Mode crystallography of distorted structures

Emergence of a Multiferroic Half-Metallic Phase in Bi_{2}FeCrO_{6} through Interplay of Hole Doping and Epitaxial Strain

Epitaxial strain has been shown to drive structural phase transitions along with novel functionalities in perovskite-based thin films. Aliovalent doping at the A site can drive an insulator-to-metal and magnetic transitions in perovskites along with a variety of interesting structural and electronic phenomena. Using first-principles calculations, we predict the formation of a multiferroic half-metallic phase with a large magnetic moment in the double perovskite, Bi_{2}FeCrO_{6}, by coupling epitaxial strain with A-site hole doping. We also demonstrate that epitaxial strain can be used to manipulate the hole states created by doping to induce half-metal to insulator, antipolar to polar, antiferromagnetic to ferromagnetic, orbital ordering and charge ordering transitions. Our work also suggests that hole doping under strain could lead to mitigation of issues related to antisite defects and lowered magnetization in thin films of the material.

Frustrated Dipole Order Induces Noncollinear Proper Ferrielectricity in Two Dimensions

Within Landau theory, magnetism and polarity are homotopic, displaying a one-to-one correspondence between most physical characteristics. However, despite widely reported noncollinear magnetism, spontaneous noncollinear electric dipole order as a ground state is rare. Here, a dioxydihalides family is predicted to display noncollinear ferrielectricity, induced by competing ferroelectric and antiferroelectric soft modes. This intrinsic of dipoles generates unique physical properties, such as Z_{2}×Z_{2} topological domains, atomic-scale dipole vortices, and negative piezoelectricity.

Pressure-dependent X-ray diffraction of the multiferroics RMn2O5

The room-temperature structural properties of the RMn₂O₅ multiferroics have been investigated under pressure, using powder X-ray scattering and density functional theory (DFT) calculations. It was possible to determine the lattice parameters and the main atomic positions as a function of pressure. Good agreement was observed between the X-ray and DFT results for most of the determined crystallographic data. From the DFT calculations, it was possible to infer the pressure evolution of the exchange interactions, and this analysis led to the conclusion that the onset of the q = (½, 0, ½) magnetic structure under pressure is related to the increase in the J₁ super-exchange terms (due to the reduction in the Mn-O distances) compared with the Mn-R exchange interactions. In addition, the 1D antiferromagnetic character of the compounds should be reinforced under pressure.

Symmetry-mode analysis for intuitive observation of structure-property relationships in the lead-free antiferroelectric (1-x)AgNbO3-xLiTaO3

Functional materials are of critical importance to electronic and smart devices. A deep understanding of the structure-property relationship is essential for designing new materials. In this work, instead of utilizing conventional atomic coordinates, a symmetry-mode approach is successfully used to conduct structure refinement of the neutron powder diffraction data of (1-x)AgNbO3-xLiTaO3 (0 ≤ x ≤ 0.09) ceramics. This provides rich structural information that not only clarifies the controversial symmetry assigned to pure AgNbO3 but also explains well the detailed structural evolution of (1-x)AgNbO3-xLiTaO3 (0 ≤ x ≤ 0.09) ceramics, and builds a comprehensive and straightforward relationship between structural distortion and electrical properties. It is concluded that there are four relatively large-amplitude major modes that dominate the distorted Pmc21 structure of pure AgNbO3, namely a Λ3 antiferroelectric mode, a T4+ a - a - c 0 octahedral tilting mode, an H2 a 0 a 0 c +/a 0 a 0 c - octahedral tilting mode and a Γ4- ferroelectric mode. The H2 and Λ3 modes become progressively inactive with increasing x and their destabilization is the driving force behind the composition-driven phase transition between the Pmc21 and R3c phases. This structural variation is consistent with the trend observed in the measured temperature-dependent dielectric properties and polarization-electric field (P-E) hysteresis loops. The mode crystallography applied in this study provides a strategy for optimizing related properties by tuning the amplitudes of the corresponding modes in these novel AgNbO3-based (anti)ferroelectric materials.

Pressure-induced phase transitions in Na2B12H12, structural investigation on a candidate for solid-state electrolyte

closo-Borates, such as Na2B12H12, are an emerging class of ionic conductors that show promising chemical, electrochemical and mechanical properties as electrolytes in all-solid-state batteries. Motivated by theoretical predictions, high-pressure in situ powder X-ray diffraction on Na2B12H12 was performed and two high-pressure phases are discovered. The first phase transition occurs at 0.5 GPa and it is persistent to ambient pressure, whereas the second transition takes place between 5.7 and 8.1 GPa and it is fully reversible. The mechanisms of the transitions by means of group theoretical analysis are unveiled. The primary-order parameters are identified and the stability at ambient pressure of the first polymorph is explained by density functional theory calculations. Finally, the parameters relevant to engineer and build an all-solid-state battery, namely, the bulk modulus and the coefficient of the thermal expansion are reported. The relatively low value of the bulk modulus for the first polymorph (14 GPa) indicates a soft material which allows accommodation of the volume change of the cathode during cycling.

Unexpected phase transition sequence in the ferroelectric Bi4Ti3O12

The high-temperature phase behaviour of the ferroelectric layered perovskite Bi₄Ti₃O₁₂ has been re-examined by high-resolution powder neutron diffraction. Previous studies, both experimental and theoretical, had suggested conflicting structural models and phase transition sequences, exacerbated by the complex interplay of several competing structural instabilities. This study confirms that Bi₄Ti₃O₁₂ undergoes two separate structural transitions from the aristotype tetragonal phase (space group I4/mmm) to the ambient-temperature ferroelectric phase (confirmed as monoclinic, B1a1). An unusual, and previously unconsidered, intermediate paraelectric phase is suggested to exist above T _C with tetragonal symmetry, space group P4/mbm. This phase is peculiar in displaying a unique type of octahedral tilting, in which the triple perovskite blocks of the layered structure alternate between tilted and untilted. This is rationalized in terms of the bonding requirements of the Bi³⁺ cations within the perovskite blocks.

Group-theoretical analysis of 1:3 A-site-ordered perovskite formation

The quadruple perovskites AA'3B4X12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.

Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calculate the lattice thermal conductivity obtaining good agreement with experiments only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.

Crystal structures and phase transition behaviour in the 5d transition metal oxides AReO4 (A = Ag, Na, K, Rb, Cs and Tl)

The structures of the six perrhenates (AReO₄ A = Ag, Na, K, Rb, Cs and Tl) at RT and the phase transitions associated with change in the orientation of the ReO₄⁻ tetrahedra seen for A = Rb, Cs and Tl are described.

Competing Polar and Antipolar Structures in the Ruddlesden-Popper Layered Perovskite Li2SrNb2O7

Over the past few years, several studies have reported the existence of polar phases in n = 2 Ruddlesden-Popper layer perovskites by trilinear coupling of oxygen octahedral rotations (OOR) and polar distortions, a phenomenon termed as hybrid improper ferroelectricity. This phenomenon has opened an avenue to expand the available compositions of ferroelectric and piezoelectric layered oxides. In this study, we report a new polar n = 2 Ruddlesden-Popper layered niobate, Li2SrNb2O7, which undergoes a structural transformation to an antipolar phase when cooled to 90 K. This structural transition results from a change in the phase of rotation of the octahedral layers within the perovskite slabs across the interlayers. First-principles calculations predicted that the antipolar Pnam phase would compete with the polar A 2 1 a m phase and that both would be energetically lower than the previously assigned centrosymmetric Amam phase. This phase transition was experimentally observed by a combination of synchrotron X-ray diffraction, powder neutron diffraction, and electrical and nonlinear optical characterization techniques. The competition between symmetry breaking to yield polar layer perovskites and hybrid improper antiferroelectrics provides new insight into the rational design of antiferroelectric materials that can have applications as electrostatic capacitors for energy storage.

Learning from Correlations Based on Local Structure: Rare-Earth Nickelates Revisited

Statistical analysis of local atomic distortions in crystalline materials is a powerful tool for understanding coupled electronic and structural phase transitions in transition metal compounds. The analyses of such complex materials, however, often require significant domain knowledge to recognize limitations in the available data, whether it be experimentally reported crystal structures, property measurements, or computed quantities, and to understand when additional experiments or simulations may be necessary. Here we show how additional descriptive statistics and computational experiments can help researchers explicitly recognize these limitations and fill in missing gaps by constructing amplitude ( a) and normalized-amplitude ( n) distortion-mode property correlation-coefficient heat maps, aCCHMs and nCCHMs, respectively. We demonstrate this utility within the rare-earth nickelate perovskites RNiO₃ (R = rare earth ≠ La), which exhibit antiferromagnetic and metal-insulator transitions with crystallographic symmetry breaking, and analyze the CCHMs obtained from experimental and first-principles derived symmetry modes. In contrast with the crystallographic trends gleaned from the reported experimental structures, the equilibrium structures obtained from density functional theory indicate that the Jahn-Teller distortion mode plays a negligible role in affecting the Néel temperature. We explain this discrepancy and discuss how different researchers might draw disparate conclusions from the same evidence, in particular from aCCHMs and nCCHMs. Last, we propose a general method for utilizing CCHMs for screening large databases of structures.

Direct Magnetization-Polarization Coupling in BaCuF_{4}

Herewith, first-principles calculations based on density functional theory are used to describe the ideal magnetization reversal through polarization switching in BaCuF_{4} which, according to our results, could be accomplished close to room temperature. We also show that this ideal coupling is driven by a single soft mode that combines both polarization, and octahedral rotation. The later being directly coupled to the weak ferromagnetism of BaCuF_{4}. This, added to its strong Jahn-Teller distortion and its orbital ordering, makes this material a very appealing prototype for crystals in the ABX_{4} family for multifunctional applications. The described mechanism behaves ideally as it couples the ferroelectric and the magnetic properties naturally and it has not been reported previously.

A paraelectric-ferroelectric phase transition of an organically templated zinc oxalate coordination polymer

Water-presence dependent switchable ferroelectricity was discovered in the hybrid organic-inorganic zinc oxalate 1D coordination polymer (DABCOH2)[Zn(C2O4)2]·3H2O (DZnOH, where DABCOH2: diprotonated 1.4-diazoniabicyclo[2.2.2]octane). The compound undergoes a reversible para-ferroelectric phase transition at 207 K from room temperature centrosymmetric phase I (space group P21/n) to low-temperature non-centrosymmetric phase II (space group P21). The microscopic mechanism of the phase transition is directly associated with the reconstruction of the hydrogen-bond network. On heating, the crystals exhibit a reversible single-crystal to single-crystal transformation concerned with the removal of all water molecules giving anhydrous DABCO zinc oxalate (DABCOH2)[Zn(C2O4)2] (DZnO). The dehydrated compound does not show ferroelectric properties.

A group-theoretical approach to enumerating magnetoelectric and multiferroic couplings in perovskites

A group-theoretical approach is used to enumerate the possible couplings between magnetism and ferroelectric polarization in the parent Pm{\overline 3}m perovskite structure. It is shown that third-order magnetoelectric coupling terms must always involve magnetic ordering at the A and B sites which either transforms both as R-point or both as X-point time-odd irreducible representations (irreps). For fourth-order couplings it is demonstrated that this criterion may be relaxed allowing couplings involving irreps at X-, M- and R-points which collectively conserve crystal momentum, producing a magnetoelectric effect arising from only B-site magnetic order. In this case, exactly two of the three irreps entering the order parameter must be time-odd irreps and either one or all must be odd with respect to inversion symmetry. It is possible to show that the time-even irreps in this triad must transform as one of: X1+, M3,5- or R5+, corresponding to A-site cation order, A-site antipolar displacements or anion rocksalt ordering, respectively. This greatly reduces the search space for type-II multiferroic perovskites. Similar arguments are used to demonstrate how weak ferromagnetism may be engineered and a variety of schemes are proposed for coupling this to ferroelectric polarization. The approach is illustrated with density functional theory calculations on magnetoelectric couplings and, by considering the literature, suggestions are given of which avenues of research are likely to be most promising in the design of novel magnetoelectric materials.

Observation of Quasi-Two-Dimensional Polar Domains and Ferroelastic Switching in a Metal, Ca3Ru2O7

Polar domains arise in insulating ferroelectrics when free carriers are unable to fully screen surface-bound charges. Recently discovered binary and ternary polar metals exhibit broken inversion symmetry coexisting with free electrons that might be expected to suppress the electrostatic driving force for domain formation. Contrary to this expectation, we report the first direct observation of polar domains in single crystals of the polar metal Ca₃Ru₂O₇. By a combination of mesoscale optical second-harmonic imaging and atomic-resolution scanning transmission electron microscopy, the polar domains are found to possess a quasi-two-dimensional slab geometry with a lateral size of ∼100 μm and thickness of ∼10 nm. Electronic structure calculations show that the coexistence of electronic and parity-lifting orders arise from anharmonic lattice interactions, which support 90° and 180° polar domains in a metal. Using in situ transmission electron microscopy, we also demonstrate a strain-tuning route to achieve ferroelastic switching of polar metal domains.

Structural, Magnetic, and Electronic Properties of CaBaCo4- xM xO7 (M = Fe, Zn)

The effect of substituting iron and zinc for cobalt in CaBaCo₄O₇ was investigated using neutron diffraction and X-ray absorption spectroscopy techniques. The orthorhombic distortion present in the parent compound CaBaCo₄O₇ decreases with increasing the content of either Fe or Zn. The samples CaBaCo₃ZnO₇ and CaBaCo_{4- x}Fe _xO₇ with x ≥ 1.5 are metrically hexagonal, but much better refinements in the neutron diffraction patterns are obtained using an orthorhombic unit cell. The two types of substitution have opposite effects on the structural and magnetic properties. Fe atoms preferentially occupy the sites at the triangular layer. Thus, the replacement of Co by Fe suppresses the ferrimagnetic ordering of the parent compound, and CaBaCo_{4- x}Fe _xO₇ (0.5 ≤ x ≤ 2) samples are antiferromagnetically ordered following a new propagation vector k = (1/3,0,0). However, the Zn atoms prefer occupying the Kagome layer, which is very detrimental for the long-range magnetic interactions giving rise to a magnetic glass-like behavior in the CaBaCo₃ZnO₇ sample. The oxidation states of iron and zinc are found to be 3+ and 2+, respectively, independently of the content, as confirmed by X-ray absorption spectroscopy. Therefore, the average Co oxidation state changes accordingly with the Fe³⁺ or Zn²⁺ doping. Also, X-ray absorption spectroscopy data confirm the different preferential occupation for both Fe and Zn cations. The combined information obtained by neutron diffraction and X-ray absorption spectroscopy indicates that cobalt atoms can be either in a fluctuating Co²⁺/Co³⁺ valence state or, alternatively, Co²⁺ and Co³⁺ ions being randomly distributed in the lattice. These results explain the occurrence of local disorder in the CoO₄ tetrahedra obtained by EXAFS. An anomaly in the lattice parameters and an increase in the local disorder are observed only at the ferrimagnetic transition for CaBaCo₄O₇, revealing the occurrence of local magneto-elastic coupling.

Structurally triggered metal-insulator transition in rare-earth nickelates

Rare-earth nickelates form an intriguing series of correlated perovskite oxides. Apart from LaNiO₃, they exhibit on cooling a sharp metal-insulator electronic phase transition, a concurrent structural phase transition, and a magnetic phase transition toward an unusual antiferromagnetic spin order. Appealing for various applications, full exploitation of these compounds is still hampered by the lack of global understanding of the interplay between their electronic, structural, and magnetic properties. Here we show from first-principles calculations that the metal-insulator transition of nickelates arises from the softening of an oxygen-breathing distortion, structurally triggered by oxygen-octahedra rotation motions. The origin of such a rare triggered mechanism is traced back in their electronic and magnetic properties, providing a united picture. We further develop a Landau model accounting for the metal-insulator transition evolution in terms of the rare-earth cations and rationalizing how to tune this transition by acting on oxygen rotation motions.

Applications of rare-earth nickelates are hampered by lack of global understanding of the interplay among various degrees of freedom. Here, Mercy et al. propose that the metal-insulator transition of nickelates arises from the softening of an oxygen breathing distortion, providing a united picture of electronic, structural and magnetic properties.

Electronic and magnetic properties of multiferroic ScFeO3 available from diffraction experiments

Electronic and magnetic properties of ferric ions (3d ⁵) in multiferroic ScFeO₃ are puzzling, in part because they are different from the only other multiferroic known to possess the same polar chemical structure, BiFeO₃. Open questions about ScFeO₃ can be addressed by confronting observations with results for G-type antiferromagnetism allowed by the lithium niobate (LiNbO₃)-like parent R3c structure. Calculated structure factors for resonant x-ray diffraction include all charge-like quadrupoles allowed by symmetry, and if experimental results for ScFeO₃ subsequently imply they are different from zero then ferric ions cannot be in the high-spin ⁶S state. The same type of experiment can reveal the moment direction in the G-type antiferromagnetism, according to our calculations, and thereby contribute to understanding magnetic anisotropy. Furthermore, structure factors for magnetic neutron diffraction by ScFeO₃ include Dirac multipoles that are time-odd and parity-odd, e.g. dipoles that are often called anapoles or toroidal moments. Apart from Dirac multipoles, the conventional approach to the interpretation of neutron Bragg diffraction data will be inadequate if ferric ions (Fe³⁺) are not in the high-spin ⁶S state, because the scattering amplitude includes more than simple dipole moments in the general case.

Hidden Antipolar Order Parameter and Entangled Néel-Type Charged Domain Walls in Hybrid Improper Ferroelectrics

Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we establish the existence of a hidden antipolar order parameter in model HIF (Ca,Sr)_{3}Ti_{2}O_{7} by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Néel-type twinlike antipolar domain walls (few nanometers) between the head-to-head and tail-to-tail domains. The finite-width Néel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient.

Surface effects on converse piezoelectricity of crystals

The contribution of surface units to bulk properties are often neglected in theoretical and computational studies of crystalline systems. We demonstrate that this assumption has to be made with caution in the case of (electric field) polarization.

ISOSUBGROUP: an internet tool for generating isotropy subgroups of crystallographic space groups

ISOSUBGROUP, the newest member of the ISOTROPY Software Suite (http://iso.byu.edu), generates isotropy subgroups of crystallographic space groups based on superpositions of multiple irreducible representations, along with a wealth of information about each one. Like the original ISOTROPY program, its scope is general rather than being restricted to common types of order parameters of a user-specified parent structure. But like the newer ISODISTORT program, its user-friendly interface has menu-driven selections. This combination of features has been oft requested but unavailable until now. Program output includes information about the subgroup symmetry, ferroic species, phase-transition continuity, active k vectors, domains and secondary order parameters.

Polar Nature of (CH3NH3)3Bi2I9 Perovskite-Like Hybrids

High-quality single crystals of perovskite-like (CH₃NH₃)₃Bi₂I₉ hybrids have been synthesized, using a layered-solution crystal-growth technique. The large dielectric constant is strongly affected by the polar ordering of its constituents. Progressive dipolar ordering of the methylammonium cation upon cooling below 300 K gradually converts the hexagonal structure (space group P6₃/mmc) into a monoclinic phase (C2/c) at 160 K. A well-pronounced, ferrielectric phase transition at 143 K is governed by in-plane ordering of the bismuth lone pair that breaks inversion symmetry and results in a polar phase (space group P2₁). The dielectric constant is markedly higher in the C2/c phase above this transition. Here, the bismuth lone pair is disordered in-plane, allowing the polarizability to be substantially enhanced. Density functional theory calculations estimate a large ferroelectric polarization of 7.94 μC/cm² along the polar axis in the P2₁ phase. The calculated polarization has almost equal contributions of the methylammonium and Bi³⁺ lone pair, which are fairly decoupled.

New insight on cubic–tetragonal–monoclinic phase transitions in ZrO2: ab initio study and symmetry analysis

A group-theory analysis of temperature-induced phase transitions in ZrO2 has been performed in the framework of the group–subgroup relationship tree (Bärnighausen tree) with the computer tools of the Bilbao Crystallographic Server. The transition paths including symmetry-allowed intermediate phases have been established. The active irreducible representations corresponding to soft phonon modes and spontaneous deformation strains responsible for the phase transitions have been determined. The phonon mode frequencies at the symmetry points of the Brillouin zones of cubic, tetragonal and monoclinic phases have been calculated using the ab initio density functional theory method. As a result, the soft modes and their symmetries have been revealed, which are in a complete agreement with the group-theoretical predictions.

Synthesis and structural phase transitions of [Mg2Sb2(C4H2O6)2(H2O)8](ClO4)2·5H2O with complex homochiral chains

A new magnesium antimony tartrate perchlorate [Mg2Sb2(C4H2O6)2(H2O)8](ClO4)2·5H2O, 1, was synthesized in single crystal form by slowly evaporating an aqueous solution of potassium antimony tartrate and magnesium perchlorate. In the temperature interval 298 K–123 K, the compound undergoes two reversible structural phase transitions. The transition from phase I to phase II at ca. 236 K is second order and the transition from phase II to phase III at ca. 144 K is first order. Phase I has an orthorhombic structure, P21212, a=11.8658(4) Å, b=16.464(1) Å, c=8.3895(4) Å at 298 K, containing infinite chains of antimony tartrate dimeric clusters bridged by MgO2(H2O)4 octahedra. The ClO4 − anions occupying the interchain space show pronounced dynamic disorder. Phase II is monoclinic, P21, a=8.3813(8) Å, b=11.760(1) Å, c=16.289(2) Å, β=92.442(2)° at 153 K. Phase III has an orthorhombic unit cell with quadrupled cell volume, P212121, a=11.6914(8) Å, b=16.176(1) Å, c=33.426(2) Å at 123 K. While the infinite chains in phases II and III are closely similar to those in phase I, the ClO4 − anions show different orientations and gradual disappearance of dynamic disorder as the temperature is lowered.

Emergence of Long-Range Order in BaTiO_{3} from Local Symmetry-Breaking Distortions

By using a symmetry motivated basis to evaluate local distortions against pair distribution function data, we show without prior bias, that the off-center Ti displacements in the archetypal ferroelectric BaTiO_{3} are zone centered and rhombohedral-like across its known ferroelectric and paraelectric phases. We construct a simple Monte Carlo model that captures our main experimental findings and demonstrate how the rich crystallographic phase diagram of BaTiO_{3} emerges from correlations of local symmetry-breaking distortions alone. Our results strongly support the order-disorder picture for these phase transitions, but can also be reconciled with the soft-mode theory of BaTiO_{3} that is supported by some spectroscopic techniques.

Coexistence of Three Ferroic Orders in the Multiferroic Compound [(CH3 )4 N][Mn(N3 )3 ] with Perovskite-Like Structure

The perovskite azido compound [(CH3 )4 N][Mn(N3 )3 ], which undergoes a first-order phase change at Tt =310 K with an associated magnetic bistability, was revisited in the search for additional ferroic orders. The driving force for such structural transition is multifold and involves a peculiar cooperative rotation of the [MnN6 ] octahedral as well as order/disorder and off-center shifts of the [(CH3 )4 N](+) cations and bridging azide ligands, which also bend and change their coordination mode. According to DFT calculations the latter two give rise to the appearance of electric dipoles in the low-temperature (LT) polymorph, the polarization of which nevertheless cancels out due to their antiparallel alignment in the crystal. The conversion of this antiferroelectric phase to the paraelectric phase could be responsible for the experimental dielectric anomaly detected at 310 K. Additionally, the structural change involves a ferroelastic phase transition, whereby the LT polymorph exhibits an unusual and anisotropic thermal behavior. Hence, [(CH3 )4 N][Mn(N3 )3 ] is a singular material in which three ferroic orders coexist even above room temperature.

Electric Field Control of Jahn-Teller Distortions in Bulk Perovskites

The Jahn-Teller distortion, by its very nature, is often at the heart of the various electronic properties displayed by perovskites and related materials. Despite the Jahn-Teller mode being nonpolar, we devise and demonstrate, in the present Letter, an electric field control of Jahn-Teller distortions in bulk perovskites. The electric field control is enabled through an anharmonic lattice mode coupling between the Jahn-Teller distortion and a polar mode. We confirm this coupling and quantify it through first-principles calculations. The coupling will always exist within the Pb2_{1}m space group, which is found to be the favored ground state for various perovskites under sufficient tensile epitaxial strain. Intriguingly, the calculations reveal that this mechanism is not only restricted to Jahn-Teller active systems, promising a general route to tune or induce novel electronic functionality in perovskites as a whole.

A-site order in rhombohedral perovskite-like oxides La2−xSrxCoTiO6(0.6 ≤x≤ 1.0)

The evolution of the room-temperature structure of the oxide series La2−xSrxCoTiO6(0.6 ≤x≤ 1.0) was studied as a function of the Sr content using different diffraction techniques and applying the symmetry-adapted modes formalism (AMPLIMODES). The title compounds adopt perovskite-like structures of rhombohedral symmetry with an octahedral tilting scheme (a−a−a−) with either space group R\overline 3c orR32. The latter symmetry is observed in those cases (forx≃ 0.6) where additional rock-salt-like ordering of La and Sr is produced in the perovskiteAsites. Two composition-driven phase transitions are observed in the whole series La2−xSrxCoTiO6(0.0 ≤x≤ 1.0). Using the concept of internal pressure, the effect of doping with Sr on the structure can be properly discussed. Both phase transitions seem to be of first order since they can be associated with discontinuities either in the entropy or in the structure. The first transition (P21/n→Pnma) occurs as theBcations become totally disordered. Along the whole compositional range the modes responsible for the out-of-phase tilting ofBO6octahedra remain active, but those associated with the in-phase octahedral tilting vanish forx≥ 0.6, this being associated with the second transition (Pnma→ R\overline 3c). Finally, forx= 1.0 the three pseudo-cubic cell parameters become very similar, pointing to a transition to a cubic structure which could be obtained by applying pressure or raising the temperature.

Phase transformations and indications for acoustic mode softening in Tb-Gd orthophosphate

At ambient conditions the anhydrous rare earth orthophosphates assume either the xenotime (zircon) or the monazite structure, with the latter favored for the heavier rare earths and by increasing pressure. Tb0.5Gd0.5PO4 assumes the xenotime structure at ambient conditions but is at the border between the xenotime and monazite structures. Here we show that, at high pressure, Tb0.5Gd0.5PO4 does not transform directly to monazite but through an intermediate anhydrite-type structure. Axial deformation of the unit cell near the anhydrite- to monazite-type transition indicates softening of the (c1133  +  c1313) combined elastic moduli. Stress response of rare-earth orthophosphate ceramics can be affected by both formation of the anhydrite-type phase and the elastic softening in the vicinity of the monazite-phase. We report the first structural data for an anhydrite-type rare earth orthophosphate.

Informatics-Based Approaches for Accelerated Discovery of Functional Materials

This chapter is aimed at readers interested in the topic of informatics-based approaches for accelerated materials discovery, but who are unfamiliar with the nuances of the underlying principles and various types of powerful mathematical tools that are involved in formulating structure–property relationships. In an attempt to simplify the workflow of materials informatics, we decompose the paradigm into several core subtasks: hypothesis generation, database construction, data pre-processing, mathematical modeling, model validation, and finally hypothesis testing. We discuss each task and provide illustrative case studies, which apply these methods to various functional ceramic materials.

Experimental and theoretical studies of structural phase transition in a novel polar perovskite-like [C2H5NH3][Na0.5Fe0.5(HCOO)3] formate

We report the synthesis and studies of a novel heterometallic formate [C₂H₅NH₃][Na_0.5Fe_0.5(HCOO)₃].

Strain tuning of ferroelectric polarization in hybrid organic inorganic perovskite compounds

Metal-organic frameworks (MOFs) are hybrid crystalline compounds comprised of an extended ordered network made up of organic molecules, organic linkers and metal cations. In particular, MOFs with the same topology as inorganic perovskites have been shown to possess interesting properties, e.g., coexistence of ferroelectric and magnetic ordering. Using first-principles density functional theory, we have investigated the effect of strain on the compounds C(NH2)3Cr(HCOO)3 and (CH3CH2NH3)Mn(HCOO)3. Here, we show that compressive strain can substantially increase the ferroelectric polarization by more than 300%, and we discuss the mechanism involved in the strain enhancement of polarization. Our study highlights the complex interplay between strain and organic cations' dipoles and put forward the possibility of tuning of ferroelectric polarization through appropriate thin film growing.

The antisymmetry of distortions

Distortions are ubiquitous in nature. Under perturbations such as stresses, fields or other changes, a physical system reconfigures by following a path from one state to another; this path, often a collection of atomic trajectories, describes a distortion. Here we introduce an antisymmetry operation called distortion reversal that reverses a distortion pathway. The symmetry of a distortion pathway is then uniquely defined by a distortion group; it has the same form as a magnetic group that involves time reversal. Given its isomorphism to magnetic groups, distortion groups could have a commensurate impact in the study of distortions, as the magnetic groups have had in the study of magnetic structures. Distortion symmetry has important implications for a range of phenomena such as structural and electronic phase transitions, diffusion, molecular conformational changes, vibrations, reaction pathways and interface dynamics.

Antisymmetric exchange in La-substituted BiFe0.5Sc0.5O3 system: symmetry adapted distortion modes approach

Neutron powder diffraction measurements on the 35 % La-substituted Bi1−x La x Fe0.5Sc0.5O3 composition revealed that the samples obtained under high-pressure (6 GPa) and high-temperature (1500 K) conditions crystalize into a distorted perovskite structure with the orthorhombic Pnma symmetry and the unit cell parameters: a o = 5.6745(2) Å, b o = 7.9834(3) Å and c o = 5.6310(2) Å. A long-range magnetic ordering takes place below 220 K and implies a G-type magnetic structure with the moments 4.10(4)μ B per Fe aligned predominately along the orthorhombic c-axis. The space group representation theory using the orthorhombic symmetry yields four bi-linear coupling schemes for the magnetic order parameters imposed by antisymmetric exchange interactions. The couplings are analysed based on symmetry adapted distortion modes defined in respect of the undistorted cubic perovskite structure. The approach allows a quantitative estimation of the coupling strength. It is shown that the experimentally found spin configuration combines the magnetic order parameters coupled by the atomic displacement modes with the largest amplitudes. The results indicate that the antisymmetric exchange is the dominant anisotropic term which fully controls the direction of the Fe3+ spins in the distorted perovskite lattice.

Coupling and electrical control of structural, orbital and magnetic orders in perovskites

Perovskite oxides are already widely used in industry and have huge potential for novel device applications thanks to the rich physical behaviour displayed in these materials. The key to the functional electronic properties exhibited by perovskites is often the so-called Jahn-Teller distortion. For applications, an electrical control of the Jahn-Teller distortions, which is so far out of reach, would therefore be highly desirable. Based on universal symmetry arguments, we determine new lattice mode couplings that can provide exactly this paradigm, and exemplify the effect from first-principles calculations. The proposed mechanism is completely general, however for illustrative purposes, we demonstrate the concept on vanadium based perovskites where we reveal an unprecedented orbital ordering and Jahn-Teller induced ferroelectricity. Thanks to the intimate coupling between Jahn-Teller distortions and electronic degrees of freedom, the electric field control of Jahn-Teller distortions is of general relevance and may find broad interest in various functional devices.

Low temperature structural studies of SrSnO3

High resolution powder neutron diffraction measurements on polycrystalline SrSnO3 between 8 and 350 K are described. SrSnO3 retains the orthorhombic Pbnm structure over this temperature range. Examination of the thermal expansion of the individual lattice parameters reveals an anomaly near 230 K that may reflect the presence of polar nanodomains associated with local disorder of the octahedral tilts.

Design of a Mott Multiferroic from a Nonmagnetic Polar Metal

We examine the electronic properties of the newly discovered "ferroelectric metal" LiOsO3 combining density-functional and dynamical mean-field theories. We show that the material is close to a Mott transition and that electronic correlations can be tuned to engineer a Mott multiferroic state in the 1/1 superlattice of LiOsO3 and LiNbO3. We use electronic structure calculations to predict that the (LiOsO3)1/(LiNbO3)1 superlattice exhibits strong coupling between magnetic and ferroelectric degrees of freedom with a ferroelectric polarization of 41.2  μC cm(-2), Curie temperature of 927 K, and Néel temperature of 379 K. Our results support a route towards high-temperature multiferroics, i.e., driving nonmagnetic polar metals into correlated insulating magnetic states.