Local-electrostatics-induced oxygen octahedral distortion in perovskite oxides and insight into the structure of Ruddlesden–Popper phases

As the physical properties of ABX3 perovskite-based oxides strongly depend on the geometry of oxygen octahedra containing transition-metal cations, precise identification of the distortion, tilt, and rotation of the octahedra is an essential step toward understanding the structure–property correlation. Here we discover an important electrostatic origin responsible for remarkable Jahn–Teller-type tetragonal distortion of oxygen octahedra during atomic-level direct observation of two-dimensional [AX] interleaved shear faults in five different perovskite-type materials, SrTiO3, BaCeO3, LaCoO3, LaNiO3, and CsPbBr3. When the [AX] sublayer has a net charge, for example [LaO]+ in LaCoO3 and LaNiO3, substantial tetragonal elongation of oxygen octahedra at the fault plane is observed and this screens the strong repulsion between the consecutive [LaO]+ layers. Moreover, our findings on the distortion induced by local charge are identified to be a general structural feature in lanthanide-based An + 1BnX3n + 1-type Ruddlesden–Popper (RP) oxides with charged [LnO]+ (Ln = La, Pr, Nd, Eu, and Gd) sublayers, among more than 80 RP oxides and halides with high symmetry. The present study thus demonstrates that the local uneven electrostatics is a crucial factor significantly affecting the crystal structure of complex oxides.

T he crystal structure of ABO 3 -type perovskites is based on the geometric stability of packing for ions of different sizes and valence states. While the relatively large cation A is coordinated with 12 oxygen anions at the dodecahedral sites, the smaller cation B is located in the oxygen octahedra connected to each other by corner-sharing, agreeing well with Pauling's first rule for ionic compounds 1 . In particular, the distortion, including tilt and rotation, of oxygen octahedra is known to be a crucial factor governing the dielectric, magnetic, optical, and catalytic properties of perovskites 2,3 . As a consequence, the direct identification and description of the geometry of oxygen octahedra in perovskites and derivative oxides have been key issues over the last decade [4][5][6][7][8][9][10] .
In addition to the relative ionic size and the cation-anion bond strength, a significant electronic contribution to the structural distortion in oxides has been noted as the Jahn-Teller effect 11,12 . The central argument of this effect is that the energy of d-orbital electrons of transition-metal ions can be significantly lowered by spontaneous tetragonal elongation in such a way as to remove the degeneracy of the d-orbital levels. As is already known very well, high-spin Mn 3+ (3d 4 ) and low-spin Cu 2+ (3d 9 ) are typical Jahn-Teller active cations, demonstrating that the splitting of the degenerate d x2−y2 and d z2 levels of the e g subshells and subsequent energy stabilization of electrons is achieved via substantial tetragonal distortion of oxygen octahedra. A key message of the Jahn-Teller effect is that the electronic structure of transitionmetal ions should be taken into account to fully understand the crystal (or molecular) structure.
Recently, intriguing local distortion of oxygen octahedra was reported in heteroepitaxial LaNiO 3 thin films 13 . Even though this nickelate has a pseudocubic structure, tetragonal elongation of {NiO 6 } octahedra was identified to take place exclusively at the planes of Ruddlesden-Popper (RP) two-dimensional shear faults. Taking into account that the shear faults, consisting of consecutive [LaO] + layers, have electrostatically repulsive instability, the protrusion of negatively charged oxygen anions toward the shear plane was reasonably claimed to be energetically favorable for alleviating the strong repulsion between the [LaO] + layers. Although this previous study was confined to a single material, LaNiO 3 , provided a physically sound explanation, further extensive work remains necessary in order to clarify and generalize the local-charge hypothesis as another important electrostatic origin responsible for the remarkable tetragonal distortion of oxygen octahedra in perovskite-derivative oxides.
To this end, in this work, we extended our atomic-scale direct observations of two-dimensional shear faults [14][15][16][17][18] into five different perovskite-type materials, SrTiO 3 , BaCeO 3 , LaCoO 3 , LaNiO 3 , and CsPbBr 3 . First, we observed substantial tetragonal distortion of {BO 6  . Furthermore, by examining a series of 87 A n + 1 B n X 3n + 1 -type Ruddlesden-Popper (RP) oxides and halides with high symmetry, we found that this local-chargeinduced tetragonal elongation of oxygen octahedra is a striking common feature observed in most of the RP phases having the charged [AO] layer. Consequently, our findings on the electrostatic origin of the distortion appear to be a general phenomenon in oxides containing multiple cations.

Results and discussion
Observation of shear faults. For fault observations, we prepared polycrystalline dense SrTiO 3 , BaCeO 3 , and LaCoO 3 sintered pellets, epitaxial LaNiO 3 thin films, and CsPbBr 3 nanocrystals (see the "Methods" section), all of which contain homologous stacking faults represented by two consecutive rocksalt [AX] layers (A = Sr, Ba, La, Cs; X = O, Br). Figure 1 shows a series of high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) [19][20][21] images at atomic resolution, verifying the presence of rocksalt [AX] faults in all five perovskite crystals (see Supplementary Fig. 1 for lower magnification images). As the atomic number, Z, of Ba (Z Ba = 56) and Ce (Z Ce = 58) is very similar, individual columns are not readily discriminated in BaCeO 3 , although the image contrast of the faults is sufficiently distinguishable at a lower magnification (Supplementary Fig. 1b). A chemical map obtained by electron energyloss spectroscopy (EELS) is thus provided in Fig. 1b  Oxygen displacement and local electrostatics. To visualize the position of light-element anions, we utilized the annular brightfield (ABF) mode in STEM [22][23][24][25][26][27][28][29] . All the ABF images acquired from the fault region in the five perovskites are provided in Fig. 2 (see Supplementary Fig. 3 for pairs of ABF and HAADF images of the bulk crystals as references). A readily recognizable structural feature from this set of atomic-scale observations is that oxygen octahedra at the faults are asymmetrically elongated along the z axis in LaCoO 3 and LaNiO 3 (Fig. 2b), while no distortion of anion octahedra is identified in the other three perovskites, SrTiO 3 , BaCeO 3 , and CsPbBr 3 , as denoted by a white square diamond in each image in Fig. 2a. In particular, more than a 20% increment in the Co-O length from 1.9 to 2.3 Å in LaCoO 3 and a 15% increment in the Ni-O length from 1.9 to 2.2 Å in LaNiO 3 are presented in the magnified images in Fig. 2b. These two perovskite groups revealing distinct octahedral aspects have their own local electrostatic characteristics from the viewpoint of a layer structure. As schematically depicted in Fig. 3a In contrast, the La-based perovskite oxides, LaCoO 3 and LaNiO 3 , contain local net charge at each of the sublayers, as described in Fig. 3b. As the valence states of La, Co (and Ni), and O are 3+, 3+, and 2−, respectively, the bulk structure of Theoretical calculations. The displacement of oxygen anions was also verified by ab initio density functional theory (DFT) calculation. Figure 3c shows the atom position variation in a LaNiO 3 supercell containing a shear fault during the DFT calculation for geometry optimization. As shown in the supercell illustration of the first self-consistent field (SCF) iteration step, the initial configuration of oxygen atoms (light red) at the fault plane was set to be identical to the position of oxygen in the bulk. It is noted that the Ni-O bonds adjacent to the fault substantially elongate even after one SCF step, as can be seen in the second illustration, together with significant stabilization of the lattice energy (see Supplementary Fig. 4 for the plot of the lattice energy variation with SCF steps). The third illustration shows the finally optimized configuration of the supercell cell, revealing that the Ni-O bond length adjacent to the fault plane is 2.1 Å in the magnified illustration. This value after geometry optimization is in fairly good agreement with the experimentally observed Ni-O length, 2.2 Å, as directly compared in the ABF-STEM image. The DFT calculation thus confirms that elongation of the Ni-O bond length at the fault is an energetically stable configuration. At the same time, La 3+ cations are also observed to displace along the z axis out of the fault plane in the series of supercell illustrations in order to facilitate the reduction of the repulsion at the fault.
We also carried out another set of DFT calculations to compare the density of states (DOS) of the Ni 3d and O 2p orbitals in LaNiO 3 with and without a fault. As demonstrated in Supplementary Fig. 5, the overall substantial degree of overlap between the Ni 3d and O 2p states in addition to the metallic behavior with no bandgap does not significantly vary between the two DOS plots. However, as indicated by arrows, the noticeable increases of O 2p and Ni 3d states at the bottom, in the middle, and at the top of the band in the DOS plot are key changes of the  EELS analyses. Atomic-column resolved EELS analyses on the RP shear faults were performed to examine the variation of energyloss spectra in addition to the oxidation state of transition metals.
As the Ni-L 3 edge seriously overlaps with the La-M 4 edge, we selected LaCoO 3 and SrTiO 3 samples containing a shear fault instead of LaNiO 3 for the EELS analyses. Figure 4 shows a comparison of Co-L and O-K edges acquired from the bulk and the fault in LaCoO 3 . First, no noticeable changes of the peak intensity and position in the Co-L 2,3 edges from the bulk and the fault were identified, directly indicating the oxidation state of Co 3+ is invariant at the fault. Second, the three major peaks in the O-K edge are represented for the hybridizations of O 2p with Co 3d (peak A), La 5d (peak B) and Co 4s/4p (peak C), respectively [34][35][36][37] . The intensity of peak A obtained from the fault substantially diminishes, as denoted by a red arrow in the plot, while the intensity of the other peaks does not significantly vary between the bulk and the fault. This reduction of the pre-peak in the O-K edge appears to consistently correlate with the elongation of the  lower intensity of peak A likely stems from the comparatively weak orbital interaction. Indeed, such a peak reduction was not observable in the O-K edge obtained from the fault in SrTiO 3 , where no elongation of Ti-O bond length is identified at the faults (see Supplementary Fig. 6 for details on the EELS analysis of the fault in SrTiO 3 ).
Local structures of RP oxides. In addition to directly demonstrating the distortion of oxygen octahedra at the faults in perovskite oxides, the findings in this work have further notable implications for the in-depth understanding of the structures of a variety of RP oxides and halides, which exhibit a very wide range of physical properties encompassing dielectric and unusual ferroic, multiferroic, electrocatalytic, and optical behavior 7-10, 40-45 .
As can be easily recognized from their general formula, A n + 1 B n X 3n + 1 or equivalently AX[ABX 3 ] n , the presence of consecutive [AX] sublayers is a common structural feature irrespective of the value of n. In particular, it is noted that every anion octahedron in layer-structured A 2 BX 4 (n = 1) (or AX[ABX 3 ]) is in contact with two shear planes, as denoted by yellow broken lines in the atomic illustration of Sr 2 TiO 4 in Fig. 5a We examined more than 80 RP-type oxides and halides with high symmetry from the open database of inorganic materials (the Materials Project) and the Inorganic Crystal Structure Database (ICSD) to scrutinize whether the local net charge of [AX] sublayers exerts a general influence on the tetragonal distortion of anion octahedra in RP phases. Note that most of the RP oxides and halides under our examination in this work were confined to centrosymmetric phases with a single composition at each of the A and B sites in order to exclude any other complexity originating from the polarity induced by either cation offcentering from the second-order Jahn-Teller effect 46,47 , octahedral rotations 5-7, 10 , or cation ordering 48,49 . Taking this into consideration, structure comparisons were made largely between RP phases with a space group, I4/mmm 9, 49 .
Supplementary Tables 1-3 list all the structural information regarding the ratios of x axis and z axis B-X bond lengths, L z /L x , in 87 RP oxides and halides (see the detailed illustration in Supplementary Table 1 for the definition of L z /L x ); Ca-, Sr-, and Ba-based RP oxides with no local charge in Supplementary Table 1, K-and Cs-based RP halides in Supplementary Table S2, and lanthanide-based RP oxides in Supplementary Table 3.    Fig. 6b, c specifically exemplify the tetragonal elongation of every oxygen octahedra in Nd 2 NiO 4 , and Pr 2 NiO 4 , in addition to La 2 NiO 4 in Fig. 6a. The Ni-O bond lengths in each RP nickelate can be directly acquired from the ABF images in the right-hand column. As denoted by yellow arrows in the enlargements, the substantial elongation (more than 15%) of z axis Ni-O bonds toward the fault planes is readily recognized. This structural feature is consistently confirmed in La-based RP cobaltates and cuprates, as demonstrated in Fig. 7. Moreover, Cu 2+ is a well-known strong Jahn-Teller cation. As a consequence, more prominent z axis elongation (>27%) of {CuO 6 } octahedra in La 2 CuO 4 (Fig. 7b) than that of {CoO 6 } in La 2 CoO 4 and {NiO 6 } in La 2 NiO 4 is identified by a combination of the [LaO] + local charge and the Jahn-Teller effect. To clarify that this >27% strong elongation of {CuO 6 } octahedra is a common aspect in Pr 2 CuO 4 and Nd 2 CuO 4 as well (Supplementary Table 3), an additional structure comparison is provided in Supplementary Fig. 63.
We summarize several representative A 2 BX 4 (n = 1) oxides and fluorides among the RP phases with the space group I4/mmm in Supplementary Fig. 64 to highlight the impact of the net charge of the sublayers on the significant elongation of oxygen octahedra. As schematically described in Supplementary Fig. 64a Supplementary Fig. 64c for Pr-and Nd-based cobaltates, therefore, substantial z axis octahedral elongation is consistently identified.
When the structure of A-site solid solution (A′A″) 2 BO 4 , (where the valence states of A′ and A″ are 3+ and 2+, respectively) is scrutinized, the effect of electrostatic charge on the elongation of oxygen octahedra is further supported. Figure 8 shows the STEM images of (A′A″) 2 BO 4 -type (La,Sr) 2 AlO 4 , (La,Sr) 2 GaO 4 , and (Nd,Ca) 2 AlO 4 (see Supplementary Fig. 65 for composition verification of A-site solid solutions). As schematically depicted in the illustrations in the left-hand column, the A-site sublayers of these RP oxides encompass [SrO] 0 (or [CaO] 0 ) with no local charge in addition to charged [LaO] + (or [NdO] + ) as a solid solution. Consequently, the positive-charge electrostatics between the consecutive shear layers should diminish, resulting in comparatively weak interlayer repulsion. Considerably strong elongation of oxygen octahedra for screening the effective positive charge at the fault is thus no longer necessary. Indeed, as denoted in each of the magnified ABF images in the right-hand column, the length of z axis Al-O and Ga-O bonds does not exceed 2.2 Å, in contrast to a value of 2.3 Å in some nickelates (Fig. 6) and cobaltates (Fig. 7a) and even 2.5 Å in cuprates (Fig. 7b). Therefore, this series of direct observations in Fig. 8 provides consistent evidence for our findings on the electrostatics-induced distortion of oxygen octahedral in RP oxides.
In conclusion, we have observed the formation of [AX]-[AX] interleaved shear faults as common planar defects in five ABX 3 perovskite-type phases, SrTiO 3 , BaCeO 3 , LaCoO 3 , LaNiO 3 , and CsPbBr 3 . As each fault generated in LaCoO 3 and LaNiO 3 consists of two positively charged [LaO] + sublayers in contrast to [AX] with no local charge in SrTiO 3 , BaCeO 3 , and CsPbBr 3 , strong electrostatic repulsion can be established at the fault plane. We identified that this charge-induced instability could remarkably diminish via the asymmetric tetragonal distortion of oxygen octahedra by the protrusion of oxygen anions toward the fault plane and thereby effectively screen the repulsion. Furthermore, via direct atomic-column-resolved visualization by ABF imaging in 14 representative RP oxides, our atomiclevel findings regarding the tetragonal distortion of oxygen octahedra at the shear faults provide crucial insight to consistently explain the octahedron elongation commonly observed in lanthanide-based RP oxides among more than 80 RP-type oxides and halides. In addition to the electronic structure of metal cations on the basis of the Jahn-Teller effect, the present study suggests that the local electrostatic instability is a significant cause of the tetragonal distortion of oxygen octahedra in complex oxides.

Methods
Preparation of polycrystalline samples. To prepare polycrystalline perovskite and RP phase samples, powders were first synthesized via a conventional solid-state reaction method using SrCO 3 (99.9%, Sigma Aldrich) and TiO 2 (99.9%, Sigma Aldrich) for SrTiO 3 Table 3. Strong local repulsion between [LnO] + sublayers is illustrated in the lefthand column. Significant elongation of the Ni-O bonds at the shear planes is denoted by yellow arrows in the ABF images, providing quantitative information on the bond lengths. Red arrows in each image indicate substantial displacement of oxygen anions.
by adding 3 mol% more of the La nitrate for LaNiO 3 films. For complete dissolution of the source materials, refluxing was carried out at 80°C for 1 h. Each of the precursor solutions was deposited on (001) LaAlO 3 and (001) SrTiO 3 (Shinkosha, Japan) single-crystal substrates by a spin-coating method at 5000 rpm for 10 s. The wet films were dried at 150°C for 10 min on a hot plate, and then annealed at 800°C for 1 h in the air for LaNiO 3 films, at 900°C for 1 h in the air for La 2 NiO 4 films, and at 1000°C for 1 h in N 2 -flow atmosphere for La 2 CoO 4 and La 4 Co 3 O 10 films for crystallization. X-ray diffractometry (X'Pert-PRO MRD, PANalytical) and STEM observation verified the epitaxy of grown films. Commercially available (001) single-crystal substrates (MTI corporation) were purchased for structure observation in LaSrAlO 4 , LaSrGaO 4 , and NdCaAlO 4 . Nanocrystal synthesis. CsPbBr 3 nanocrystals were synthesized by a microwaveassisted method 50 . A solvent mixture was prepared by using 1-octadecene (5 mL), oleylamine (0.5 mL), and oleic acid (0.5 mL). This mixture was degassed by evacuation and stirred in a round bottom flask at 170°C on a hot plate for 30 min. After the degassing process, the mixture was transferred into a 10-mL vial and followed by adding and dispersing Cs 2 CO 3 (0.0217 g, 99.995%, Sigma Aldrich) and PbBr 2 (0.0738 g, 99.999%, Sigma Aldrich) with a vortex mixer. This vial was placed into a microwave oven and subsequent microwave irradiation was carried out at 700 W for 5 min. The 5-min irradiation together with 1-min intermission was further repeated eight more times, resulting in irradiation for 45 min in total. To separate residual solvents and a solid product, the mixture after the microwave irradiation was centrifuged at 1398×g for 5 min. The solid product was dispersed in toluene and further purified by centrifugation at 5590×g for 5 min so as to finally acquire a toluene solution containing homogeneously dispersed CsPbBr 3 nanocrystals.
STEM, EELS, and specimen preparation. Specimens for STEM observation of sintered polycrystalline samples were prepared by mechanical grinding to a thickness of 80 μm, dimpling to a thickness of <10 μm, and finally ion-beam thinning by using a precision ion polishing system (PIPS, Gatan Inc.) for electron transparency. STEM specimens for LaNiO 3 and NdNiO 3 thin films were prepared by lift out via ion-beam milling in a focused ion-beam system (Quanta 3D FEG and Helios G4 UX, ThermoFisher Scientific). Protective amorphous carbon and thin Pt layers were applied over the region of interest before milling. To minimize the sidewall damage and sufficiently thin the specimen for electron transparency, final milling was carried out at a voltage of~2 kV. HAADF-and ABF-STEM images were acquired with a transmission electron microscope (Titan cubed G2 60-300, ThermoFisher Scientific) at 200 kV or 300 kV with a spherical aberration (Cs) corrector (CEOS GmbH). The optimum size of the electron probe was~1 Å with a convergence semiangle of 19 mrad. The collection semiangles of the STEM detectors were set to 40.0-200 mrad for HAADF imaging and 9.61−53.6 (or 10.1-19.1) mrad for ABF imaging. EELS analysis was performed with a Gatan Image Filter (GIF Quantum 965, Gatan Inc.). Electron energy-loss spectra for the Ba-M 5 (781 eV) and Ce-M 5 (883 eV) edges were acquired for atomic-column spectrum imaging in BaCeO 3 and with a dispersion of 0.25 eV per channel and a collection aperture of 5 mm in diameter. The O-K, Ti-L 2,3 , and Co-L 2,3 edges were also collected in SrTiO 3 and LaCoO 3 samples containing shear faults to examine whether the oxidation states of Ti and Co and the orbital hybridization with oxygen vary at the fault plane.
DFT calculations. Ab initio DFT calculations for DOS variation in LaNiO 3 were carried out using the spin-polarized local density approximation (LDA) functional for exchange-correlation, along with the ultrasoft pseudopotentials for ionic cores, as implemented in the CASTEP code (Biovia Inc.). To consider the electron localization around Ni ions, the LDA + U method with the Hubbard U parameter (U = 4.0 eV for Ni 3d states) was employed. A low-spin (t 2g 6 )(e g 1 ) for d 7 Ni 3+ configuration was assumed for the spin-polarized calculations. The plane-wave basis set for the kinetic energy cutoff was 500 eV. Relaxation of the internal coordinates for each atom was performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm with convergence tolerances of 0.1 eV/Å for the maximum ionic force, 5 × 10 −5 eV/atom for the total energy, and 0.005 Å for the maximum ionic displacement.