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Abstract Structural domains and domain walls, inherent in single crystalline perovskite oxides, can significantly influence the properties of the material and therefore must be considered as a vital part of the design of the epitaxial oxide thin films. We employ 4D-STEM combined with machine learning (ML) to comprehensively characterize domain structures at both high spatial resolution and over a significant spatial extent. Using orthorhombic LaFeO₃as a model system, we explore the application of unsupervised and supervised ML in domain mapping, which demonstrates robustness against experiment uncertainties. The results reveal the consequential formation of multiple domains due to the structural degeneracy when LaFeO₃film is grown on cubic SrTiO₃. In situ annealing of the film shows the mechanism of domain coarsening that potentially links to phase transition of LaFeO₃at high temperatures. Moreover, synthesis of LaFeO₃on DyScO₃illustrates that a less symmetric orthorhombic substrate inhibits the formation of domain walls, thereby contributing to the mitigation of structural degeneracy. High fidelity of our approach also highlights the potential for the domain mapping of other complicated materials and thin films. 

Abstract Polarons and spin-orbit (SO) coupling are distinct quantum effects that play a critical role in charge transport and spin-orbitronics. Polarons originate from strong electron-phonon interaction and are ubiquitous in polarizable materials featuring electron localization, in particular 3d transition metal oxides (TMOs). On the other hand, the relativistic coupling between the spin and orbital angular momentum is notable in lattices with heavy atoms and develops in 5d TMOs, where electrons are spatially delocalized. Here we combine ab initio calculations and magnetic measurements to show that these two seemingly mutually exclusive interactions are entangled in the electron-doped SO-coupled Mott insulator Ba₂Na_1−xCa_xOsO₆(0 < x < 1), unveiling the formation ofspin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os 5d¹spin-orbital J_eff = 3/2 levels, characteristic of the parent compound Ba₂NaOsO₆(BNOO), into a bipolaron 5d²J_eff = 2 manifold, leading to the coexistence of different J-effective states in a single-phase material. The gradual increase of bipolarons with increasing doping creates robust in-gap states that prevents the transition to a metal phase even at ultrahigh doping, thus preserving the Mott gap across the entire doping range from d¹BNOO to d²Ba₂CaOsO₆(BCOO). 

The synthesis, crystal structures, and optical properties of four ternary and six quaternary halides containing the Rh3+ ion are reported here. Rb3RhCl6 adopts a monoclinic structure with isolated [RhCl6]3− octahedra. Rb3Rh2Cl9, Cs3Rh2Cl9, and Cs3Rh2Br9 crystallize in a vacancy ordered variant of the 6H hexagonal perovskite structure, which contains isolated Rh2X93− (X = Cl, Br) dimers of face-sharing octahedra. Cs2AgRhCl6 and Cs2NaRhCl6 adopt the 12R rhombohedral perovskite structure, featuring [M2RhCl12]7− face-sharing octahedral trimers, connected to one another through rhodium-centered octahedra. A4AgRhCl8 and A4AgRhBr8 (A = CH3CH2CH2CH2NH3+, (CH3)2CHCH2CH2NH3)+) crystallize in a cation-ordered variant of the n = 1 Ruddlesden Popper structure, which features layers of corner-connected octahedra with a chessboard ordering of Ag+ and Rh3+ ions separated by double layers of organic cations. The diffuse reflectance spectra of all compositions studied feature peaks in the visible that can be attributed to spin-allowed d-to-d transitions and peaks in the UV that arise from charge transfer transitions. Electronic structure calculations reveal moderate Rh–X–Ag hybridization when rhodium- and silver-centered octahedra share corners, but minimal hybridization when they share faces. Many of the compositions studied have an electronic structure that is effectively zero-dimensional, but Cs2AgRhCl6 is found to possess a two-dimensional electronic structure. The results are instructive for controlling the electronic dimensionality of compositionally complex halide perovskite derivatives. 

Hybrid n = 1 Ruddlesden-Popper perovskites with aromatic ammonium cations like benzylammonium (BzA) and phenethylammonium (PEA) have been shown to adopt polar structures and exhibit ferroelectricity, but many of the examples discovered thus far contain either Pb or Cd. Here, we describe the synthesis and structural characteriza-tion of four layered halide double perovskites: (BzA)4AgBiBr8, (PEA)4AgBiBr8, (BzA)4AgInCl8, and (PEA)4AgInCl8. In all four compounds the inorganic layers exhibit a chessboard ordering of Ag+ and Bi3+/In3+ and the layers stack in a coherent pattern that maintains the ordering over three-dimensional space. The octahedra sur-rounding Ag+ show a large axial compression, which results in much shorter bonds to the terminal halide ions than to the bridging halide ions, whereas the bismuth- and indium-centered octahedra show only small distortions. There appears to be a competition between polar distortions of the octahedra and octahedral tilting, both of which can optimize hydrogen bonding interactions between the ammonium cations and the inorganic layers. Unlike the Pb- or Cd-containing analogs, the double perovskites seem to favor patterns of octahedral tilting that suppress po-lar ordering of the organic cations. The packing of the organic cations depends on both their conformational flexi-bility and the lateral dimensions of the inorganic layer. These forces favor intra-layer edge-to-face interaction be-tween aromatic rings in the three of the four compounds. The lone exception is (PEA)4AgBiBr8, which forms weak inter-layer edge-to-face interactions between aromatic rings and slip-stacked packing within each organic layer. 

A symmetry mode analysis yields 47 symmetrically distinct patterns of octahedral tilting in hybrid organic–inorganic layered perovskites that adopt then= 1 Ruddlesden–Popper (RP) structure. The crystal structures of compounds belonging to this family are compared with the predictions of the symmetry analysis. Approximately 88% of the 140 unique structures have symmetries that agree with those expected based on octahedral tilting alone, while the remaining compounds have additional structural features that further lower the symmetry, such as asymmetric packing of bulky organic cations, distortions of metal-centered octahedra or a shift of the inorganic layers that deviates from thea/2 +b/2 shift associated with the RP structure. The structures of real compounds are heterogeneously distributed amongst the various tilt systems, with only 9 of the 47 tilt systems represented. No examples of in-phase ψ-tilts about theaand/orbaxes of the undistorted parent structure were found, while at the other extreme ∼66% of the known structures possess a combination of out-of-phase ϕ-tilts about theaand/orbaxes and θ-tilts (rotations) about thecaxis. The latter combination leads to favorable hydrogen bonding interactions that accommodate the chemically inequivalent halide ions within the inorganic layers. In some compounds, primarily those that contain either Pb²⁺or Sn²⁺, favorable hydrogen bonding interactions can also be achieved by distortions of the octahedra in combination with θ-tilts.