# Fileset

[BTO_HAXPES_published.pdf](https://mdr.nims.go.jp/filesets/0cdfbbee-709d-4474-825c-76718213588b/download)

## Creator

[Takeo Ohsawa](https://orcid.org/0000-0001-7528-8940), [Shigenori Ueda](https://orcid.org/0000-0001-9425-0614), [Takao Shimizu](https://orcid.org/0000-0001-9508-7601), [Naoki Ohashi](https://orcid.org/0000-0002-4011-0031)

## Rights

©2025 American Physical Society[Copyright not evaluated](http://rightsstatements.org/vocab/CNE/1.0/)

## Other metadata

[Changes in the electronic structure of <math>  <msub>    <mi>BaTiO</mi>    <mn>3</mn>  </msub></math> due to ferroelectric phase transition investigated via polarization-dependent hard x-ray photoemission spectroscopy](https://mdr.nims.go.jp/datasets/d123e8db-873a-4974-aee5-67b54909109e)

## Fulltext

Changes in the electronic structure of BaTiO3 due to ferroelectric phase transition viapolarization-dependent hard x-ray photoemission spectroscopyTakeo OhsawaResearch Center for Electronic and Optical Materials,National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, JapanShigenori UedaResearch Center for Electronic and Optical Materials,National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, JapanandSynchrotron X-ray Station at SPring-8,National Institute for Materials Science,1-1 Kouto, Sayo, Hyogo 679-5148, JapanTakao ShimizuResearch Center for Electronic and Optical Materials,National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, JapanNaoki OhashiResearch Center for Electronic and Optical Materials,National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, JapanandMaterials Research Center for Element Strategy,Tokyo Institute of Technology, Yokohama 226-8503, Japan(Dated: April 3, 2025)This study explored the changes in the electronic structure due to ferroelectric phase transitionbehavior of BaTiO3. The temperature variations in the electronic structure of a ferroelectric BaTiO3crystal were investigated via hard X-ray photoemission spectroscopy (HAXPES) using linearly polar-ized X-rays and density functional theory calculations. The observed valence band HAXPES spectraexhibited distinct temperature-dependent shapes owing to the crystalline phase transitions from ahigh-temperature paraelectric cubic phase to low-temperature ferroelectric phases with tetragonal,orthorhombic, and rhombohedral symmetries. The changes in the valence band spectra agreed withthe simulated HAXPES spectra derived from the projected densities of states in the crystallinephases multiplied by the photoionization cross-sections. This result suggests that the ferroelectricmechanism in BaTiO3 is of the displacive type, which involves structural phase transformations.I. INTRODUCTIONFerroelectric materials are attractive for a broad rangeof applications such as actuators, capacitors, and mem-ory devices [1–8]. These materials exhibit a switchablemacroscopic polarization. One of the most technologi-cally important ferroelectric oxides is the perovskite-typeBaTiO3, and the origin of its ferroelectric properties haslong been controversial [9–11]. BaTiO3, which has beenextensively studied, exhibits rhombohedral (Rhom.), or-thorhombic (Orth.), tetragonal (Tet.), and cubic (Cub.)phases. However, the microscopic nature of the phasesand transitions in BaTiO3 remains uncertain. In the pop-ular displacive model [9, 10], the equilibrium position ofeach Ti atom is at the center of the oxygen octahedron inthe Cub. phase. However, the Ti atoms are microscop-ically displaced along the <111>, <011>, and <001>directions in the Rhom., Orth., and Tet. phases, respec-tively. These displacements are regarded as the originof ferroelectricity. Displacive-type transitions, which areassumed to occur in BaTiO3, are described by the con-densation of a soft phonon mode [10, 12]. This modewas observed in the Cub. phase via inelastic neutronscattering [13]. On the other hand, an order–disordermodel, which was proposed to explain the phase tran-sition behavior of BaTiO3, has been supported by sev-eral experiments [14–16] and theoretical considerations[17, 18]. In this model, all Ti atoms are located in one ofeight equivalent off-center positions, which are consideredas potential minima along the <111> directions, for allcrystalline phases [19]. In particular, the Ti atoms dis-tort in the same direction in the low-temperature Rhom.2phase. Further investigation of the electronic structuresof BaTiO3 with different crystalline symmetries is neededto better understand its ferroelectric transitions, and onetechnical approach consists of using X-ray probes [20–23].X-ray photoemission spectroscopy is a useful techniquefor studying electronic band structures in solids. In par-ticular, hard X-ray photoemission spectroscopy (HAX-PES) enables bulk-sensitive measurements of solid-statematerials [24–26]. Owing to the relatively high kineticenergy (Ek of ∼4 keV or higher) of photoelectrons, re-sulting in a large inelastic mean free path (IMFP), HAX-PES enables to probe the bulk electronic structures ofsolids, where the estimated information depth, IMFP ×3, is larger than 20 nm. Using linear dichroism in valenceband (VB) HAXPES, electron orbitals can be selectivelycharacterized [27–31]. Because the photoionization cross-section (σ) depends on the orbital character of the elec-trons (s, p, d, or f ), principal quantum number, atomicnumber, and photon energy [32, 33], the σ values areclosely correlated with the profiles of the HAXPES spec-tra and reflect the nature of the chemical bonding char-acteristics. Furthermore, the σ values are affected by theexperimental geometry and X-ray polarization [27, 29–31]. Consequently, the HAXPES spectra measured atvarious temperatures using two different linearly polar-ized X-rays, which achieve linear dichroism in HAXPES,contain considerable information on the electronic bandstructures in solids. Hence, the combination of densityfunctional theory (DFT) calculations and HAXPES of-fers a promising approach to revealing the changes inthe electronic structure of BaTiO3 due to the structuralphase transitions caused by either displacive or order-disorder characteristics.Herein, we investigate the phase transition behaviorof BaTiO3 based on observed and simulated VB HAX-PES spectra. Temperature-dependent HAXPES mea-surements with linear dichroism revealed that the ferro-electric phase transitions of BaTiO3 are of the displacivetype, which is attributed to the displacement of the B-site ions. These results are critical for understandingthe properties of ferroelectric materials and for provid-ing guidance for improving nanoelectronic devices.II. METHODSA. Experimental detailsHAXPES measurements were performed on BaTiO3single crystals at the undulator beamline BL15XU [25]of SPring-8, Japan. The BaTiO3 crystals were prelim-inarily annealed in a gas mixture of hydrogen and ni-trogen at 1120 ◦C to enhance the electrical conductivitybefore the crystals were introduced into the HAXPESapparatus [34]. The resistivity and carrier density of theannealed BaTiO3 crystal measured in this study are 10Ω cm and 3×1016 cm−3, respectively, at 300 K, indi-cating that the conductivity does not interfere with theHAXPES measurements. An excitation energy (hν) of 6keV was employed. All measurements were performed inthe near-normal-emission geometry, where the incidenceangle of the X-rays and the take-off angle of the pho-toelectrons were set to 2◦ and 88◦, respectively, relativeto the BaTiO3(001) surface. The IMFP of the 6 keVphotoelectrons inside BaTiO3 was calculated to be ∼8.4nm using the TPP-2M equation [35], leading to an infor-mation depth of ∼25.2 nm in this work. The VB lineardichroism in HAXPES was achieved using horizontal lin-early polarized X-rays [E (H)], with an electric field vec-tor (E⃗) parallel to the photoelectron trajectory (ν⃗e) to anelectron analyzer, and vertical linearly polarized X-rays[E (V)], with E⃗ perpendicular to ν⃗e. The degrees of lin-ear polarization (PL) for the E (H) and E (V) X-rays were∼1.00 and ∼0.70, respectively. The details of the experi-mental setup have been reported previously [36]. A totalenergy resolution of approximately 150 meV, evaluatedfrom the Fermi edge of a pure gold film, was employedfor the HAXPES measurements. For both the E (H) andE (V) X-rays, we measured the VB spectra at 118–426K to investigate the spectroscopic characteristics inducedby the phase transitions. The spectra were obtained froma multidomain structure when the crystalline form wasin the Orth. and Rhom. phases at low temperatures.B. Theoretical calculationThe electronic structures of BaTiO3 were calculatedusing a plane-wave-based pseudo-potential method im-plemented in the CASTEP code [37]. The norm-conserved pseudopotentials were adopted, and theexchange-correlation energy was calculated using thePerdew-Burke-Ernzerhof functional revised for solids,known as PBEsol [38]. The plane-wave cut-off energywas set to 1050 eV, and a Monkhorst-Pack grid was used[39]. Structural optimizations were performed using theBroyden-Fletcher-Goldfarb-Shanno scheme [40], and theconvergence of the energy minimization and structuralrelaxation was judged using the following tolerances: thetolerance for electronic energy mineralization was set to5.0 × 10−7 eV/atom, the energy tolerance for structuraloptimization to 5.0 × 10−6 eV/atom, the force toleranceto 0.01 eV/Å, the stress tolerance to 0.02 GPa, and theatomic displacement tolerance to 5.0 × 10−4 Å. To repro-duce the changes in the electronic structure due to phasetransition, the electronic structures of Cub., Tet., Orth.,and Rhom. BaTiO3 were calculated by applying the sym-metry constraints Pm3m, P4mm, Amm2, and R3m, re-spectively. After structural optimizations, the electronicstructures were calculated using the hybrid PBE0 func-tional [41, 42] to better reproduce the electronic structurecharacteristics, such as a bandgap energy3III. RESULTS AND DISCUSSIONA. Hard X-ray photoemission spectroscopy ofBaTiO3First, we present the VB spectra of BaTiO3 obtainedat several sets of temperatures. The VB spectra obtainedusing E (H) and E (V) X-rays and normalized by the pho-ton flux are compared in Fig. 1(a). The normalizedspectra are referred to as E (H)-VB and E (V)-VB. Notethat the E (V)-VB spectra, which were corrected to PLof ∼1.0, are shown in the figure by considering the inten-sity ratio of E (H) and E (V) X-rays [29, 36]. Regardlessof the temperature, the intensities of the E (H)-VB spec-tra are higher than those of the E (V)-VB spectra. Thisdifference is attributed to the variations in the σ valuesof all electron orbitals of BaTiO3, as summarized in Ta-ble S1 for hν = 6 keV [33, 43, 44], and involves orbitalcharacteristics, because the σ values depend on hν, E⃗,ν⃗e, and the electron orbitals.The temperature-dependent shapes of the E (H)-VBand E (V)-VB spectra are not clearly distinguishableeven across the phase transitions (Rhom.–Orth.–Tet.–Cub. transitions). Figure 1(b) compares the E (H)-VBand E (V)-VB spectra normalized at a peak intensityaround a binding energy (EB) of 6 eV. At each temper-ature, the spectral shapes around EB = 7.8 eV differ be-tween the E (H)-VB and E (V)-VB spectra. This discrep-ancy can be attributed to variations in the polarization-dependent σ values of the Ti 4s orbital (Table S1), asmentioned later. Except for this discrepancy, significantdifferences are not observed between the E (H)-VB andE (V)-VB spectra.The temperature dependence of the E (H)-VB andE (V)-VB spectra was carefully analyzed. Figures 2(a)and (b) show the temperature dependences of the E (H)-VB and E (V)-VB spectra, respectively. The colors cor-respond to the crystalline phases shown in Fig. 1. Thespectral shapes at each temperature are similar for theE (H)-VB and E (V)-VB spectra. Moreover, the spec-tral weight shifts monotonically to the lower EB sideas the temperature increases. This shift is more pro-nounced around the top of VB than at its bottom. Fig-ures 2(c) and (d) show zoomed-in views of Figs. 2(a)and (b), respectively, in the vicinity of the top of VB.The temperature-dependent spectra can be categorizedinto four groups according to the phases: Rhom. (blue),Orth. (green), Tet. (orange), and Cub. (red). Thetemperature-dependent changes in the spectral shapesobserved at EB ≈ 4 eV are also evident in the energyrange around EB ≈ 5.5 eV. In contrast, the shoulderat the bottom of VB shows a narrowing spectral width;however, this change is less pronounced than the shiftsobserved around EB ≈ 4 eV and 5.5 eV. The spectralweight apparently shifts to the higher EB side with de-creasing temperature, suggesting a narrowing of the bandwidth with reduced crystalline symmetry. This findingindicates that the band width increases with tempera-FIG. 1. (a) Valence band (VB) spectra of BaTiO3 measuredat several temperatures using 6 keV E(H) and E(V) X-rays.The colors correspond to the cubic (red), tetragonal (orange),orthorhombic (green), and rhombohedral (blue) crystallinephases. The inset shows the experimental geometry, where ν⃗eand Ps indicate the photoelectron trajectory to the analyzerand the spontaneous polarization, respectively. (b) Normal-ized E(H)-VB and E(V)-VB spectra.ture and corresponds to different crystal forms.In this context, we discuss the location of the Fermilevel (EF). The behavior of the VB maximum (VBM)is shown in Figs. 2(c) and (d). Two possible expla-nations are considered: a shift in EF with temperatureand a change in the bandgap width with temperature.We investigated Ba 4d, Ti 2p, and O 1s core level spec-tra obtained using E (H) X-rays at various temperatures.These results reveal the EB positions remain unchangedwithin each phase but exhibit very slight shifts acrossphase transitions. These slight shifts suggest changesin the chemical bonding states. Consequently we pro-pose that the observed behavior is due to changes in thebandgap width rather than a shift in EF, as DFT calcula-tions indicate a systematic change in the bandgap widthfor different crystalline forms. In addition, because thecrystal was heated in a hydrogen-containing gas streamat high temperature, the presence of significant chargecarriers (electrons) at the bottom of the conduction bandcan be reasonably assumed. Actually, the VBM valuesshown in Fig. 2 are approximately 3.2–3.5 eV, which isconsistent with the band gap values [45, 46]. Therefore,we assume that EF remains very close to the bottom ofthe conduction band, regardless of the crystalline form.These temperature-dependent spectral changes werenot observed in n-type Nb:SrTiO3(001) crystals with anelectron density of ∼1020 cm−3, even without annealingunder the gas mixture (Fig. S1) because of the absence4FIG. 2. Temperature dependence of the (a) E(H)-VB and (b)E(V)-VB spectra. Zoomed-in (c) E(H)-VB and (d) E(V)-VBspectra in the vicinity of the top of VB.of phase transitions in this temperature range. Addition-ally, Fig. S1 indicates that the peak broadening causedby thermal excitation does not account for the spectralchanges observed in the E (H)-VB and E (V)-VB spec-tra of BaTiO3, assuming similar magnitudes of thermalbroadening for SrTiO3 and BaTiO3. Based on these re-sults, we can assume that the spectral shifts near thetop of VB and the increases in the band width, whichare present in the E (H)-VB and E (V)-VB spectra, areassociated with ferroelectric phase transitions.B. Density functional theory calculationsAll structural optimization calculations successfullysatisfied the convergence tolerances. The crystal struc-tures optimized using the PBEsol functional are providedas supplemental information in the CIF format, includingR3m.cif, Amm2.cif, P4mm.cif, and Pm3m.cif. The elec-tronic structures described below were calculated basedon these optimized structures. Figure 3 shows the totaland projected densities of states (PDOSs) for (a) Cub.,(b) Tet., (c) Orth., and (d) Rhom. BaTiO3 crystals ob-tained from DFT calculations using the PBE0 functional.As shown in the upper panels of Fig. 3, the VB is domi-nated by O 2p states, regardless of the crystalline form.In addition to the O 2p band, the Ti 3d, 4s, 4p and Ba 5p,5d bands contribute to the VB, as seen in the lower pan-els. Notably, the calculated energy bandgap decreasesfrom that of Rhom. (4.20 eV) to that of Cub. (3.75 eV),FIG. 3. Total and projected densities of states (DOSs) in thevalence band region of BaTiO3 for the (a) cubic (Cub.), (b)tetragonal (Tet.), (c) orthorhombic (Orth.), and (d) rhombo-hedral (Rhom.) phases. The upper and lower panels displaythe full and zoom-in scaled DOSs, respectively. The energyis referred to the valence band maximum (VBM).as shown in Fig. S2. From Figs. 2 and 3, it is observedthat the bandwidth increases, while the bandgap energydecreases with increasing temperature.C. Simulated HAXPESUsing the PDOSs (Fig. 3) and σ values (Table S1),we simulated the HAXPES spectra [36]. The simulatedHAXPES spectra were obtained by summing the PDOSsweighted with the σ values based on our experimentalconfiguration. Figures 4(a) and (b) compare the sim-ulated E (H)-VB and E (V)-VB spectra (upper plot) tothe experimental spectra (lower plot). The energy wasaligned to the bottom of VB at 6.0 eV in both the simu-lated and experimental spectra for comparison.The shapes of the total DOSs and simulated spectraare not very similar. This is due to the variation in theσ values with respect to the elements and orbitals. Ac-cording to Table S1 and Fig. 3, it is evident that theBa 5p band is dominant in the simulated E (H)-VB andE (V)-VB spectra, as shown in Fig. S3. Although the VBis dominated by O 2p in terms of PDOS, the σ values forO 2p are very small under the experimental conditionsemployed in this study. As the σ value for Ti 4s is largein the E (H) configuration, the simulated E (H)-VB spec-tra represent the energy dispersion of Ba 5d (EB ∼3 eV)5FIG. 4. Simulated (upper) and experimental (lower) VB spec-tra for (a) E(H) and (b) E(V) X-rays. The energy is alignedto the bottom of VB at 6.0 eV.and Ti 4s (EB ∼5 eV). Moreover, the Ba 5p, Ba 5d,and O 2p orbitals are relatively strong contributors tothe simulated E (V)-VB spectra, where the Ti 4s band issuppressed owing to its small σ value in the E (V) config-uration. As shown in Fig. 2, the band widths in both theE (H)-VB and E (V)-VB spectra increase with increasingtemperature. This is consistent with the simulated spec-tra.Here, the variation in the VB width is attributed tochanges in the local structure, including the bond dis-tance and angles. In the Cub. phase, the O–Ti–O anglesare 180◦, whereas in the other phases, these angles de-viate from 180◦ owing to the structural distortion of theTiO6 octahedron. Indeed, in the Rhom. phase, the angleis 173.15◦, and in the Orth. phase, it ranges from 171.33◦to 178.48◦. In addition, for distorted TiO6 coordination,the Ti–O distances vary in the ranges 1.887–2.111 Å inthe Rhom. phase, 1.984–2.141 Å in the Orth. phase,and 1.848–2.189 Å in the Tet. phase. Regarding thecoordination structure around Ba, the Ba–O distance inthe Cub. phase is 2.81 Å, and it varies from 2.769 to2.883 Å in the Rhom. phase, from 2.785 to 2.917 Åin the Orth. phase, and from 2.782 to 2.875 Å in theTet. phase. Such distortions in the TiO6 octahedronand BaO12 polyhedron can lead to the formation of a dis-crete electronic structure, resulting in a band structurewith a small dispersion in the k -space. As shown in Figs.2(c) and (d), the profiles of the HAXPES spectra can beclassified into four groups according to their crystallinesymmetry, and the variation in the spectral shapes doesnot change monotonically with temperature. Hence, themost important parameter for describing the electronicstructures in BaTiO3 should be the crystalline symmetry.As mentioned in subsection III.A, spectral features de-pending on the crystalline symmetry were observed atEB ≈ 4 and 5.5 eV in Fig. 2, manifesting as the narrow-ing of the major peaks in the E (H)-VB and E (V)-VBspectra. These features were well reproduced in the sim-ulated E (H)-VB and E (V)-VB spectra. For example,the simulated spectra of the Cub. (red) and Tet. (or-ange) phases showed an extended tail around the VBMas well as in the range of approximately 2 eV on theenergy scale, as shown in Fig. 4. The changes in the ex-perimental VB width along the phase transition sequenceagree with those in the DFT calculations.In other words, the electronic structures probed usinghard-X-ray photoemission technique indicated that thechanges in the crystal structure accompanying the phasetransition were reasonable.A previous study indicated that the electronic struc-ture of the Ti 3d orbital in Cub. BaTiO3 is differentfrom those in the other polar phases, as evidenced by X-ray absorption and fluorescence measurements [23]. Be-cause the HAXPES spectra obtained in this study probethe electron orbital of Ba in BaTiO3, the VB shift andchanges in the band width provide evidence that the lo-cal structure and distortion of the BaO12 polyhedron re-sponds to the phase-transition sequence. Although theBa–O bond is nearly purely ionic, the electronic struc-ture of the BaO12 polyhedron is strongly influenced bychanges in the crystalline symmetry. Because the ox-ide ions in the BaO12 polyhedron are completely sharedwith the TiO6 octahedron, the present results indicatethat the electronic structure of the Ti–O bond is stronglyaffected by phase transition. Therefore, since such lo-cal distortion has been known as the displacive-type forthe origin of ferroelectricity, we can conclude that thedisplacive model is more consistent in describing phasetransitions in BaTiO3 than the order-disorder model.IV. CONCLUSIONSSpectroscopic investigations of the phase transi-tion behavior of BaTiO3 were performed using lin-ear polarization-dependent HAXPES measurements andDFT calculations. The combination of these methodsshowed that the variation in the spectroscopic profileswith temperature occurs stepwise rather than monoton-ically. The spectral features can be classified accordingto the Rhom., Orth., Tet., and Cub. crystalline phasesof BaTiO3. The simulated VB spectra derived from thePDOS and σ values agreed with the observed E (H)-VBand E (V)-VB spectra. This agreement suggests thatthe ferroelectric transition in BaTiO3 is of the displacivetype, which involves structural phase transformations.The measurements and analyses performed in this study,characterized by the large probing depth of HAXPES,provide detailed insights into the bulk electronic statesof ferroelectric materials and emergent semiconductors.This technique constitutes a powerful diagnostic methodfor determining the band-selective electronic states ofsolids.6ACKNOWLEDGMENTSThe authors thank the staff of HiSOR, HiroshimaUniversity, and JAEA/SPring-8 for the development ofHXPES at BL15XU of SPring-8. The HXPES experi-ments were performed with the approval of the NIMSSynchrotron X-ray Station (Proposals Nos. 2014B4604,2015A4603, 2015B4604, 2016B4603, 2019A4602, and2019B4603). This work was also supported by MEXTProgram: Data Creation and Utilization Type MaterialResearch and Development Project Grant Number JP-MXP1122683430. S.U. and N.O. acknowledge supportfrom the Tokodai Institute for Elemental Strategy (TIES:Grant No. JPMXP0112101001) funded by the Ministryof Education, Culture, Sports, Science and Technology(MEXT), Japan.AUTHOR CONTRIBUTIONST.O., S.U., and N.O. designed research; T.O., S.U., andN.O. performed the experiments; All authors discussedthe results and wrote the paper.[1] Z.-G. Ye, Handbook of Advanced Dielectric, Piezoelec-tric and Ferroelectric Materials (Woodhead Publishing,2008).[2] J. F. Scott and C. A. Paz de Araujo, Ferroelectric Mem-ories, Science 246, 1400 (1989).[3] S.-E. Park and T. R. Shrout, Ultrahigh strain and piezo-electric behavior in relaxor based ferroelectric single crys-tals, Journal of Applied Physics 82, 1804 (1997).[4] L. E. Cross, Relaxor ferroelectrics, Ferroelectrics 76, 241(1987).[5] G. H. Haertling, Ferroelectric Ceramics: History andTechnology, in Ferroelectricity , Vol. 818 (Wiley-VCHVerlag GmbH, Weinheim, Germany, 2007) pp. 157–178.[6] J. F. Scott, Applications of Modern Ferroelectrics, Sci-ence 315, 954 (2007).[7] M. Dawber, K. M. Rabe, and J. F. Scott, Physics of thin-film ferroelectric oxides, Reviews of Modern Physics 77,1083 (2005).[8] D. Damjanovic, Ferroelectric, dielectric and piezoelectricproperties of ferroelectric thin films and ceramics, Re-ports on Progress in Physics 61, 1267 (1998).[9] W. Cochran, Crystal Stability and the Theory of Ferro-electricity, Physical Review Letters 3, 412 (1959).[10] W. Cochran, Crystal stability and the theory of ferro-electricity, Advances in Physics 9, 387 (1960).[11] R. E. Cohen, Origin of ferroelectricity in perovskite ox-ides, Nature 358, 136 (1992).[12] J. C. Slater, The lorentz correction in barium titanate,Physical Review 78, 748 (1950).[13] J. Harada, J. D. Axe, and G. Shirane, Neutron-scatteringstudy of soft modes in cubic BaTiO3, Physical Review B4, 155 (1971).[14] I. Bersuker, On the origin of ferroelectricity in perovskite-type crystals, Physics Letters 20, 589 (1966).[15] R. Comes, M. Lambert, and A. Guinier, The chain struc-ture of BaTiO3 and KNbO3, Solid State Communications6, 715 (1968).[16] K. Tsuda, R. Sano, and M. Tanaka, Nanoscale lo-cal structures of rhombohedral symmetry in the or-thorhombic and tetragonal phases of BaTiO3 studied byconvergent-beam electron diffraction, Physical Review B86, 214106 (2012).[17] H. Takahasi, A Note on the Theory of Barium Titanate,Journal of the Physical Society of Japan 16, 1685 (1961).[18] M. Stachiotti, A. Dobry, R. Migoni, and A. Bussmann-Holder, Crossover from a displacive to an order-disordertransition in the nonlinear-polarizability model, PhysicalReview B 47, 2473 (1993).[19] A. S. Chaves, F. C. S. Barreto, R. A. Nogueira, andB. Zẽks, Thermodynamics of an eight-site order-disordermodel for ferroelectrics, Physical Review B 13, 207(1976).[20] B. Ravel, E. A. Stern, R. I. Vedrinskii, and V. Kraizman,Local structure and the phase transitions of BaTiO3, Fer-roelectrics 206-207, 407 (1998).[21] Y. Isohama, N. Nakajima, H. Maruyama, Y. Tezuka, andT. Iwazumi, Tetragonal-cubic phase transition in BaTiO3probed by resonant X-ray emission spectroscopy, Journalof Electron Spectroscopy and Related Phenomena 184,207 (2011).[22] A. Pancotti, J. Wang, P. Chen, L. Tortech, C.-M. Teodor-escu, E. Frantzeskakis, and N. Barrett, X-ray photoelec-tron diffraction study of relaxation and rumpling of fer-roelectric domains in BaTiO3(001), Physical Review B87, 184116 (2013).[23] Y. Tezuka, S. Nozawa, N. Nakajima, and T. Iwazumi,Temperature dependence of electronic structure on theferroelectric phase transition of BaTiO3, Physical ReviewB 104, 235148 (2021).[24] K. Kobayashi, Hard X-ray photoemission spectroscopy,Nuclear Instruments and Methods in Physics Research,Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment 601, 32 (2009).[25] S. Ueda, Y. Katsuya, M. Tanaka, H. Yoshikawa, Y. Ya-mashita, S. Ishimaru, Y. Matsushita, K. Kobayashi,R. Garrett, I. Gentle, K. Nugent, and S. Wilkins, PresentStatus of the NIMS Contract Beamline BL15XU atSPring-8, in AIP Conf. Proc., Vol. 1234 (2010) pp. 403–406.[26] A. X. Gray, C. Papp, S. Ueda, B. Balke, Y. Yamashita,L. Plucinski, J. Minár, J. Braun, E. R. Ylvisaker, C. M.Schneider, W. E. Pickett, H. Ebert, K. Kobayashi, andC. S. Fadley, Probing bulk electronic structure with hardX-ray angle-resolved photoemission, Nature Materials10, 759 (2011).[27] A. Sekiyama, J. Yamaguchi, A. Higashiya, M. Obara,H. Sugiyama, M. Y. Kimura, S. Suga, S. Imada, I. A.Nekrasov, M. Yabashi, K. Tamasaku, and T. Ishikawa,The prominent 5d-orbital contribution to the conduc-tion electrons in gold, New Journal of Physics 12, 043045(2010).[28] A. Sekiyama, A. Higashiya, and S. Imada, Polarization-7dependent hard X-ray photoemission spectroscopy ofsolids, Journal of Electron Spectroscopy and RelatedPhenomena 190, 201 (2013).[29] S. Ueda and I. Hamada, Polarization Dependent Bulk-sensitive Valence Band Photoemission Spectroscopy andDensity Functional Theory Calculations: Part I. 3d Tran-sition Metals, Journal of the Physical Society of Japan86, 124706 (2017).[30] S. Ueda and I. Hamada, Polarization dependent bulk-sensitive valence band photoemission spectroscopy anddensity functional theory calculations: Part II. 4d tran-sition metals, Journal of the Physical Society of Japan90, 1 (2021).[31] S. Ueda and I. Hamada, Polarization-dependent Bulk-sensitive Valence Band Photoemission Spectroscopy andDensity Functional Theory Calculations: Part III. 5dTransition Metals, Journal of the Physical Society ofJapan 91, 1 (2022).[32] J. Yeh and I. Lindau, Atomic subshell photoionizationcross sections and asymmetry parameters: 1 < Z < 103,Atomic Data and Nuclear Data Tables 32, 1 (1985).[33] M. Trzhaskovskaya, V. Nikulin, V. Nefedov, andV. Yarzhemsky, Non-dipole second order parametersof the photoelectron angular distribution for elementsZ=1–100 in the photoelectron energy range 1–10keV,Atomic Data and Nuclear Data Tables 92, 245 (2006).[34] T. Ohsawa, S. Hirose, and N. Ohashi, Potential bar-rier formed at domain boundaries in twinned tetrago-nal BaTiO3 single crystals, Applied Physics Letters 110,011604 (2017).[35] S. Tanuma, C. J. Powell, and D. R. Penn, Calculationsof electron inelastic mean free paths. V. Data for 14 or-ganic compounds over the 50–2000 eV range, Surface andInterface Analysis 21, 165 (1994).[36] T. Ohsawa, S. Ueda, M. Suzuki, Y. Tateyama, J. R.Williams, and N. Ohashi, Investigating crystalline-polarity-dependent electronic structures of GaN by hardx-ray photoemission and ab-initio calculations, AppliedPhysics Letters 107, 171604 (2015).[37] S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip,M. I. J. Probert, K. Refson, and M. C. Payne, First prin-ciples methods using CASTEP, Zeitschrift für Kristallo-graphie - Crystalline Materials 220, 567 (2005).[38] J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vy-drov, G. E. Scuseria, L. A. Constantin, X. Zhou, andK. Burke, Restoring the Density-Gradient Expansion forExchange in Solids and Surfaces, Physical Review Letters100, 136406 (2008).[39] J. D. Pack and H. J. Monkhorst, Special points forBrillouin-zone integrations, Physical Review B 16, 1748(1977).[40] B. G. Pfrommer, M. Côté, S. G. Louie, and M. L. Cohen,Relaxation of Crystals with the Quasi-Newton Method,Journal of Computational Physics 131, 233 (1997).[41] J. P. Perdew, M. Ernzerhof, and K. Burke, Rationale formixing exact exchange with density functional approx-imations, The Journal of Chemical Physics 105, 9982(1996).[42] C. Adamo and V. Barone, Toward reliable density func-tional methods without adjustable parameters: ThePBE0 model, The Journal of Chemical Physics 110, 6158(1999).[43] M. Trzhaskovskaya, V. Nefdov, and V. Yarzhemsky, Pho-toelectron angular distribution parameters for elementsZ=1 to Z=54 in the photoelectron energy range 100–5000eV, Atomic Data and Nuclear Data Tables 77, 97 (2001).[44] J. Scofield, Lawrence Livermore Laboratory; Tech. Rep.UCRL-; 51326 , Tech. Rep. (Divison of Technical In-formation Extension, U.S. Atomic Energy Commission,1973).[45] M. Cardona, Optical Properties and Band Structure ofSrTiO3 and BaTiO3, Physical Review 140, A651 (1965).[46] J. Narvaez, F. Vasquez-Sancho, and G. Catalan, En-hanced flexoelectric-like response in oxide semiconduc-tors, Nature 538, 219 (2016).