An orbital strategy for regulating the Jahn-Teller effect

The Jahn-Teller effect (JTE) arising from lattice-electron coupling is a fascinating phenomenon that profoundly affects important physical properties in a number of transition-metal compounds. Controlling JT distortions and their corresponding electronic structures is highly desirable to tailor the functionalities of materials. Here, we propose a local coordinate strategy to regulate the JTE through quantifying occupancy in the [Formula: see text] and [Formula: see text] orbitals of Mn and scrutinizing the symmetries of the ligand oxygen atoms in MnO6 octahedra in LiMn2O4 and Li0.5Mn2O4. The effectiveness of such a strategy has been demonstrated by constructing P2-type NaLi x Mn1 - x O2 oxides with different Li/Mn ordering schemes. In addition, this strategy is also tenable for most 3d transition-metal compounds in spinel and perovskite frameworks, indicating the universality of local coordinate strategy and the tunability of the lattice-orbital coupling in transition-metal oxides. This work demonstrates a useful strategy to regulate JT distortion and provides useful guidelines for future design of functional materials with specific physical properties.

The pressure response of Jahn-Teller-distorted Prussian blue analogues

Jahn-Teller (JT) distorted CuII-containing compounds often display interesting structural and functional behaviour upon compression. We use high-pressure X-ray and neutron diffraction to investigate four JT-distorted Prussian blue analogues: Cu[Co(CN)6]0.67, CuPt(CN)6, and ACuCo(CN)6 (A = Rb, Cs), where the first two were studied in both their hydrated and dehydrated forms. All compounds are less compressible than the JT-inactive MnII-based counterparts, indicating a coupling between the electronic and mechanical properties. The effect is particularly strong for Cu[Co(CN)6]0.67, where the local JT distortions are uncorrelated (so-called orbital disorder). This sample amorphises at 0.5 GPa when dehydrated. CuPt(CN)6 behaves similarly to the MnII-analogues, with phase transitions at around 1 GPa and low sensitivity to water. For ACuCo(CN)6, the JT distortions reduce the propensity for phase transitions, although RbCuCo(CN)6 transitions to a new phase (P2/m) around 3 GPa. Our results have a bearing on both the topical Prussian blue analogues and the wider field of flexible frameworks.

Van Vleck analysis of angularly distorted octahedra using VanVleckCalculator

Van Vleck modes describe all possible displacements of octahedrally coordinated ligands about a core atom. They are a useful analytical tool for analysing the distortion of octahedra, particularly for first-order Jahn-Teller distortions, but determination of the Van Vleck modes of an octahedron is complicated by the presence of angular distortion of the octahedron. This problem is most commonly resolved by calculating the bond distortion modes (Q 2, Q 3) along the bond axes of the octahedron, disregarding the angular distortion and losing information on the octahedral shear modes (Q 4, Q 5 and Q 6) in the process. In this paper, the validity of assuming bond lengths to be orthogonal in order to calculate the Van Vleck modes is discussed, and a method is described for calculating Van Vleck modes without disregarding the angular distortion. A Python package for doing this, VanVleckCalculator, is introduced and some examples of its use are given. Finally, it is shown that octahedral shear and angular distortion are often, but not always, correlated, and a parameter η is proposed as the shear fraction. It is demonstrated that η can be used to predict whether the values will be correlated when varying a tuning parameter such as temperature or pressure.

The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

K-Ion Slides in Prussian Blue Analogues

We study the phenomenology of cooperative off-centering of K+ ions in potassiated Prussian blue analogues (PBAs). The principal distortion mechanism by which this off-centering occurs is termed a "K-ion slide", and its origin is shown to lie in the interaction between local electrostatic dipoles that couple through a combination of electrostatics and elastic strain. Using synchrotron powder X-ray diffraction measurements, we determine the crystal structures of a range of low-vacancy K2M[Fe(CN)6] PBAs (M = Ni, Co, Fe, Mn, Cd) and establish an empirical link between composition, temperature, and slide-distortion magnitude. Our results reflect the common underlying physics responsible for K-ion slides and their evolution with temperature and composition. Monte Carlo simulations driven by a simple model of dipolar interactions and strain coupling reproduce the general features of the experimental phase behavior. We discuss the implications of our study for optimizing the performance of PBA K-ion battery cathode materials and also its relevance to distortions in other, conceptually related, hybrid perovskites.

Jahn-Teller distortion in Sr2FeO4: group-theoretical analysis and hybrid DFT calculations

We present theoretical justification for distorted Ruddlesden-Popper (RP) phases of the first-order by using hybrid density functional theory (DFT) calculations and group-theoretical analysis. We, thus, demonstrate the existence of the Jahn-Teller effect around an Fe[Formula: see text] ion in Sr[Formula: see text]FeO[Formula: see text]. On the calculation side, we have established a combination of Wu-Cohen (WC) exchange and Perdew-Wang (PW) correlation in a three-parameter functional WC3PW, giving the most accurate description of Sr[Formula: see text]FeO[Formula: see text] from the comparison of three hybrid DFT functionals. Self-consistently obtained Hartree-Fock exact exchange of 0.16 demonstrates consistent results with the experimental literature data. Importantly, we explain conditions for co-existing proper and pseudo-Jahn-Teller effects from the crystalline orbitals, symmetry-mode analysis and irreps products. Moreover, phonon frequency calculations support and confirm the results of symmetry-mode analysis. In particular, the symmetry-mode analysis identifies a dominating irreducible representation of the Jahn-Teller mode (X2+) and corresponding space group (SG) of ground state structure (SG Cmce model). Therefore, the usually suggested high-symmetry tetragonal crystal structure (SG I4/mmm model) is higher in energy by 121 meV/f.u. (equivalent to the Jahn-Teller stabilization energy) compared with the distorted low-symmetry structure (SG Cmce model). We also present diffraction patterns for the two crystal symmetries to discuss the differences. Therefore, our results shed light on the existence of low-symmetry RP phases and make possible direct comparisons with future experiments.

Magnetoelastic and Magnetoelectric Coupling in Two-Dimensional Nitride MXenes: A Density Functional Theory Study

Two-dimensional multiferroic (2D) materials have garnered significant attention due to their potential in high-density, low-power multistate storage and spintronics applications. MXenes, a class of 2D transition metal carbides and nitrides, were first discovered in 2011, and have become the focus of research in various disciplines. Our study, utilizing first-principles calculations, examines the lattice structures, and electronic and magnetic properties of nitride MXenes with intrinsic band gaps, including V2NF2, V2NO2, Cr2NF2, Mo2NO2, Mo2NF2, and Mn2NO2. These nitride MXenes exhibit orbital ordering, and in some cases the orbital ordering induces magnetoelastic coupling or magnetoelectric coupling. Most notably, Cr2NF2 is a ferroelastic material with a spiral magnetic ordered phase, and the spiral magnetization propagation vector is coupled with the direction of ferroelastic strain. The ferroelectric phase can exist as an excited state in V2NO2, Cr2NF2, and Mo2NF2, with their magnetic order being coupled with polar displacements through orbital ordering. Our results also suggest that similar magnetoelectric coupling effects persist in the Janus MXenes V8N4O7F, Cr8N4F7O, and Mo8N4F7O. Remarkably, different phases of Mo8N4F7O, characterized by orbital ordering rearrangements, can be switched by applying external strain or an external electric field. Overall, our theoretical findings suggest that nitride MXenes hold promise as 2D multiferroic materials.

Strategy for a Rational Design of Deep-Ultraviolet Nonlinear Optical Materials from Zeolites

Deep-ultraviolet (DUV) nonlinear optical (NLO) materials play a crucial role in cutting-edge laser technology. In order to solve the serious layered growth tendency of the sole commercial DUV NLO crystal KBe2BO3F2 (KBBF), developing alternative systems of compounds with bulk crystal habits has become an urgent task for practical applications. Herein, a novel strategy was developed by applying non-centrosymmetric (NCS) cancrinite (CAN)-type zincophosphates {Na6(OH)2(H2O)2}Cs2[ZnPO4]6 with bulk-crystal habits as the prototype to design new DUV NLO crystals. Two new anhydrous alkali zincophosphates, namely, {(Li6 -xNaxO)A2}[(ZnPO4)6] (A = Cs, Rb; x = 2-3) crystallizing in the NCS hexagonal space group P63 (no. 173) with a CAN-type framework, were successfully synthesized via a modified fluoro-solvo-hydrothermal method by applying triethylamine (TEA) and concentrated NaF solution as a co-solvent. Interestingly, the rigidity of the NCS CAN-type framework acting as the host ensures the non-centrosymmetry of the resulting new compounds. Meanwhile, the replacement of water molecules by guest cationic species in the channels or cages can greatly improve the thermal stability of the resultant crystal and tune its NLO properties. The synergetic effect of the host framework and the guest species makes the two compounds transparent down to the DUV region (<200 nm) and exhibit SHG effects. Therefore, the proposed rational design strategy of applying the known zeotype NCS frameworks as prototypes together with the modified fluoro-solvo-hydrothermal method opens a great avenue for highly effectively exploring new DUV NLO materials.

The Pillar Effect of Large-Size Alkaline Ions on the Electrochemical Stability of Sodium Manganese Hexacyanoferrate for Sodium-Ion Batteries

Sodium manganese hexacyanoferrate (NaMnHCF) is an attractive candidate as a cathode material for sodium-ion batteries due to its low cost and high energy density. However, its practical application is hindered by poor electrochemical stability caused by the Jahn-Teller effect of Mn and the unstable structure of NaMnHCF. Here, this paper aims to address this issue by introducing highly stable AMnHCF (where A = K, Rb, or Cs) through a facile method to composite with NaMnHCF. The findings reveal that all AMnHCFs have a "pillar effect" on the crystal structure of NaMnHCF. It is observed that the degree of pillar effect varies depending on the specific AMnHCF used. The less electrochemically inactive the alkaline ion is and the greater the degree of compositing with NaMnHCF, the more dramatic the pillar effect. KMnHCF shows limited pillar effect due to its rough composition with NaMnHCF and the loss of K+ upon (de)intercalation. RbMnHCF has lower electrochemical activity and can be better composited with NaMnHCF. On the other hand, CsMnHCF exhibits the strongest pillar effect due to the inactivation of Cs+ and the excellent coherent structure formed by CsMnHCF and NaMnHCF. This research provides a new perspective on stabilizing NaMnHCF with other alkaline elements.

Understanding the Role of Entropy in High Entropy Oxides

The field of high entropy oxides (HEOs) flips traditional materials science paradigms on their head by seeking to understand what properties arise in the presence of profound configurational disorder. This disorder, which originates from multiple elements sharing a single lattice site, can take on a kaleidoscopic character due to the vast numbers of possible elemental combinations. High configurational disorder appears to imbue some HEOs with functional properties that far surpass their nondisordered analogs. While experimental discoveries abound, efforts to characterize the true magnitude of the configurational entropy and understand its role in stabilizing new phases and generating superior functional properties have lagged behind. Understanding the role of configurational disorder in existing HEOs is the crucial link to unlocking the rational design of new HEOs with targeted properties. In this Perspective, we attempt to establish a framework for articulating and beginning to address these questions in pursuit of a deeper understanding of the true role of entropy in HEOs.

Geometric frustration of Jahn-Teller order in the infinite-layer lattice

The Jahn-Teller effect, in which electronic configurations with energetically degenerate orbitals induce lattice distortions to lift this degeneracy, has a key role in many symmetry-lowering crystal deformations¹. Lattices of Jahn-Teller ions can induce a cooperative distortion, as exemplified by LaMnO₃ (refs. ^2,3). Although many examples occur in octahedrally⁴ or tetrahedrally⁵ coordinated transition metal oxides due to their high orbital degeneracy, this effect has yet to be manifested for square-planar anion coordination, as found in infinite-layer copper^6,7, nickel^8,9, iron^10,11 and manganese oxides¹². Here we synthesize single-crystal CaCoO₂ thin films by topotactic reduction of the brownmillerite CaCoO_2.5 phase. We observe a markedly distorted infinite-layer structure, with ångström-scale displacements of the cations from their high-symmetry positions. This can be understood to originate from the Jahn-Teller degeneracy of the d_xz and d_yz orbitals in the d⁷ electronic configuration along with substantial ligand-transition metal mixing. A complex pattern of distortions arises in a [Formula: see text] tetragonal supercell, reflecting the competition between an ordered Jahn-Teller effect on the CoO₂ sublattice and the geometric frustration of the associated displacements of the Ca sublattice, which are strongly coupled in the absence of apical oxygen. As a result of this competition, the CaCoO₂ structure forms an extended two-in-two-out type of Co distortion following 'ice rules'¹³.

Ultrathin ferrite nanosheets for room-temperature two-dimensional magnetic semiconductors

The discovery of magnetism in ultrathin crystals opens up opportunities to explore new physics and to develop next-generation spintronic devices. Nevertheless, two-dimensional magnetic semiconductors with Curie temperatures higher than room temperature have rarely been reported. Ferrites with strongly correlated d-orbital electrons may be alternative candidates offering two-dimensional high-temperature magnetic ordering. This prospect is, however, hindered by their inherent three-dimensional bonded nature. Here, we develop a confined-van der Waals epitaxial approach to synthesizing air-stable semiconducting cobalt ferrite nanosheets with thickness down to one unit cell using a facile chemical vapor deposition process. The hard magnetic behavior and magnetic domain evolution are demonstrated by means of vibrating sample magnetometry, magnetic force microscopy and magneto-optical Kerr effect measurements, which shows high Curie temperature above 390 K and strong dimensionality effect. The addition of room-temperature magnetic semiconductors to two-dimensional material family provides possibilities for numerous novel applications in computing, sensing and information storage.

A Novel 19 $\sqrt {19} $ × 19 $\sqrt {19} $ Superstructure in Epitaxially Grown 1T-TaTe2

The spontaneous formation of electronic orders is a crucial element for understanding complex quantum states and engineering heterostructures in 2D materials. A novel 19 $\sqrt {19} $ × 19 $\sqrt {19} $ charge order in few-layer-thick 1T-TaTe₂ transition metal dichalcogenide films grown by molecular beam epitaxy, which has not been realized, is report. The photoemission and scanning probe measurements demonstrate that monolayer 1T-TaTe₂ exhibits a variety of metastable charge density wave orders, including the 19 $\sqrt {19} $ × 19 $\sqrt {19} $ superstructure, which can be selectively stabilized by controlling the post-growth annealing temperature. Moreover, it is found that only the 19 $\sqrt {19} $ × 19 $\sqrt {19} $ order persists in 1T-TaTe₂ films thicker than a monolayer, up to 8 layers. The findings identify the previously unrealized novel electronic order in a much-studied transition metal dichalcogenide and provide a viable route to control it within the epitaxial growth process.

Uncovering the Interplay of Competing Distortions in the Prussian Blue Analogue K2Cu[Fe(CN)6]

We report the synthesis, crystal structure, thermal response, and electrochemical behavior of the Prussian blue analogue (PBA) K2Cu[Fe(CN)6]. From a structural perspective, this is the most complex PBA yet characterized: its triclinic crystal structure results from an interplay of cooperative Jahn-Teller order, octahedral tilts, and a collective "slide" distortion involving K-ion displacements. These different distortions give rise to two crystallographically distinct K-ion channels with different mobilities. Variable-temperature X-ray powder diffraction measurements show that K-ion slides are the lowest-energy distortion mechanism at play, as they are the only distortion to be switched off with increasing temperature. Electrochemically, the material operates as a K-ion cathode with a high operating voltage and an improved initial capacity relative to higher-vacancy PBA alternatives. On charging, K+ ions are selectively removed from a single K-ion channel type, and the slide distortions are again switched on and off accordingly. We discuss the functional importance of various aspects of structural complexity in this system, placing our discussion in the context of other related PBAs.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in tetrahedral and octahedral symmetries

Heavy element compounds with high symmetries often feature both spin-orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be three-fold degenerate and experience complicated Jahn-Teller and pseudo-Jahn-Teller interactions. To accurately describe these interactions, high quality spin-orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin-orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes, and generates Hamiltonian expansion formulas of arbitrarily high order.

Charged Domain Wall and Polar Vortex Topologies in a Room-Temperature Magnetoelectric Multiferroic Thin Film

Multiferroic topologies are an emerging solution for future low-power magnetic nanoelectronics due to their combined tuneable functionality and mobility. Here, we show that in addition to being magnetoelectric multiferroic at room temperature, thin-film Aurivillius phase Bi6TixFeyMnzO18 is an ideal material platform for both domain wall and vortex topology-based nanoelectronic devices. Utilizing atomic-resolution electron microscopy, we reveal the presence and structure of 180°-type charged head-to-head and tail-to-tail domain walls passing throughout the thin film. Theoretical calculations confirm the subunit cell cation site preference and charged domain wall energetics for Bi6TixFeyMnzO18. Finally, we show that polar vortex-type topologies also form at out-of-phase boundaries of stacking faults when internal strain and electrostatic energy gradients are altered. This study could pave the way for controlled polar vortex topology formation via strain engineering in other multiferroic thin films. Moreover, these results confirm that the subunit cell topological features play an important role in controlling the charge and spin state of Aurivillius phase films and other multiferroic heterostructures.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

Role of fluorine on the structure and second-harmonic-generation property of inorganic selenites and tellurites

Fluorine, as the most electronegative element, can replace the oxygen ligands of functional groups under given conditions. These fluoride groups are more or less different from the pure oxide groups in composition, symmetry, polarizability, transmittancy, etc. The rational use of these differences is expected to improve the probability of noncentrosymmetric structures and the comprehensive performance of second-harmonic-generation (SHG) materials. In this feature article, we introduce the recent developments in fluoride selenite and tellurite SHG materials together with highlighting our contributions, including Se(IV) and Te(IV) compounds with (i) d⁰ transition metal oxyfluoride octahedron, (ii) IIIA metal oxyfluoride octahedron, (iii) fluoride lone pair cation polyhedron, and (iv) other fluoride polyhedron. The future perspectives of fluoride selenite and tellurite SHG materials are also discussed.

Improving the Comprehensive Performance of Na0.7MnO2 for Sodium Ion Batteries by ZrO2 Atomic Layer Deposition

Sodium ion batteries with Na-Mn-O compounds as cathodes have been widely studied as substitutes for lithium ion batteries due to their abundant resources. However, the relatively poor cycling stability and low capacity of Na-Mn-O compounds significantly limit their applications. Different approaches, including element substitution and surface modification, have been applied to improve the electrochemical performance of those cathode materials. Herein, element doping and coating of ZrO₂ on Na_0.7MnO₂ particles have been achieved by atomic layer deposition followed by post-annealing. The rate capability and cycling stability of the modified materials were significantly improved, and the mechanism of performance enhancement was revealed. The ZrO₂ coatings acted as a stable interfacial layer to enhance the cycling stability of Na_0.7MnO₂ by suppressing side reactions between the electrode and electrolyte. The doping of transition metal ions reduced energy barriers for sodium ion insertion and deintercalation during charge/discharge cycling, further improving the charge/discharge capacity and rate performance of Na_0.7MnO₂.

Chloride Reduction of Mn3+ in Mild Hydrothermal Synthesis of a Charge Ordered Defect Pyrochlore, CsMn2+Mn3+F6, a Canted Antiferromagnet with a Hard Ferromagnetic Component

Geometrically frustrated systems play an important role in studying new physical phenomena and unconventional thermodynamics. Charge ordered defect pyrochlores AM²⁺M³⁺F₆ offer a convenient platform for probing the interplay between electron distribution over M²⁺ and M³⁺ sites and structural distortions; however, they are limited to compounds with M^2+/3+ = V, Fe, Ni, and Cu due to difficulties in the simultaneous stabilization of other 3d elements in the +2 and +3 oxidation states. Herein, we employ Cl^- anions under hydrothermal conditions for the mild reduction of Mn₂O₃ in concentrated HF to obtain the CsMn²⁺Mn³⁺F₆ composition as a phase pure sample and study its properties. The magnetism of CsMn₂F₆ was characterized by measuring the magnetic susceptibility and isothermal magnetization data, and a magnetic transition to a canted antiferromagnet state was found at 24.1 K. We determined the magnetic structure of CsMn₂F₆ using powder neutron diffraction, which revealed successive long-range ordering of the Mn²⁺ and Mn³⁺ sites that is accompanied by a second transition. The role and strength of magnetic exchange interactions were characterized using DFT calculations.

Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibrational modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E₃^″⊗e₁^' Jahn-Teller interaction is used to demonstrate the correctness of the formalism. A Python program is developed to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems and interface the expansions to the MCTDH quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn-Teller and pseudo-Jahn-Teller problems. Also it is the only one.

Local electronic structure rearrangements and strong anharmonicity in YH3 under pressures up to 180 GPa

The discovery of superconductivity above 250 K at high pressure in LaH₁₀ and the prediction of overcoming the room temperature threshold for superconductivity in YH₁₀ urge for a better understanding of hydrogen interaction mechanisms with the heavy atom sublattice in metal hydrides under high pressure at the atomic scale. Here we use locally sensitive X-ray absorption fine structure spectroscopy (XAFS) to get insight into the nature of phase transitions and the rearrangements of local electronic and crystal structure in archetypal metal hydride YH₃ under pressure up to 180 GPa. The combination of the experimental methods allowed us to implement a multiscale length study of YH₃: XAFS (short-range), Raman scattering (medium-range) and XRD (long-range). XANES data evidence a strong effect of hydrogen on the density of 4d yttrium states that increases with pressure and EXAFS data evidence a strong anharmonicity, manifested as yttrium atom vibrations in a double-well potential.

Symmetry Origin of the Dzyaloshinskii-Moriya Interaction and Magnetization Reversal in YVO3

We have investigated magneto-structural phase transitions in polycrystalline YVO₃ using high-resolution neutron powder diffraction toward understanding the phenomenon of magnetization reversal. Contrary to earlier reports, our study reveals that both C-type and G-type antiferromagnetic ordering, corresponding to G-type and C-type orbital ordered phases, respectively, occur at the same temperature (T_N = 115 K) with the G-type antiferromagnetic phase growing at the expense of the C-type one on cooling. These processes cease at T_S ∼ 77 K; however, a minor (∼4%) untransformed C-type phase remains unchanged down to 1.7 K. The symmetry analysis indicates different symmetry origins of the Dzyaloshinskii-Moriya interaction in each phase, which can explain the magnetization reversal observed between T_N and T_S. We discuss that magnetic phase separation and associated weak ferromagnetism may be the common mechanism underlying the magnetization reversal phenomenon observed in other RVO₃ systems (R = rare earth).

Proton-Induced Disproportionation of Jahn-Teller-Active Transition-Metal Ions in Oxides Due to Electronically Driven Lattice Instability

The interfacial chemical reactivity of Jahn-Teller-active transition-metal oxides remains an enigmatic area, often leading to uncontrollable phase transformations in the oxide-based technological applications. In particular, the higher tendency of unwanted transition-metal-ion dissolution and side-reactions in Jahn-Teller-active oxides is accompanied by performance degradation in many electrochemical systems, for example, lithium-ion batteries. We show here that the fundamental electronic structure instability that leads to Jahn-Teller (lattice) distortion in an octahedral ligand field is the active chemical driving force for the spontaneous disproportionation, phase transformation, and metal-ion dissolution in transition-metal oxides upon exposure to protons. On the basis of electronic structure analyses and ¹⁸O isotope labeling, we present a mechanism comprising a coupled acid-base/redox reaction that leads to a proton-induced disproportionation of Jahn-Teller-active transition-metal ions, as exemplified by the broad classes of respective oxides.

Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.

Electronic parameters in cobalt-based perovskite-type oxides as descriptors for chemocatalytic reactions

Perovskite-type transition metal (TM) oxides are effective catalysts in oxidation and decomposition reactions. Yet, the effect of compositional variation on catalytic efficacy is not well understood. The present analysis of electronic characteristics of B-site substituted LaCoO₃ derivatives via in situ X-ray absorption spectroscopy (XAS) establishes correlations of electronic parameters with reaction rates: TM t_2g and e_g orbital occupancy yield volcano-type or non-linear correlations with NO oxidation, CO oxidation and N₂O decomposition rates. Covalent O 2p-TM 3d interaction, in ultra-high vacuum, is a linear descriptor for reaction rates in NO oxidation and CO oxidation, and for N₂O decomposition rates in O₂ presence. Covalency crucially determines the ability of the catalytically active sites to interact with surface species during the kinetically relevant step of the reaction. The nature of the kinetically relevant step and of surface species involved lead to the vast effect of XAS measurement conditions on the validity of correlations.

Design of efficient catalysts requires understanding the decisive electronic parameters for catalytic efficacy and their dependence on elemental composition. Here, the authors report covalency as suitable descriptor of perovskite-type transition metal oxides as chemo-catalysts.

Broken translational and rotational symmetries in LiMn1.5Ni0.5O4 spinel

In condensed matter physics broken symmetries and emergence of quasi-particles are intimately linked to each other. Whenever a symmetry is broken, it leaves its fingerprints, and that may be observed indirectly via its influence on the other quasi-particles. Here, we report the strong signature of broken spin rotational symmetry induced due to long range-ordering of spins in Mn - sublattice of LiMn_1.5Ni_0.5O₄ below T _c ~ 113 K reflected with the marked changes in the lattice vibrations using Raman scattering. In particular, the majority of the observed first-order phonon modes show a sharp shift in frequency in the vicinity of long range magnetic-ordering temperature. Phonons exist in a crystalline system because of broken translational symmetry, therefore any renormalization in the phonon-spectrum could be a good gauge for broken translational symmetry. Anomalous evolution of the few modes associated with stretching of Mn/NiO₆ octahedra in the intermediate temperature range (~60-260 K) marked the broken translational symmetry attributed to the charge ordering. Interestingly same modes also show strong coupling with magnetic degrees of freedom, suggesting that charge-ordering and magnetic transition may be linked to each other.

Electric-Field Control of Magnetization, Jahn-Teller Distortion, and Orbital Ordering in Ferroelectric Ferromagnets

Controlling the direction of the magnetization by an electric field in multiferroics that are both ferroelectric and strongly ferromagnetic will open the door to the design of the next generation of spintronics and memory devices. Using first-principles simulations, we report that the discovery that the PbTiO_{3}/LaTiO_{3} (PTO/LTO) superlattice possesses such highly desired control, as evidenced by the electric-field-induced rotation of 90° and even a possible full reversal of its magnetization in some cases. Moreover, such systems also exhibit Jahn-Teller distortions, as well as orbital orderings, that are switchable by the electric field, therefore making PTO/LTO of importance for the tuning of electronic properties too. The origin for such striking electric-field controls of magnetization, Jahn-Teller deformations, and orbital orderings resides in the existence of three different types of energetic coupling: one coupling polarization with antiphase and in-phase oxygen octahedral tiltings, a second one coupling polarization with antiphase oxygen octahedra tilting and Jahn-Teller distortions, and finally a biquadratic coupling between antiphase oxygen octahedral tilting and magnetization.

Density Functional Theory Calculations of Structural, Electronic, and Magnetic Properties of the 3d Metal Trifluorides MF3 (M = Ti-Ni) in the Solid State

We employ density functional theory with Hubbard U correction or hybrid functionals to study the series of magnetic 3d metal trifluorides MF₃ (M = Ti-Ni). Experimental lattice parameters are reproduced with an error margin of 0.5%-4.3%. Cooperative Jahn-Teller distortions are reproduced for MnF₃ , but also found in TiF₃ and CoF₃ at smaller levels compared to MnF₃ . Trends in electronic structure with respect to positions of the d bands are linked to the magnetic properties where M = Ti-Cr are weak magnetic Mott-Hubbard insulators, M = Fe-Ni are strong magnetic charge-transfer insulators and MnF₃ falls in between. Our work contributes to the characterization of the relatively unknown NiF₃ , since FeF₃ and CoF₃ have similar electronic and magnetic properties. However, NiF₃ does not show a Jahn-Teller distortion as present in CoF₃ . © 2019 Wiley Periodicals, Inc.

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.

Geometry Distortion and Small Polaron Binding Energy Changes with Ionic Substitution in Halide Perovskites

Halide perovskites have demonstrated remarkable performance in optoelectronic applications. Despite extraordinary progress, questions remain about device stability. We report an in-depth computational study of small polaron formation, electronic structure, charge density, and reorganization energies of several experimentally relevant halide perovskites using isolated clusters. Local lattice symmetry, electronic structure, and electron-phonon coupling are interrelated in polaron formation in these materials. To illustrate this, first-principles calculations are performed on (MA/Cs/FA)Pb(I/Br)₃ and MASnI₃. Across the materials studied, electron small polaron formation is manifested by Jahn-Teller-like distortions in the central octahedron, with apical PbI bonds expanding significantly more than the equatorial bonds. In contrast, hole polarons cause the central octahedron to uniformly contract. This difference in manifestation of electron and hole polaron formation can be a tool to determine what is taking place in individual systems to systematically control performance. Other trends as the anion and cations are changed are established for optimization in specific optoelectronic applications.

High-Pressure Synthesis, Crystal Structure, Chemical Bonding, and Ferroelectricity of LiNbO3-Type LiSbO3

A polar LiNbO₃ (LN)-type oxide LiSbO₃ was synthesized by a high-temperature heat treatment under a pressure of 7.7 GPa and found to exhibit ferroelectricity. The crystal structural refinement using the data of synchrotron powder X-ray diffraction and neutron diffraction and the electronic structure calculation of LN-type LiSbO₃ suggest a covalent-bonding character between Sb and O. When comparing the distortion of BO₆ in LN-type ABO₃, the distortions of SbO₆ in LiSbO₃ and SnO₆ in ZnSnO₃, which included a B cation with a d¹⁰ electronic configuration, were smaller than those of BO₆ in LN-type oxides having the second-order Jahn-Teller active B cation, e.g., LiNbO₃ and ZnTiO₃. The temperature dependence of the lattice parameters, second harmonic generation, dielectric permittivity, and differential scanning calorimetry made it clear that a second-order ferroelectric-paraelectric phase transition occurs at a Curie temperature of T_c = 605 ± 10 K in LN-type LiSbO₃. Further, first-principles density functional theory calculation suggested that perovskite-type LiSbO₃ is less stable than LN-type LiSbO₃ under even high pressure, and the ambient phase of LiSbO₃ directly transforms to LN-type LiSbO₃ under high pressure. The phase stability of LN-type LiSbO₃ and the polar and ferroelectric properties are rationalized by the covalent bonding of Sb-O and the relatively weak Coulomb repulsion between Li⁺ and Sb⁵⁺.

Aggregate frequency width, nuclear hyperfine coupling and Jahn-Teller effect of Cu2+ impurity ion ESR in SrLaAlO4 dielectric resonator at 20 millikelvin

The impurity paramagnetic ion, [Formula: see text] substitutes Al in the [Formula: see text] single crystal lattice, this results in a [Formula: see text] elongated octahedron, and the resulting measured g-factors satisfy four-fold axes variation condition. The aggregate frequency width of the electron spin resonance with the required minimum level of impurity concentration has been evaluated in this single crystal [Formula: see text] at 20 millikelvin. Measured parallel hyperfine constants, [Formula: see text], were determined to be [Formula: see text] and [Formula: see text] at [Formula: see text] for the nuclear magnetic quantum number [Formula: see text], and [Formula: see text] respectively. The anisotropy of the hyperfine structure reveals the characteristics of the static Jahn-Teller effect. The second-order-anisotropy term, [Formula: see text], is significant and cannot be disregarded, with the local strain dominating over the observed Zeeman-anisotropy-energy difference. The Bohr electron magneton, [Formula: see text], (within [Formula: see text] so-called experimental error) has been found using the measured spin-Hamiltonian parameters. Measured nuclear dipolar hyperfine structure parameter [Formula: see text] shows that the mean inverse third power of the electron distance from the nucleus is [Formula: see text] a.u. for [Formula: see text] ion in the substituted [Formula: see text] ion site assuming nuclear electric quadruple moment [Formula: see text] barn.

Strain-induced ferroelectricity and lattice coupling in BaSnO3 and SrSnO3

Perovskite stannates such as BaSnO₃ and SrSnO₃ exhibit promising photovoltaic properties, and hold promise for application in solar cell devices. However, the lack of ferroelectricity and the wide band gap in these materials limit their potential for photovoltaic applications. Here, by first-principles calculations, we demonstrate the realization of a primary ferroelectric polarization in non-ferroelectric BaSnO₃ and SrSnO₃ through strain engineering. In addition to the appearance of polarization, the band gaps of the materials are greatly narrowed when the paraelectric to ferroelectric phase transition takes place under compressive strain. Furthermore, an intriguing Q₂ mode triggered by lattice coupling with the polar mode is found in the stannates subjected to a sufficient tensile strain and this mode has a significant effect on the band gap, which suggests another pathway to narrow the band gap through the electric field control of the Q₂ mode. The fruitful electronic, structural, and energetic properties are discussed in detail to achieve a fundamental understanding of the strain-induced ferroelectricity, tunable band gap, and lattice couplings between the Q₂ mode and different polar/rotational distortions in the perovskite stannates.