Manipulation of octahedral distortion at atomic length scale is an effective means to tune the physical ground states of functional oxides. Previous work demonstrates that epitaxial strain and film thickness are variable parameters to modify the octahedral rotation and tilt. However, selective control of bonding geometry by structural propagation from adjacent layers is rarely studied. Here we propose a new route to tune the ferromagnetic response in SrRuO3 (SRO) ultrathin layers by oxygen coordination of adjacent SrCuO2 (SCO) layers. The infinite-layered CuO2 in SCO exhibits a structural transformation from "planar-type" to "chain-type" as reducing film thickness. These two orientations dramatically modify the polyhedral connectivity at the interface, thus altering the octahedral distortion of SRO. The local structural variation changes the spin state of Ru and hybridization strength between Ru 4d and O 2p orbitals, leading to a significant change in the magnetoresistance and anomalous Hall resistivity of SRO layers. These findings could launch further investigations into adaptive control of magnetoelectric properties in quantum oxide heterostructures using oxygen coordination.
Oxygen octahedral distortions including tilts/rotations, deformations and off-centering in (layered) perovskites play the key role in their numerous functional properties. At the polar-centrosymmetric phase boundary in bi-layered perovskite Ca3-xSrxTi2O7 with x~1, we found the presence of abundant topological Z8 vortex-antivortex pairs, associated with four oxygen octahedral tilts at domains and another four different oxygen octahedral tilts at domain boundaries. Our discovery opens a new revenue to unveil topological defects associated with various types of oxygen octahedral distortions.
NiO6-octahedral tilts in ultrathin LaNiO3 films were studied using position averaged convergent beam electron diffraction (PACBED) in scanning transmission electron microscopy. Both the type and magnitude of the octahedral tilts were determined by comparing PACBED experiments to frozen phonon multislice simulations. It is shown that the out-of-plane octahedral tilt of an epitaxial film under biaxial tensile stress (0.78 % in-plane tensile strain) increases by ~ 20%, while the in-plane rotation decreases by ~ 80%, compared to the unstrained bulk material.
The rotation of octahedra (octahedral tilting) is common in ABO3 perovskites and relevant to many physical phenomena, ranging from electronic and magnetic properties, metal-insulator transitions to improper ferroelectricity. Hydrostatic pressure is an efficient way to tune and control octahedral tiltings. However, the pressure behavior of such tiltings can dramatically differ from one material to another, with the origins of such differences remaining controversial. In this work, we discover several new mechanisms and formulate a set of simple rules that allow to understand how pressure affect…
We investigate the effect of epitaxial strain on [001]-oriented LaAlO3 using first-principles density functional calculations. We find a series of structural phase transitions between states characterized by distinct patterns of tilting of the AlO6 octahedra. By tuning the biaxial strain from compressive to tensile, we induce an evolution in the crystal structure in which the tilt axis changes from out-of-plane to in-plane, corresponding to space groups I4/mcm and Imma. We also study the effect of uniaxial relaxation of the usual biaxial epitaxial constraint and explore this as a mechanism for…
The octahedral tilting and ferroelectric-like structural transition of LiOsO3 metallic perovskite [Nature Materials 12, 1024 (2013)] was examined using first-principles density-functional theory. In LiOsO3, a-a-a- octahedral titling mode is responsible for the cubic to rhombohedral structural transition, which is stable phase at room temperature. At low temperatures, a non-centrosymmetric transition to a rhombohedra phase was realized due to zone center phonon softening. The phase transition behavior of LiOsO3 can be explained fully by density functional calculations and phonon calculations. T…
A mathematical framework is developed to describe tilted perovskites using a tensor description of octahedral deformations. The continuity of octahedral tilts through the crystal is described using an operator which relates the deformations of adjacent octahedra; examination of the properties of this operator upon application of symmetry elements allows the space group of tilted perovskites to be obtained. It is shown that the condition of octahedral continuity across a planar defect such as an anti-phase boundary or domain wall necessarily leads to different octahedral tilting at the defect, …
High-temperature phase behavior in the system LixNa1-xNbO3 has been studied by using high-resolution powder neutron diffraction. Each of the three compositions studied in the Na-rich part of the phase diagram (x = 0.03, 0.08 and 0.12) shows evidence for distinct and complex structural modulations based on different tilting schemes of NbO6 octahedral units. Whilst octahedral tilting is prevalent in the structural chemistry of perovskites the nature of complexity of the phases observed here is unprecedented. Neither of the long-range tilt phases observed in NaNbO3 itself occurs here; instead a n…
Octahedral tilting is key to the structure and functionality of perovskites. Here we show how these distortions manifest in the related Prussian blue analogues (PBAs): cyanide versions of double perovskites with formula A$_x$M[M$^{\prime}$(CN)$_6$]$_{1-y}\Box _y\cdot n$H$_2$O (A = alkali metal, M and M$^{\prime}$ = transition metals, $\Box$ = vacancy/defect). Tilts are favoured by high values of $x$ if A = Na or K, whereas the transition metals play a less important role. External hydrostatic pressure can induce tilt transitions nearly irrespective of the stoichiometry, whereas thermal transit…
The effects of octahedral tilting of RbANb2O7 (A = Bi, Nd) compounds was studied using density-functional theory. In this compound, the structural phase transition was correlated with two octahedral tilting modes (a-a-c0 tilting and a0a0c+ tilting), and magnitude of the octahedral tilting mode was analyzed in the optimized structure. The theoretical results correlated well with the recent experimental results on the ferroelectricity of RbBiNb2O7. The hybrid improper ferroelectricity resulting from the coupling of two octahedral tilting modes and off center displacement mode was analyzed by gro…
Interface engineering in perovskite oxide superlattices has developed into a flourishing field, enabling not only further tuning of the exceptional properties, but also giving access to emergent physical phenomena. Here, we reveal a new mechanism for enhancing the electric polarization by the interface-induced oxygen octahedral tilts in BaTiO3/CaTiO3 superlattices. By combining a novel genetic algorithm with density functional theory (DFT), we predict that the true ground states in 1:1 and 2:2 BaTiO3/CaTiO3 superlattices grown on SrTiO3 adopt Pc symmetry with a large proper electric polarizati…
Structural modelling of octahedral tilts in perovskites is typically done using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports on the development of constraints for modelling pure octahedral tilts and implemented the constraints in diffpy-CMI, a powerful package to analyse pair distributio…
A theoretically supported experimental study of the (1-x)LaFeO3.xLaMnO3 (LFO-LMO) solid solution is being reported for the first time which reveals a phase transformation from the Pbnm and R3-c phase at a chemical composition of x=0.625. Correlation of octahedral distortion and phase transition was extensively investigated using x-ray photoelectron spectroscopy (XPS), Raman and x-ray diffraction (XRD) measurements and density functional theory (DFT) calculation. A detailed study of the structural lattice parameters, bond lengths, bond angles have been done, supported by valence state and elect…
Ruddelsden-Popper halide perovskites are highly versatile quasi-two-dimensional energy materials with a wide range of tunable optoelectronic properties. Here we use the all-inorganic Cs$_{n+1}$Pb$_n$X$_{3n+1}$ Ruddelsden-Popper perovskites with X=I, Br, and Cl to systematically model the effect of octahedral tilting distortions on the energy landscape, band gaps, macroscopic polarization, and the emergence of Rashba-/Dresselhaus splitting in these materials. We construct all unique $n=1$ and $n=2$ structures following from octahedral tilts and use first-principles density functional theory to …
We present a resonant x-ray scattering study of the octahedral tilt order between 50K and 310K in La_7/8Sr_1/8MnO_3. At the La L_II-edge the resonant (300) reflection probes cooperative tilts of the MnO_6-octahedra in this material, as verified by a model caclulation as well as a LDA+U study. The investigation of the octahedral tilts as a function of temperature and the comparison to the lattice parameters, the magnetization and the superlattice reflections related to charge and/or orbital order reveal an intimate coupling between electronic and tilt degrees of freedom in La_7/8Sr_1/8MnO_3.
Structural disorder is common in metal-halide perovskites and important for understanding the functional properties of these materials. First-principles methods can address structure variation on the atomistic scale, but they are often limited by the lack of structure-sampling schemes required to characterize the disorder. In this work, structural disorder in the benchmark inorganic halide perovskites CsPbI$_3^{}$ and CsPbBr$_3^{}$ is computationally studied in terms of the three octahedral-tilting angles. The consequent variation in energetics and properties are described by three-dimensional…
Topological spin textures as an emerging class of topological matter offer a medium for information storage and processing. The recently discovered topological Hall effect (THE) is considered as a fingerprint for electrically probing non-trivial spin-textures. But the origin of THE in oxides has remained elusive. Here we report an observation of the THE in ultrathin (unit cells. u.c.) 4d ferromagnetic SrRuO3 films grown on SrTiO3(001) substrates, which can be attributed to the chiral ordering of spin structure (i.e., skyrmion-like) in the single SrRuO3 layer without contacting 5d oxide SrIrO3 …
Polarized neutron reflectometry measurements are presented exploring the evolution of ferrimagnetism in GdTiO$_3$ films as they are confined between SrTiO$_3$ layers of variable thicknesses. As GdTiO$_3$ films approach the thin layer limit and are confined within a substantially thicker SrTiO$_3$ matrix, the TiO$_6$ octahedral tilts endemic to GdTiO$_3$ coherently relax toward the undistorted, cubic phase of SrTiO$_3$. Our measurements reveal that the ferrimagnetic state within the GdTiO$_3$ layers survives as the TiO$_6$ octahedral tilts in the GdTiO$_3$ layers are suppressed. Furthermore, ou…
We present a systematic study of the effect of Y doping and hydration level on the structural transformations of BaCeO3 based on anelastic spectroscopy experiments. The temperature of the intermediate transformation between rhombohedral and orthorhombic Imma phases rises with increasing the molar fraction x of Y roughly as (500 K)x in the hydrated state, and is depressed of more than twice that amount after complete dehydration. This is explained in terms of the effect of doping on the average (Ce/Y)-O and Ba-O bond lengths, and of lattice relaxation from O vacancies. The different behavior of…
The results are presented of anelastic and dielectric spectroscopy measurements on large grain ceramic PZT with compositions near the two morphotropic phase boundaries (MPBs) that the ferroelectric (FE) rhombohedral phase has with the Zr-rich antiferroelectric and Ti-rich FE tetragonal phases. These results are discussed together with similar data from previous series of samples, and reveal new features of the phase diagram of PZT, mainly connected with octahedral tilting and its coupling with the polar modes. Additional evidence is provided of what we interpret as the onset of the tilt instab…
Nuclear site analysis methods are used to enumerate the normal modes of $ABX_{3}$ perovskite polymorphs with octahedral rotations. We provide the modes of the fourteen subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the $BX_{6}$ octahedra with different sense and amplitude about high symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generate…
Bonding geometry engineering of metal-oxygen octahedra is a facile way of tailoring various functional properties of transition metal oxides. Several approaches, including epitaxial strain, thickness, and stoichiometry control, have been proposed to efficiently tune the rotation and tilting of the octahedra, but these approaches are inevitably accompanied by unnecessary structural modifications such as changes in thin-film lattice parameters. In this study, we propose a method to selectively engineer the octahedral bonding geometries, while maintaining other parameters that might implicitly in…
We present a systematic first-principles study of the structural and vibrational properties of perovskite-structure EuTiO3. Our calculated phonon spectrum of the high-symmetry cubic structural prototype shows strong M- and R-point instabilities, indicating a tendency to symmetry-lowering structural deformations composed of rotations and tilts of the oxygen octahedra. Subsequent explicit study of 14 different octahedral tilt-patterns showed that the I4/mcm, Imma, and R\bar{3}c structures, all with antiferrodistortive rotations of the octahedra, have significantly lower total energy than the pro…
The effect of octahedral tilting on the acentric structural transitions in AGaO$_{3}$/A'GaO$_{3}$ [001], [110], and [111] superlattices (A, A' = La, Pr, Nd) is studied using density functional theory. We find the displacive transitions are driven by two octahedral rotations modes (a$^{-}$a$^{-}$c$^{0}$ and a$^{0}$a$^{0}$c$^{+}$ tilting), with amplitudes that depend on the A and A' chemistry and cation ordering direction. We find the ground states structures of the [001] and [111] ordered superlattices are polar. The coupling of octahedral tilting modes through a hybrid improper ferroelectric m…
Emergent phenomena at heterointerfaces are directly associated with the bonding geometry of adjacent layers. Effective control of accessible parameters, such as the bond length and bonding angles, offers an elegant method to tailor competing energies of the electronic and magnetic ground states. In this study, we construct unit thick syntactic layers of cobaltites within a strongly tilted octahedral matrix via atomically precise synthesis. The octahedral tilt patterns of adjacent layers propagate into cobaltites, leading to a continuation of octahedral tilting while maintaining significant mis…
Two-dimensional (2D) ferroelectricity has attracted extensive attention since its discovery in the monolayers of van der Waals materials. Here we show that 2D ferroelectricity induced by octahedral rotation distortion is widely present in the perovskite bilayer system through first-principles calculations. The perovskite tolerance factor plays a crucial role in the lattice dynamics and ground-state structure of the perovskite monolayers and bilayers, thus providing an important indicator for screening this hybrid improper ferroelectricity. Generally, the ferroelectric switching via an orthorho…
Antiferromagnetic PbMnTeO6, also known as mineral kuranakhite, has been reported recently to have all three cations in trigonal prismatic coordination, which is extremely unusual for both Mn(4+) and Te(6+). In this work, the phase was reproduced with the same lattice parameters and Néel temperature TN = 20 K. However, powder neutron diffraction unambiguously determined octahedral (trigonal antiprismatic) coordination for all cations within the chiral space group P312. The same symmetry was proposed for SrMnTeO6 and PbGeTeO6, instead of the reported space groups P-62m and P31m, respectively. Pb…
Epitaxial oxide interfaces with broken translational symmetry have emerged as a central paradigm behind the novel behaviors of oxide superlattices. Here, we use scanning transmission electron microscopy to demonstrate a direct, quantitative unit-cell-by-unit-cell mapping of lattice parameters and oxygen octahedral rotations across the BiFeO3-La0.7Sr0.3MnO3 interface to elucidate how the change of crystal symmetry is accommodated. Combined with low-loss electron energy loss spectroscopy imaging, we demonstrate a mesoscopic antiferrodistortive phase transition and elucidate associated changes in…
Rare earth based cobalt-ruthenium double perovskites A$_2$CoRuO$_6$ (A = La, Pr, Nd and Sm) were synthesized and investigated for their structural and magnetic properties. All the compounds crystallize in the monoclinic $P2_1/n$ structure with the indication of antisite disorder between Co and Ru sites. While, La compound is already reported to have an antiferromagnetic state below 27 K, the Pr, Nd and Sm systems are found to be ferrimagnetic below $T_c$ = 46, 55 and 78 K respectively. Field dependent magnetization data indicate prominent hysteresis loop below $T_c$ in the samples containing m…
Recently, layered hybrid perovskites have been attracting huge interest due to a wide range of possible chemical compositions and the resulting tunability of the materials properties. In this study, we investigate the effect of the chain length of the organic ligands on the optical properties of stacks of two dimensional perovskite layers consisting of alkylammonium lead iodide (CnH2n+1NH3)2PbI4 with n=4-18. Photoluminescence and absorption spectroscopy reveal a blueshift with increasing chain length n including a jump of 110 meV between the n=10 and n=12 ligands due to a change in octahedral …
Doping ferroelectrics with carriers is often detrimental to polarization. This makes the design and discovery of metals that undergo a ferroelectric-like transition challenging. In this letter, we show from first principles that the oxygen octahedral rotations in perovskites are often enhanced by electron doping, and this can be used as a means to strengthen the structural polarization in certain hybrid-improper ferroelectrics -- compounds in which the polarization is not stabilized by the long range Coulomb interactions but is instead induced by a trilinear coupling to octahedral rotations. W…
We present a comprehensive review of the structural chemistry of hybrid lead halides of stoichiometry APbX4, A2PbX4 or AAPbX4, where A and A are organic ammonium cations and X = Cl, Br or I. These compounds may be considered as layered perovskites, containing isolated, infinite layers of corner-sharing PbX4 octahedra separated by the organic species. We first extract over 250 crystal structures from the CCDC and classify them in terms of unit cell metrics and crystal symmetry. Symmetry mode analysis is then used to identify the nature of key structural distortions of the [PbX4] layers. Two gen…
NiO6 octahedral tilts in the LaNiO3/SrTiO3 superlattices are quantified using position averaged convergent beam electron diffraction in scanning transmission electron microscopy. It is shown that maintaining oxygen octahedra connectivity across the interface controls the octahedral tilts in the LaNiO3 layers, their lattice parameters and their transport properties. Unlike films and layers that are connected on one side to the substrate, subsequent LaNiO3 layers in the superlattice exhibit a relaxation of octahedral tilts towards bulk values. This relaxation is facilitated by correlated tilts i…
We model short-period superlattices of WO$_3$ and ReO$_3$ with first-principles calculations. In fully-relaxed superlattices, we observe that octahedral tilts about an axis in the planes of the superlattices do not propagate from one material, despite the presence of the corner-shared oxygen atoms. However, we find that octahedral rotation is enhanced within WO$_3$ layers in cases in which strain couples with native antiferroelectric displacements of tungsten within their octahedral cages. Resulting structures remain antiferroelectric with low net global polarization. Thermodynamic analysis re…
The effect of rare-earth ion size on the octahedral distortions in rare-earth chromites (RCrO3, R = Lu, Tb, Gd, Eu, Sm) crystallizing in the orthorhombic structure has been studied using Raman scattering and synchrotron powder x-ray diffraction up to 20 GPa. From our studies on RCrO3 we found that the octahedral tilts (distortions) increase with pressure. This is contrary to the earlier report which suggests that in LaCrO3, the distortions decrease with pressure leading to a more ordered phase at high pressure. Here we observe that the rate of increase in distortion decreases with the increase…
Determining the 3-dimensional crystallography of a material with sub-nanometre resolution is essential to understanding strain effects in epitaxial thin films. A new scanning transmission electron microscopy imaging technique is demonstrated that visualises the presence and strength of atomic movements leading to a period doubling of the unit cell along the beam direction, using the intensity in an extra Laue zone ring in the back focal plane recorded using a pixelated detector method. This method is used together with conventional atomic resolution imaging in the plane perpendicular to the be…
Computational and Experimental Investigation of Chiral and Achiral 2D Organic Lead Bromide Perovskites: Octahedral Distortions and Electronic and Optical Properties
Thickness driven electronic phase transitions are broadly observed in different types of functional perovskite heterostructures. However, uncertainty remains whether these effects are solely due to spatial confinement, broken symmetry or rather to a change of structure with varying film thickness. Here, we present direct evidence for the relaxation of oxygen 2p and Mn 3d orbital (p-d) hybridization coupled to the layer dependent octahedral tilts within a La2/3Sr1/3MnO3 film driven by interfacial octahedral coupling. An enhanced Curie temperature is achieved by reducing the octahedral tilting v…
Strain engineering of functional properties in epitaxial thin films of strongly correlated oxides exhibiting octahedral-framework structures is hindered by the lack of adequate misfit relaxation models. Here we present unreported experimental evidences of a four-stage hierarchical development of octahedral-framework perturbations resulting from a progressive imbalance between electronic, elastic and octahedral tilting energies in La0.7Sr0.3MnO3 epitaxial thin films grown on SrTiO3 substrates. Electronic softening of the Mn - O bonds near the substrate leads to the formation of an interfacial l…
Octahedral tilting is most common distortion process observed in centrosymmetric perovskite compounds (ABO$_{3}$). Indeed, crucial physical properties of this oxide stem from the tilts of BO$_{6}$ rigid octahedra. In microwave ceramics with perovskite-type structure, there is a close relation between the temperature coefficient of resonant frequency and tilt system of the perovskite structure. However, in many cases, limited access facilities are needed to assign correctly the space group, including neutron scattering and transmission electron microscopy. Here, we combine the Raman scattering …
Motivated by the recently observed unconventional Hall effect in ultra-thin films of ferromagnetic SrRuO$_3$ (SRO) we investigate the effect of strain-induced oxygen octahedral distortion in the electronic structure and anomalous Hall response of the SRO ultra-thin films by virtue of density functional theory calculations. Our findings reveal that the ferromagnetic SRO films grown on SrTiO$_3$ (in-plane strain of $-$0.47$\%$) have an orthorhombic (both tilting and rotation) distorted structure and with an increasing amount of substrate-induced compressive strain the octahedral tilting angle is…
We investigate the structural and magnetic phase transitions in EuTi1-xNbxO3 with synchrotron powder X-ray diffraction (XRD), resonant ultrasound spectroscopy (RUS), and magnetization measurements. Upon Nb-doping, the Pm-3m to I4/mcm structural transition shifts to higher temperatures and the room temperature lattice parameter increases while the magnitude of the octahedral tilting decreases. In addition, Nb substitution for Ti destabilizes the antiferromagnetic ground state of the parent compound and long range ferromagnetic order is observed in the samples containing more than 10% Nb. The st…
Octahedral distortion plays a key role in engineering the physical properties of heterostructures composed of perovskite oxides. We observe a strong in-plane uniaxial magnetic anisotropy in a strain-enabled multiferroic EuTiO3 thin film epitaxially grown on a (110)o DyScO3 substrate. First principles calculations show that the magnetic anisotropy is closely correlated with the uniaxial TiO6 octahedral tilting and the ferroelectric polarization of the film, indicating potential strong magnetoelectric coupling in the strain-engineered multiferroic system.
The crystal structures of the triangular lattice, layered anhydrous alums KCr(SO4)2, RbCr(SO4)2 and KAl(SO4)2 are characterized by X-ray and neutron powder diffraction at temperatures between 1.4 and 773 K. The compounds all crystallize in the space group P-3, with octahedral coordination of the trivalent cations. In all cases, small amounts of disorder in the stacking of the triangular layers of corner sharing MO6 octahedra and SO4 tetrahedra is seen, with the MO6-SO4 network rotated in opposite directions between layers. The electron diffraction study of KCr(SO4)2 supports this model, which …
The electro-magnetic properties of ultrathin epitaxial ruthenate films have long been the subject of debate. Here we combine experimental with theoretical investigations of (SrTiO3)5-(SrRuO3)n-(SrTiO3)5 (STO5-SROn-STO5) heterostructures with n = 1 and 2 unit cells, including extensive atomic-resolution scanning-transmission-electron-microscopy imaging, electron-energy-loss-spectroscopy chemical mapping, as well as transport and magneto-transport measurements. The experimental data demonstrate that the STO5-SRO2-STO5 heterostructure is stoichiometric, metallic, and ferromagnetic with TC ~ 128 K…
We study the effects of specimen mistilt on the picometer-scale measurement of local structure by combing experiment and simulation in annular bright-field scanning transmission electron microscopy (ABF-STEM). A relative distance measurement method is proposed to separate the tilt effects from the scan noise and scan distortion. We find that under a typical experimental condition a small specimen tilt (~6 mrad) in 25 nm thick SrTiO3 along [001] causes 11.9 pm artificial displacement between O and Sr/TiO columns in ABF image, which is more than 3 times of scan noise and sample drift induced ima…
We have investigated the crystal, electronic, and magnetic structure of Mn5O8 by means of state of-the-art density functional theory calculations and neutron powder diffraction (NPD) measurements. This compound stabilizes in the monoclinic structure with space group C2/m where the Mn ions are in the distorted octahedral and trigonal prismatic coordination with oxygen atoms. The calculated structural parameters based on total energy calculations are found to be in excellent agreement with low temperature NPD measurements when we accounted correct magnetic structure and Coulomb correlation effec…
We report the pressure dependence of perovskite distortions in rare-earth (R) orthochromites (RCrO3) probed using Raman scattering in order to investigate the origin of structural transition from orthorhombic Pnma to rhombohedral R-3C phase in LaCrO3. The pressure induced changes in octahedral tilt modes demonstrates that tilt distortions are suppressed in LaCrO3 and are enhanced in the remaining members of RCrO3 family. This crossover between the two opposite pressure behaviors occurs at a critical R-ion radius of 1.20 Å. We attempted to establish the relation between this unusual crossover a…
We survey the most important kinds of structural complexity in Prussian blue analogues, their implications for materials function, and how they might be controlled through judicious choice of composition. We focus on six particular aspects: octahedral tilts, A-site `slides', Jahn--Teller distortions, A-site species and occupancy, hexacyanometallate vacancies, and framework hydration. The promising K-ion cathode material K$_x$Mn[Fe(CN)$_6$]$_y$ serves as a recurrent example that illustrates many of these different types of complexity. Our article concludes with a discussion of how the interplay…
