, Fe2TiAl, was almost epitaxially grown on the substrate from an initial amorphous state owing to a small mismatch of less than 3%. The thermoelectric properties of Fe2TiAl-based thin films were modulated by changing the material composition. We found that they strongly depend on not only the valence electron concentration and the Fe amount as was observed in typical thermoelectric full-Heusler, Fe2VAl, but also the electronic band structures. The flat band in the conduction band strongly affects not only the n-type thermoelectric performance but also the p-type ones; the large density of states in the conduction band prevents the p-type Seebeck coefficient from increasing. The Seebeck coefficient of a V-added Fe2TiAl thin film with a composition of Fe2.01Ti0.56V0.67Al0.76 was increased to 99 µV/K by controlling the flat band in the conduction band away from the valence band to reduce the effects of the flat band, resulting in a dimensionless figure of merit of 0.12 at room temperature.

There is a strong demand for the recovery of wasted heat at room temperature (RT) because over two-thirds of wasted heat is known to exist below 300 °C. Although thermoelectric (TE) conversion is a promising solution to this problem, only a few TE materials such as Bi2Te3 and related compounds exhibit good performance (ZT > 1) at room temperature.1–3 Here, ZT is a dimensionless figure of merit given by S2T/ρ(κe + κl), where S is the Seebeck coefficient, ρ is the resistivity, T is the temperature, κe is the electrical thermal conductivity, and κl is the lattice thermal conductivity. Fe-based full-Heusler (FH) alloys are promising candidates for such room-temperature applications because of the low cost, abundance, and non-toxicity of their constituent elements. For example, Fe2VAl-based FH alloys show a large power factor (PF) defined by S2/ρ compared to well-known TE materials such as Bi2Te3.4,5 Although several FH alloys such as Fe2TiSn1−xSix have been predicted to show high TE performance owing to the electronic flat band with a large density of states (DOS) in the Γ–X region,6,7 not many FH alloys are known to be chemically stable, except for Fe2VAl and Fe2TiSn.8,9 Recently, thin-film techniques have been shown to be effective for stabilizing meta-stable phases, as clarified in the case of Fe2TiSi films grown on MgAlO4 substrates with simultaneous annealing.10,11 As various compositions are required to realize high-performance TE materials, rapid processing such as post-annealing is strongly desired.

In this study, the growth conditions of Fe-based FH alloys in the post-annealing process were investigated. Furthermore, the importance of lattice matching with the substrate and the initial amorphous state was clarified in the growth of FH phase. In the case of Fe2TiAl-based FH alloys, almost epitaxially grown FH phases were obtained and the valence electron concentration (VEC) was modulated by adding chips of other elements on the sputtering target to improve the TE properties. Not only the VEC and Fe amount but also the bandgap strongly affected the PF; consequently, a large S of 99 µV/K and a ZT of 0.12 were obtained in the case of in Fe2.01Ti0.56V0.67Al0.76 as a p-type TE material.

The samples were prepared as follows: FH thin films were deposited on MgO (001) substrates by magnetron sputtering under a base pressure of 10−6 Pa at room temperature (RT). The sputtering targets used were Fe2TiSn, Fe2NbAl, Fe2TiAl, Fe2VAl, Fe2TiSi, and Fe2VSi, which have been investigated as potential TE materials.4–9,11–15 To vary the composition of the thin films, various square chips of V, Cr, Mn, Fe, and Co (side, 10 mm) were placed on circular FH alloy targets (diameter, 120 mm). The samples are abbreviated as “target + chip(n).” Here, “target” refers to the material of the used target, “chip” refers to the material placed on the target, and “n” denotes the number of chips placed on the target. The samples were then annealed at a temperature of 800 °C under a base pressure of 10−6 Pa for 1 h. The thickness of the deposited thin films was 200 nm in the as-deposited state, and it was reduced to around 180 nm by the post-annealing process.

The film structure was characterized by cross-sectional transmission electron microscopy (TEM) (Hitachi, H-9000UHR), cross-sectional high-angle annular dark-field scanning TEM (HAADF-STEM) (Hitachi, HD-2700), and electron diffractometry. The crystal structure of the films was characterized on the basis of out-of-plane x-ray diffraction (XRD) measurements (Rigaku, RINT1400) with a Cu Kα radiation source. The diffraction patterns were collected via ω–2θ scanning in the 2θ range of 25°–70°. The film composition of the entire film was determined via inductively coupled plasma-atomic emission spectroscopy (ICP-AES), and the local film composition was evaluated via energy dispersive x-ray spectroscopy (EDX). The in-plane S and ρ at temperatures above RT were measured using two- and four-probe methods, respectively (ADVANCE RIKO, ZEM-3). Careful configurations were adopted to evaluate intrinsic S of thin films because shunts of electric and thermal flow to the substrates prevent evaluations of the intrinsic S in the case of substrates with low resistivity such as Si substrates (see supplementary material 1). The in-plane S and ρ at temperatures below RT were measured using the two-probe method and the van der Pauw method, respectively (TOYO Technica, ResiTest8300). The out-of-plane κ at RT was evaluated using the picosecond thermo-reflectance method (PicoTherm), which has been reported in a previous study,16 and Mo(105) was applied on the top of the film as a reflective coating. The Hall measurements were obtained under a maximum magnetic field of 0.56 T using the van der Pauw method (TOYO Technica, ResiTest8300). The electronic structures of the FH alloys were determined after optimizing the lattice constants by first-principles calculations using OPENMX code based on density-functional theory (DFT) under the generalized gradient approximation (GGA).17–19 

Figure 1(a) shows the out-of-plane XRD patterns of a ω–2θ scan of the Fe-based FH alloy thin films in the as-deposited state. Here, the vertical axis representing the intensity is shown in the logarithmic scale. All the films except for Fe2VAl show no specific diffraction peak other than the peaks from the MgO substrates with the (001) orientation, indicating amorphous films. In the case of Fe2VAl, which is known to be a stable ternary material, the diffraction peak was observed at 2θ of ∼64.5°, indicating the existence of body-centered-cubic (BCC) Fe along the (002) direction or disordered Fe2VAl along the (004) direction. Figure 1(b) shows the out-of-plane XRD patterns of a ω–2θ scan of the Fe-based FH alloy thin films annealed at 800 °C. For all the films, strong (00L) diffraction peaks were observed in addition to those from the MgO substrates, indicating that the FH alloy phases grew almost epitaxially along the (001) orientation in the majority of the films, as observed in previous studies.20–22 Note that the adopted fabrication method, i.e., crystallization from amorphous states with MgO seed layers, facilitated the crystallization of not only stable FH alloys such as Fe2TiSn, Fe2TiAl, and Fe2VSi but also unstable FH alloys such as Fe2NbAl and Fe2TiSi, which have not been obtained in bulk. However, the diffraction peak of an impurity phase was observed at 2θ of ∼41° in the case of Fe2NbAl possibly because of the instability of Fe2V1−xNbxAl bulk, as reported previously.13 The (022) diffraction peak was also observed in the case of Fe2VAl, while such a peak was not observed in the case of other Fe-based FH alloys. As Fe2VAl is known as a fairly stable ternary material, these results suggest that stable phases could be easily formed by post-annealing without the seed effects from the MgO substrates and that initial crystallization would prevent the epitaxial growth of the FH phases. In fact, a recent study on Co2(Mn, Fe)Ge showed that the initial amorphous states are important for the growth of FH phases from seed layers.23,24

FIG. 1.

XRD patterns of Fe-based FH thin films sputtered on MgO substrates: (a) as-deposited and (b) annealed at 800 °C.

FIG. 1.

XRD patterns of Fe-based FH thin films sputtered on MgO substrates: (a) as-deposited and (b) annealed at 800 °C.

Close modal

Hereafter, we focus on Fe2TiAl because this material has a small lattice mismatch without any impurity phase, as clarified in Fig. 1(b) (see also supplementary material 2 and 3). The cross-sectional TEM image of Fe2TiAl is shown in Fig. 2(a). Large grains with a size of ∼100 nm were observed. The local compositions were evaluated via EDX point analysis, and all the points shown in Fig. 2(a), denoted as 1–6, were clarified to have nearly the same composition, suggesting homogeneously grown films. The local composition measured via EDX (Fe2.24Ti0.78Al0.98) was comparable to the film composition measured via ICP-AES (Fe2.18Ti0.73Al1.09). Figure 2(b) shows a cross-sectional DF-STEM image of region b in Fig. 2(a). In the vicinity of the interface between the Fe2TiAl film and the MgO substrate, both lattices seem to connect smoothly, suggesting an epitaxial growth from the substrate. Figure 2(c) shows an image of the inverse fast Fourier transformation in region c, where the grain boundary exists. There is a small contrast between the grains, suggesting a small stress, whereas the lattice seems to be distributed nearly homogeneously. Figures 2(d)–2(f) show electron diffraction patterns of points 4, 5, and 6, respectively. The difference in the crystal orientation both between the grains and between the Fe2TiAl film and the MgO substrate was less than 1%. These results suggest that the Fe2TiAl film fabricated by the post-annealing process was an epitaxially grown single phase with homogeneous elemental compositions.

FIG. 2.

Cross-sectional TEM analysis of the Fe2TiAl film: the (a) TEM image, (b) DF-STEM image, and (c) inverse FFT image. Electron diffraction patterns at (d) point 4, (e) point 5, and (f) point 6.

FIG. 2.

Cross-sectional TEM analysis of the Fe2TiAl film: the (a) TEM image, (b) DF-STEM image, and (c) inverse FFT image. Electron diffraction patterns at (d) point 4, (e) point 5, and (f) point 6.

Close modal

Next, we investigated the thermoelectric properties of the element-added Fe2TiAl-based films. To improve the thermoelectric performance, the carrier concentration should be reduced because, in general, the metallic states are known to have small S. The composition of the film was varied by adding other element chips, as explained in the experimental section (see also supplementary material 4). Figures 3(a) and 3(b) show S and ρ, respectively, of Fe2TiAl + TM(n) films (TM ≡ V, Fe, Cr, Mn, and Co) as a function of VEC. Here, S and ρ of the Fe2TiAl-based bulks (Fe2−xCoxTiAl) are also plotted in the figures.14 Our Fe2TiAl-based thin films showed relatively large S compared to the Fe2TiAl-based bulks although the annealing temperature of 800 °C is lower than the FH bulks. If the initial state of the film has metastable states such as amorphous or nanocrystals same as our cases, a high free energy for crystallization or crystal growth enables the chemical ordering at relatively low temperatures as discussed in the literature.23 In addition, most of our films have the Fe amount larger than the stoichiometric value of 2.0, which is known to increase p-type S larger owing to the created anti-sites.5 If we consider the dependence of S on VEC in further detail, we find that most of the films show nearly the same trend whereby S increases gradually and becomes ∼40 µV/K at a VEC of ∼6.0 when the VEC is decreased. These observations suggest that the fabricated films were successfully carrier-doped by adding other elements on the Fe2TiAl target. Both S and ρ of the films varied depending on VEC; however, the change was small compared to those of the bulks, which rapidly changed at a VEC of ∼6.0, originating from the carrier-type change as clarified in previous studies on semiconducting FH bulks.4,5 The observed weak dependence of the films on the VEC may be because the addition of elements as chips in this study caused not only a change in the VEC but also a reduction in the Fe amount. Doped thermoelectric FH alloys such as Fe2V1−aXaAl and Fe2VAl1−bYb show a change in S mainly depending on the VEC owing to the change in both the carrier concentration and the carrier type in a rigid band model, consequently showing a universal curve of S depending on not kinds of substituents but only VEC.4,25 On the other hand, the decrease in Fe is known to affect the amount of anti-sites and consequently shift the universal curve of S depending on VEC to the lower VEC side.5,26,27 When the chip is added on the Fe2TiAl target with the valence electron count different from the VEC of thin films without the addition, the added chip causes not only a change in the VEC but also a reduction in the Fe amount, simultaneously causing a shift of the universal curve to the lower VEC side. Our films are considered to show weaker dependence on the VEC than the bulks owing to the above-mentioned reasons.

FIG. 3.

Dependence of thermoelectric properties of Fe2TiAl-based films on VEC: (a) the Seebeck coefficient and (b) resistivity. The dashed line represents Fe2−xCoxTiAl bulks.14 

FIG. 3.

Dependence of thermoelectric properties of Fe2TiAl-based films on VEC: (a) the Seebeck coefficient and (b) resistivity. The dashed line represents Fe2−xCoxTiAl bulks.14 

Close modal

Most of the Fe2TiAl-based films, except for those with V-additions and Fe2TiAl-based bulks, shown in Fig. 3(a) have small S and ρ less than 50 µV/K and 7 μΩ m, respectively, even at a VEC of ∼6.0. This suppression may be due to the strong bipolar effects of a flat band in the conduction band. Figures 4(a) and 4(b) show the band structure around the Fermi level of Fe2TiAl and Fe2VAl, respectively. Both band structures have several characteristic bands: a parabolic band in the conduction band at the X-point (“para-1”) originating from the Ti and V eg orbitals, a flat band in the conduction band in the Γ–X direction (“flat”) originating from the Fe eg orbitals, and a parabolic band in the valence band at the Γ-point (“para-2”) originating from the Fe t2g orbitals. The flat band is known to have a larger density of states than the parabolic bands and strong effects on the thermoelectric properties, as clarified in previous reports.6,7,28 As shown in Fig. 4(a), in the case of Fe2TiAl, the flat band is located at the bottom of the conduction band, and the energy difference between the conduction band and the valence band is only 0.18 eV. As shown in Fig. 4(c), a sharp rise in the density of state (DOS) originating from the flat band (“flat”) is observed at the bottom of the conduction band when the composition is stoichiometric, while a rather small DOS originating from the parabolic band (“para-2”) exists at the top of the valence band. As the energy gap of Fe2TiAl is small, bipolar conduction affects S as follows:

S=σpSp+σnSnσp+σn,
(1)

where σp, σn, Sp, and Sn are the conductivities and Seebeck coefficients for p-type and n-type carriers, respectively. The flat band is known to show a large Sn and thus prevents p-type S from taking large values when the majority carriers are not electrons but holes. In other words, the large DOS of the minority carriers (electrons) makes it difficult to shift the chemical potential η when the temperature increases, thereby increasing the thermoelectromotive force at a constant temperature difference because η is known to maintain the carrier concentration and is affected by bands with a large DOS. Therefore, it is important to increase the p-type S to move the flat band away from the valence band (“para2”). In fact, only small Sp less than 50 µV/K was observed in previous reports on Fe2TiSn, which also has a flat band at the bottom of the conduction band, and the energy gap is small (0.07 eV).6 

FIG. 4.

Calculated band structures of (a) Fe2TiAl and (b) Fe2VAl, (c) the DOS of Fe16Ti8−xVxAl8, and (d) energy difference of Fe16Ti8−xVxAl8.

FIG. 4.

Calculated band structures of (a) Fe2TiAl and (b) Fe2VAl, (c) the DOS of Fe16Ti8−xVxAl8, and (d) energy difference of Fe16Ti8−xVxAl8.

Close modal

It is worth noting that the V-doped films, namely, Fe2TiAl + V(n) and Fe2TiAl + V(6) + Fe(n), showed a larger S than the other films, which reached a maximum of 99 µV/K in the case of Fe2TiAl + V(6) + Fe(3), as shown in Fig. 3(a). We suspect that the enhancement of S in the case of the Fe2.01Ti0.56V0.67Al0.76 film originated from the modifications of the band structures induced by the substitution of Ti by V. In the case of Fe2TiAl, the flat band with a large DOS is located at the bottom of the conduction band, and it strongly affects the thermoelectric properties as discussed above. Meanwhile, the parabolic band (“para1”) is located at the bottom of the conduction band and the flat band (“flat”) exists in the high-energy state in the case of Fe2VAl, as shown in Fig. 4(b). From these results, by substituting Ti of Fe2TiAl by V, the flat band can be moved to a higher energy, and the parabolic band can be moved to a lower energy. In fact, as shown in Fig. 4(c), the bottom of the conduction band of Fe16Ti4V4Al8 has a small DOS owing to the parabolic band (“para1”), whereas that of Fe16Ti6V2Al8 has a large DOS owing to the flat band (“flat”). The calculated energy difference between the flat band (“flat”) and the parabolic band in the valence band (“para2”) monotonically increases with the V amount in the case of Fe16Ti8−xVxAl8, as shown in Fig. 4(d). Meanwhile, the calculated energy difference between the valence and conduction bands is nearly the same for Fe16Ti8Al8 and Fe16Ti4V4Al8.

To clarify the origin of the enhancement of S experimentally, we focus on the temperature dependence of the thermoelectric properties. Figures 5(a) and 5(b) show S and ρ, respectively, of Fe2TiAl + V(6) + Fe(3) and Fe2TiAl + Cr(4) films with those of the Fe2TiAl film as a function of temperature. The compositions of Fe2TiAl + V(6) + Fe(3) and Fe2TiAl + Cr(4) are Fe2.01Ti0.56V0.67Al0.76 and Fe1.99Ti0.66Cr0.45Al0.90, respectively. These films have nearly the same Fe amount (2.01 and 1.99) and nearly the same VEC (5.96 and 5.99), while the former showed S and ρ values around twice as high as those of the latter in the entire temperature range. As the third element (in this case, Al) is known to have a small effect on the band structures around the Fermi level,29 the VEC can be controlled by adjusting the third element within the scheme of the rigid band model. A possible reason for the observed enhancement is the smaller carrier concentration in the Fe2.01Ti0.56V0.67Al0.76 film because both S and ρ are inversely proportional to the carrier concentration. The measured carrier concentration of the Fe2.01Ti0.56V0.67Al0.76 film might be lower because of the slight difference in the Fe amount and VEC. However, the lower carrier concentration may not be the main origin because not only other films such as Fe2TiAl + Cr(n) and Fe2TiAl + Mn(n) but also Fe2Ti1−xCrxAl and Fe2−yCoyTiAl bulks showed small S of at most 50 µV/K even when the VEC was ∼6.0.14 

FIG. 5.

Thermoelectric properties of Fe2TiAl (Fe2.18Ti0.73Al1.09 film), Fe2TiAl + Cr(4) (Fe1.99Ti0.66Cr0.45Al0.90 film), and Fe2TiAl + V(6) + Fe(3) (Fe2.01Ti0.56V0.67Al0.76 film): (a) the Seebeck coefficient and (b) resistivity.

FIG. 5.

Thermoelectric properties of Fe2TiAl (Fe2.18Ti0.73Al1.09 film), Fe2TiAl + Cr(4) (Fe1.99Ti0.66Cr0.45Al0.90 film), and Fe2TiAl + V(6) + Fe(3) (Fe2.01Ti0.56V0.67Al0.76 film): (a) the Seebeck coefficient and (b) resistivity.

Close modal

The other possible reason is that the flat band in the conduction band strongly affects the thermoelectric properties, as theoretically suggested above. The bandgap could be estimated from the temperature dependence of S shown in Fig. 5(a) by using the Goldsmid–Sharp formulation,30 

Eg=2e|Smax|Tmax,
(2)

where Smax is the maximum S and Tmax is the temperature for Smax. The estimated value of 0.07 eV for the Fe2.01Ti0.56V0.67Al0.76 film is much greater than that of 0.04 eV for the Fe2.18Ti0.73Al1.09 films; nevertheless, 50% Ti substitution by V does not change the energy difference between the valence and conduction bands significantly, as discussed above. Previous studies have reported a similar phenomenon in which n-type ZrNiSn with a weighted mobility ratio (A) of 5 has a larger S than p-type ZrNiSn with a weighted mobility ratio of 1/5.31,32 The weighted mobility ratio is defined as

A=μmajμminmmajmmin32,
(3)

where μ is the mobility and mmaj and mmin are the effective masses for majority and minority carriers, respectively. As clarified by the calculations, Ti substitutions by V cause both a reduction in m and an increase in μ in n-type conductions owing to the change in the dominant band from the flat band (“flat”) to the parabolic band (“para1”), while the valence band does not change significantly(“para2”). These results suggest that V-additions caused an increase in A and a simultaneous increase in S. The effect of the impurity bands resulting from the off-stoichiometry of Fe was not considered in the above-mentioned discussion.

Finally, we comment on the ZT of our fabricated Fe2TiAl-based films. The thermal conductivity κ was evaluated using the thermoreflectance method at room temperature. The κ of the Fe2.18Ti0.73Al1.09 film was 7.2 W/K m and the lattice thermal conductivity κlat was estimated to be 2.7 W/K m using the Wiedemann–Franz law. The κlat was small compared to the Fe2TiAl-based bulks;14 nevertheless, the film was almost epitaxially grown on the MgO substrates. The reduction may be attributed to both alloy scattering and boundary scattering owing to the off-stoichiometry and the small thickness compared to the phonon mean free path, respectively, as observed previously in the case of other FH films.11,20–22 Consequently, the ZT of the Fe2.18Ti0.73Al1.09 and Fe2.01Ti0.56V0.67Al0.76 films was 0.067 and 0.12, respectively. Note that no element with large mass such as W and Ta was used in our study, and a further increase in ZT could be expected by combining heavy-element doping with flat-band engineering.

In conclusion, we synthesized Fe-based FH thin films on MgO substrates by a post-annealing process. The films grew nearly epitaxially when the initial state was amorphous and the lattice mismatch was small. The TE properties of Fe2TiAl-based films were investigated by modulating the composition of the films, and the p-type S was found to increase only when V was added. It was clarified that the flat band of Fe2TiAl moves away from the valence band by substitutions of Ti by V, and consequently, the p-type S increases because of the increase in the weighted mobility ratio. As a result, almost the maximum of p-type ZT in FH alloys was realized even without heavy element doping owing to both large S and small κ. Our results strongly suggest that not only parabolic-band engineering, such as realizing degenerate states, but also flat-band engineering is important for realizing materials with high ZT.

See the supplementary material for methods of measuring the Seebeck coefficient of the thin films, detailed analysis of crystal structures by XRD, and electric transport properties.

The data that support the findings of this study are available within the article and its supplementary material.

1.
G. J.
Snyder
and
E. S.
Toberer
,
Nat. Mater.
7
,
105
(
2008
).
2.
B.
Poudel
,
Q.
Hao
,
Y.
Ma
,
Y.
Lan
,
A.
Minnich
,
B.
Yu
,
X.
Yan
,
D.
Wang
,
A.
Muto
,
D.
Vashaee
,
X.
Chen
,
J.
Liu
,
M. S.
Dresselhaus
,
G.
Chen
, and
Z.
Ren
,
Science
320
,
634
(
2008
).
3.
R.
Venkatasubramanian
,
E.
Siivola
,
T.
Colpitts
, and
B.
O’Quinn
,
Nature
413
,
597
(
2001
).
4.
Y.
Nishino
,
H.
Kato
, and
M.
Kato
,
Phys. Rev. B
63
,
233303
(
2001
).
5.
Y.
Nishino
and
Y.
Tamada
,
J. Appl. Phys.
115
,
123707
(
2014
).
6.
S.
Yabuuchi
,
M.
Okamoto
,
A.
Nishide
,
Y.
Kurosaki
, and
J.
Hayakawa
,
Appl. Phys. Express
6
,
025504
(
2013
).
7.
D. I.
Bilc
,
G.
Hautier
,
D.
Waroquiers
,
G.-M.
Rignanese
, and
P.
Ghosez
,
Phys. Rev. Lett.
114
,
136601
(
2015
).
8.
Y.
Nishino
,
M.
Kato
,
S.
Asano
,
K.
Soda
,
M.
Hayasaki
, and
U.
Mizutani
,
Phys. Rev. Lett.
79
,
1909
(
1997
).
9.
S.
Chaudhuri
,
V.
Srihari
,
A. K.
Nigam
, and
P. A.
Bhobe
,
J. Appl. Phys.
126
,
083904
(
2019
).
10.
M.
Meinert
,
M. P.
Geisler
,
J.
Schmalhorst
,
U.
Heinzmann
,
E.
Arenholz
,
W.
Hetaba
,
M.
StȔger-Pollach
,
A.
Hütten
, and
G.
Reiss
,
Phys. Rev. B
90
,
085127
(
2014
).
11.
Y.
Shimanuki
,
K.
Kudo
,
T.
Ishibe
,
A.
Masago
,
S.
Yamada
,
Y.
Nakamura
, and
K.
Hamaya
,
J. Appl. Phys.
127
,
055106
(
2020
).
12.
C. S.
Lue
and
Y.-K.
Kuo
,
J. Appl. Phys.
96
,
2681
(
2004
).
13.
C. S.
Lue
,
R. F.
Liu
,
M. Y.
Song
,
K. K.
Wu
, and
Y. K.
Kuo
,
Phys. Rev. B
78
,
165117
(
2008
).
14.
R. O.
Suzuki
and
T.
Kyono
,
J. Alloys Compd.
377
,
38
(
2004
).
15.
C. S.
Lue
,
Y.-K.
Kuo
,
S.-N.
Horng
,
S. Y.
Peng
, and
C.
Cheng
,
Phys. Rev. B
71
,
064202
(
2005
).
16.
T.
Baba
,
Jpn. J. Appl. Phys., Part 1
48
,
05EB04
(
2009
).
17.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
18.
See http://www.openmx-square.org/ for referring used pseudo-potentials.
19.
T.
Ozaki
,
K.
Nishio
, and
H.
Kino
,
Phys. Rev. B
69
,
195113
(
2004
).
20.
A.
Nishide
,
Y.
Kurosaki
,
H.
Yamamoto
,
S.
Yabuuchi
,
M.
Okamoto
, and
J.
Hayakawa
,
J. Jpn. Inst. Metals
76
,
541
(
2012
).
21.
S.
Hiroi
,
M.
Mikami
, and
T.
Takeuchi
,
Mater. Trans.
57
,
1628
(
2016
).
22.
N.
Fukatani
,
Y.
Kurosaki
,
S.
Yabuuchi
,
A.
Nishide
, and
J.
Hayakawa
,
Appl. Phys. Lett.
112
,
033902
(
2018
).
23.
Y.-s.
Choi
,
T.
Nakatani
,
J. C.
Read
,
M. J.
Carey
,
D. A.
Stewart
, and
J. R.
Childress
,
APEX
10
,
013006
(
2017
).
24.
S.
Li
,
T.
Nakatani
,
K.
Masuda
,
Y.
Sakuraba
,
X. D.
Xu
,
T. T.
Sasaki
,
H.
Tajiri
,
Y.
Miura
,
T.
Furubayashi
, and
K.
Hono
,
Acta Mater.
142
,
49
(
2018
).
25.
Y.
Nishino
,
IOP Conf. Ser.: Mater. Sci. Eng.
18
,
142001
(
2011
).
26.
K.
Soda
,
S.
Harada
,
M.
Kato
,
S.
Yagi
,
Y.
Sandaiji
, and
Y.
Nishino
,
IOP Conf. Ser.: Mater. Sci. Eng.
18
,
142004
(
2011
).
27.
K.
Kudo
,
S.
Yamada
,
J.
Chikada
,
Y.
Shimanuki
,
Y.
Nakamura
, and
K.
Hamaya
,
Jpn. J. Appl. Phys.
57
,
040306
(
2018
).
28.
J.
Park
,
Y.
Xia
, and
V.
Ozolins
,
Phys. Rev. Appl.
11
,
014058
(
2019
).
29.
Y.
Nishino
,
S.
Kamizono
,
H.
Miyazaki
, and
K.
Kimura
,
AIP Adv.
9
,
125003
(
2019
).
30.
H. J.
Goldsmid
and
J. W.
Sharp
,
J. Electron. Mater.
28
,
869
(
1999
).
31.
J.
Schmitt
,
Z. M.
Gibbs
,
G. J.
Snyder
, and
C.
Felser
,
Mater. Horiz.
2
,
68
(
2015
).
32.
Z. M.
Gibbs
,
H.-S.
Kim
,
H.
Wang
, and
G. J.
Snyder
,
Appl. Phys. Lett.
106
,
022112
(
2015
).

Supplementary Material