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 transitions are only reported for $x>1$. Interstitial water can alter the transitions induced by a different stimulus, but (de)hydration \textit{per se} does not lead to tilts. Implications for rational design of critical functionality -- including improper ferroelectricity and electrochemical performance -- are discussed. The results are important for a fundamental understanding of phase transitions as well as for the development of functional materials based on PBAs.
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…
The effect of the octahedral tilting of ASnO3 (A = Ca, Sr, Ba) parent compound and bi-color ASnO3/BSnO3 superlattice (A, B = Ca, Sr, Ba) was predicted from density-functional theory. In the ASnO3 parent compound, the structural phase transition as a function of the A-site cation size was correlated with the magnitude of the two octahedral tilting modes (a-a-c0 tilting and a0a0c+ tilting). The magnitude of the octahedral tilting modes in the superlattices was analyzed quantitatively and found to be associated with that of the constituent parent materials. The ASnO3/BSnO3 superlattices showed hy…
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.
Instabilities relating to cooperative octahedral tilting is common in materials with perovskite structures, and in particular in the sub class of halide perovskites. In this work, the energetics of octahedral tilting in the inorganic metal halide perovskites CsPbI$_3$ and CsSnI$_3$ are investigated using first-principles density functional theory calculations. Several low energy paths between symmetry equivalent variants of the stable orthorhombic (\textit{Pnma}) perovskite variant are identified and investigated. The results are in favor of the presence of dynamic disorder in the octahedral t…
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…
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…
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…
Observations by in-situ transmission electron microscopy (TEM) reveal the changes in domains morphology in 0.885(Bi1/2Na1/2)TiO3-0.05(Bi1/2K1/2)TiO3-0.015(Bi1/2Li1/2)TiO3-0.05BaTiO3 ceramics. Evolution of the macroscopic ferroelectric domains has been observed at 25 oC to 180 oC. The ferroelectric domains and their walls reduce progressively with increasing temperature. In the selected-area electron diffraction (SAED) patterns the crystallographic evidence of antiferroelectric domain is not found over the temperature range, which provides the evidence that the ferroelectric-antiferroelectric t…
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…
The perovskite-like compounds ACu3Ru4O12 (A=Na,Ca,Sr,La,Nd) are studied by means of density functional theory based electronic structure calculations using the augmented spherical wave (ASW) method. The electronic properties are strongly influenced by covalent type bonding between transition metal d and oxygen p states. The characteristic tilting of the RuO6 octahedra arises mainly from the Cu--O bonding, allowing for optimal bond lengths between these two atoms. Our results provide a deeper understanding of octahedral tilting as a universal mechanism, applicable to a large variety of multinar…
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 …
The local crystal structures of many perovskite-structured materials deviate from the average space group symmetry. We demonstrate, from lattice-dynamics calculations based on quantum chemical force constants, that all the caesium-lead and caesium-tin halide perovskites exhibit vibrational instabilities associated with octahedral titling in their high-temperature cubic phase. Anharmonic double-well potentials are found for zone-boundary phonon modes in all compounds with barriers ranging from 108 to 512 meV. The well depth is correlated with the tolerance factor and the chemistry of the compos…
Naturals and synthetic perovskites are widely used functional materials thanks to their particular physical properties, such as superconductivity, ferroelectricity and photo-activity. Many of these properties are related to static or dynamic motion of octahedral units; Yet a full understanding of the relationships between perovskite crystal structure, chemical bonding and physical properties is currently missing. Several studies indicate the existence of dynamic disorder generated by anharmonic motion of octahedral units e.g. in halide perovskite structures. In this work, we derive all possibl…
Anelastic and dielectric spectroscopy measurements on PZT close to the morphotropic (MPB) and antiferroelectric boundaries provide new insight in some controversial aspects of its phase diagram. No evidence is found of a border separating monoclinic (M) from rhombohedral (R) phases, in agreement with recent structural studies supporting a coexistence of the two phases over a broad composition range x < 0.5, with the fraction of M increasing toward the MPB. It is also discussed why the observed maximum of elastic compliance appears to be due to a rotational instability of the polarisation and t…
The oxygen octahedral tilted domains in 0.90(Bi1/2Na1/2)TiO3-0.5(Bi1/2K1/2)TiO3-0.5BaTiO3 lead-free perovskite piezoelectric ceramic have been studied by transmission electron microscopy (TEM). Selected-area electron diffraction patterns shows the 1/2ooo and 1/2ooe reflections, indicating the presence of antiphase (a-a-a-) and in-phase (aoaoc+) octahedral tilting, respectively. The morphology and distributions of these tilted domains are shown in the centered dark-field images. Further, the Bragg-filtered high-resolution TEM image reveals that the size of the in-phase tilted domains varies fro…
With increasing temperature, ${\rm Sr}_2{\rm ScSbO}_6$ undergoes three structural phase transitions at approximately ${\rm 400K}$, ${\rm 560K}$ and ${\rm 650K}$, leading to the following sequence of phases: $P2_1/n \rightarrow I2/m \rightarrow I4/m \rightarrow Fm\bar{3}m$, making it an ideal candidate to study the effects of octahedral tilting keeping other parameters fixed. To ascertain the isolated effects of octahedral distortions, the electronic and optical properties of the monoclinic $P2_1/n$ (at room temperature), monoclinic $I2/m$ (at ${\rm 430K}$), tetragonal $I4/m$ (at ${\rm 613K}$) …
Mixed Orbital Ground States of Fe2+ in Prussian Blues
Mössbauer Effect Data Center, Dalian Institute of Chemical Physics, Chinese Academy of Sciences（中国科学院大连化学物理研究所）；School of Engineering, The University of Tokyo（东京大学工学部）
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…
Despite the technological significance of the tetragonal PbTiO3 for the piezoelectric transducer industry, its high pressure behaviour is quite controversial as two entirely different scenarios, involving pressure induced (1) morphotropic phase boundary (MPB) like structural transition with concomitant rotation of the ferroelectric polarization vector and (2) antiferrodistortive (AFD) phase transition followed by emergence of a reentrant ferroelectric phase, have been proposed in recent theoretical and experimental studies. We have attempted to address these controversies through a high resolu…
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…
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…
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…
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…
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 …
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…
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…
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…
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, …
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…
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 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…
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…
The list of possible commensurate phases obtained from the parent tetragonal phase of Ruddlesden-Popper systems, A$_{n+1}$B$_n$C$_{3n+1}$ for general $n$ due to a single phase transition involving the reorienting of octahedra of C (oxygen) ions is reexamined using a Landau expansion. This expansion allows for the nonlinearity of the octahedral rotations and the rotation-strain coupling. It is found that most structures allowed by symmetry are inconsistent with the constraint of rigid octahedra which dictates the form of the quartic terms in the Landau free energy. For A$_2$BC$_4$ our analysis …
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…
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 …
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…
A complete solid solution series between the t2g^4 perovskite ferromagnet SrRuO3 and the diamagnetic t2g^6 perovskite LaRhO3 has been prepared. The evolution with composition x in (SrRuO3)(1-x)(LaRhO3)(x) of the crystal structure and electrical and magnetic properties has been studied and is reported here. As x increases, the octahedral tilt angle gradually increases, along with the pseudocubic lattice parameter and unit cell volume. Electrical resistivity measurements reveal a compositionally driven metal to insulator transition between x = 0.1 and 0.2. Ferromagnetic ordering gives over to gl…
The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to competition between onsite Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of posessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multi-band Hubbard model and performing SOC tunable DFT+$U$ calculations on a prototype SrIrO$_3$ and extending the analysis to other iso-structural and is…
Insulating band gaps both below and above the Néel temperature in d-electron LaTiO3, LaVO3, SrMnO3, and LaMnO3 perovskites as a symmetry-breaking event
