Mode crystallography of distorted structures

Lattice symmetry relaxation as a cause for anisotropic line broadening and peak shift in powder diffraction

In powder diffraction, lattice symmetry relaxation causes a peak to split into several components which are not resolved if the degree of desymmetrization is small (pseudosymmetry). Here the equations which rule peak splitting are elaborated for the six minimal symmetry transitions, showing that the resulting split peaks are generally broader and asymmetric, and suffer an hkl-dependent displacement with respect to the high-symmetry parent peak. These results will be of help in Rietveld refinement of pseudosymmetric structures where an exact interpretation of peak deformation is required.

Nearly linear orbital molecules on a pyrochlore lattice

The interplay of spin-orbit coupling with other relevant parameters gives rise to the rich phase competition in complex ruthenates featuring octahedrally coordinated Ru4+. While locally, spin-orbit coupling stabilizes a nonmagnetic Jeff = 0 state, intersite interactions resolve one of two distinct phases at low temperatures: an excitonic magnet stabilized by the magnetic exchange of upper-lying Jeff = 1 states or Ru2 molecular orbital dimers driven by direct orbital overlap. Pyrochlore ruthenates A2Ru2O7 (A = rare earth, Y) are candidate excitonic magnets with geometrical frustration. We synthesized In2Ru2O7 with covalent In─O bonds. This pyrochlore ruthenate hosts a local Jeff = 0 state at high temperatures; however, at low temperatures, it forms a unique nonmagnetic ground state with nearly linear Ru─O─Ru molecules, in stark contrast to other A2Ru2O7 compounds. The disproportionation of covalent In─O bonds drives Ru2O molecule formation, quenching not only the local spin-orbit singlet but also geometrical frustration.

Magnetic space groups versus representation analysis in the investigation of magnetic structures: the happy end of a strained relationship

In recent decades, sustained theoretical and software developments have clearly established that representation analysis and magnetic symmetry groups are complementary concepts that should be used together in the investigation and description of magnetic structures. Historically, they were considered alternative approaches, but currently, magnetic space groups and magnetic superspace groups can be routinely used together with representation analysis, aided by state-of-the-art software tools. After exploring the historical antagonism between these two approaches, we emphasize the significant advancements made in understanding and formally describing magnetic structures by embracing their combined use.

A short note on the use of irreducible representations for tilted octahedra in perovskites

It is pointed out that many authors are unaware that the particular choice of unit-cell origin determines the irreducible representations to which octahedral tilts in perovskites belong. Furthermore, a recommendation is made that the preferred option is with the origin at the B-cation site rather than that of the A site.

Unraveling the Role of Structural Topology on Chirality Transfer and Chiroptical Properties in Chiral Germanium Iodides

Chiral hybrid organic-inorganic metal halides are highly promising chiroptoelectronic materials with potential applications in several fields, such as circularly polarized photodetectors, second-order nonlinear optics, and spin-selective devices. However, the ability of manipulating the chiroptical response and the chirality transfer from the organic ligands require one to shed light on structure-property correlations. Herein, we devised and prepared two novel Ge-based chiral hybrid organic-inorganic metal halides showing a different structural topology, namely, a 1D and a 2D arrangement, but composed of the same chemical building blocks: (R/S-ClMBA)3GeI5 and (R/S-ClMBA)2GeI4. Through a combined experimental and computational investigation on these samples, we discuss the impact of structural dimensionality on chiroptical properties, chirality transfer, and spin-splitting effects; also, we highlight the impact of structural distortions. The approach presented here paves the way for a solid understanding of the factors affecting the properties of chiral metal halides, thus allowing a future wise materials engineering.

Exploring Phase Transition and Structural Complexity in the Mixed Cation Uranium Oxide CaUNb2O8

The structures and high-temperature phase transition of CaUNb2O8 were studied in situ using synchrotron X-ray and neutron powder diffraction. Rietveld refinements provided an accurate description of the crystal structures of both the monoclinic fergusonite-type I2/b structure observed at room temperature and the tetragonal scheelite-type I41/a structure found at high temperatures. Bond valence sum analysis showed Nb5+ to be octahedrally coordinated in the monoclinic fergusonite-type structure, akin to other ANbO4 materials. Rietveld analysis of the variable temperature data allowed for the determination of accurate unit cell parameters and atomic coordinates, as well as revealing a reversible phase transition around ∼750 °C. The Nb-O bond distances display anomalous behavior, with a discontinuity in the longer Nb-O(1') distance coinciding with the phase transition suggestive of a reconstructive phase transition. Mode analysis identified the Γ2+ mode as the primary mode that drives the phase transition; this is linearly coupled to the induced spontaneous strain within the monoclinic fergusonite-type structure. Analysis of the temperature dependence of the Nb(z) positional parameter, as well as of the ϵ1-ϵ2 and ϵ6 strain parameters, showed that the phase transition is not strictly second order, with the critical exponent β ≠ 1/2. This study demonstrates the complex structural features of mixed cation metal oxides at elevated temperatures.

A correlated ferromagnetic polar metal by design

Polar metals have recently garnered increasing interest because of their promising functionalities. Here we report the experimental realization of an intrinsic coexisting ferromagnetism, polar distortion and metallicity in quasi-two-dimensional Ca3Co3O8. This material crystallizes with alternating stacking of oxygen tetrahedral CoO4 monolayers and octahedral CoO6 bilayers. The ferromagnetic metallic state is confined within the quasi-two-dimensional CoO6 layers, and the broken inversion symmetry arises simultaneously from the Co displacements. The breaking of both spatial-inversion and time-reversal symmetries, along with their strong coupling, gives rise to an intrinsic magnetochiral anisotropy with exotic magnetic field-free non-reciprocal electrical resistivity. An extraordinarily robust topological Hall effect persists over a broad temperature-magnetic field phase space, arising from dipole-induced Rashba spin-orbit coupling. Our work not only provides a rich platform to explore the coupling between polarity and magnetism in a metallic system, with extensive potential applications, but also defines a novel design strategy to access exotic correlated electronic states.

Creating Ferroelectricity in Monoclinic (HfO_{2})_{1}/(CeO_{2})_{1} Superlattices

Ferroelectricity in CMOS-compatible hafnia (HfO_{2}) is crucial for the fabrication of high-integration nonvolatile memory devices. However, the capture of ferroelectricity in HfO_{2} requires the stabilization of thermodynamically metastable orthorhombic or rhombohedral phases, which entails the introduction of defects (e.g., dopants and vacancies) and pays the price of crystal imperfections, causing unpleasant wake-up and fatigue effects. Here, we report a theoretical strategy on the realization of robust ferroelectricity in HfO_{2}-based ferroelectrics by designing a series of epitaxial (HfO_{2})_{1}/(CeO_{2})_{1} superlattices. The designed ferroelectric superlattices are defects free, and most importantly, on the base of the thermodynamically stable monoclinic phase of HfO_{2}. Consequently, this allows the creation of superior ferroelectric properties with an electric polarization >25  μC/cm^{2} and an ultralow polarization-switching energy barrier at ∼2.5  meV/atom. Our work may open an avenue toward the fabrication of high-performance HfO_{2}-based ferroelectric devices.

Ultrastrong Coupling between Polar Distortion and Optical Properties in Ferroelectric MoBr2O2

Tuning the properties of materials by using external stimuli is crucial for developing versatile smart materials. Strong coupling among the order parameters within a single-phase material constitutes a potent foundation for achieving precise property control. However, cross-coupling is fairly weak in most single materials. Leveraging first-principles calculations, we demonstrate a layered mixed anion compound MoBr2O2 that exhibits electric-field switchable spontaneous polarization and ultrastrong coupling between polar distortion and electronic structures as well as optical properties. It offers feasible avenues of achieving tunable Rashba spin-splitting, electrochromism, thermochromism, photochromism, and nonlinear optics by applying an external electric field to a single domain sample and heating, as well as intense light illumination. Additionally, it exhibits an exceptionally large photostrictive effect. These findings not only showcase the feasibility of achieving multiple order parameter coupling within a single material but also pave the way for comprehensive applications based on property control, such as energy harvesting, information processing, and ultrafast control.

Influence of Composition and Structure on the Optoelectronic Properties of Photocatalytic Bi4NbO8Cl-Bi2GdO4Cl Intergrowths

Mixed metal oxyhalides are an exciting class of photocatalysts, capable of the sustainable generation of fuels and remediation of pollutants with solar energy. Bismuth oxyhalides of the types Bi4MO8X (M = Nb and Ta; X = Cl and Br) and Bi2AO4X (A = most lanthanides; X = Cl, Br, and I) have an electronic structure that imparts photostability, as their valence band maxima (VBM) are composed of O 2p orbitals rather than X np orbitals that typify many other bismuth oxyhalides. Here, flux-based synthesis of intergrowth Bi4NbO8Cl-Bi2GdO4Cl is reported, testing the hypothesis that both intergrowth stoichiometry and M identity serve as levers toward tunable optoelectronic properties. X-ray scattering and atomically resolved electron microscopy verify intergrowth formation. Facile manipulation of the Bi4NbO8Cl-to-Bi2GdO4Cl ratio is achieved with the specific ratio influencing both the crystal and electronic structures of the intergrowths. This compositional flexibility and crystal structure engineering can be leveraged for photocatalytic applications, with comparisons to the previously reported Bi4TaO8Cl-Bi2GdO4Cl intergrowth revealing how subtle structural and compositional features can impact photocatalytic materials.

Structural phase transition, s±-wave pairing, and magnetic stripe order in bilayered superconductor La3Ni2O7 under pressure

Motivated by the recently discovered high-Tc superconductor La3Ni2O7, we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y2- mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y2- mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector (π, 0) was stable at the intermediate region. Pairing is induced in the s±-wave channel due to partial nesting between the M = (π, π) centered pockets and portions of the Fermi surface centered at the X = (π, 0) and Y = (0, π) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La3Ni2O7 is qualitatively different from infinite-layer nickelates and cuprate superconductors.

Pressure-induced structural and magnetic ordering transitions in the J1-J2 square lattice antiferromagnets AMoOPO4Cl (A = K, Rb)

By means of ab initio density functional theory calculations taking into account electronic correlation and van der Waals force, we conducted comprehensive studies of the electronic and magnetic properties, as well as structural and magnetic ordering evolution under pressure of the square lattice antiferromagnets AMoOPO4Cl (A = K, Rb) containing Mo5+ ions with , theoretically predicted as the potential candidates for achieving quantum phases, existing in the boundary regimes for square lattice magnets. Our results indicate that the columnar antiferromagnetic ordering, experimentally determined, is the magnetic ground state of the ambient P4/nmm phase, stabilized by the predominant antiferromagnetic next nearest neighbor interaction J2 in the diagonal directions of the square lattice, regardless of the effective Hubbard amendment values. More importantly, the P4/n phase, involving the mutual twisting of the MoO5Cl and PO4 polyhedra, satisfactorily reproduces the experimentally observed structural transition and the subsequent magnetic ordering transition from columnar antiferromagnetic ordering to Néel antiferromagnetic one, identified to be the appropriate high pressure structure. Furthermore, the mechanism underlined responsible for the magnetic ordering transition at high pressure has been disclosed in terms of density of states and spin density isosurface analysis across the transition. The loss of mirror plane symmetry in the P4/n phase activates the P 3s orbitals to participate in the magnetic interaction, giving rise to a competitive ferromagnetic superexchange interaction, in addition to antiferromagnetic direct one, and consequently initiating the magnetic ordering transition. The insights revealed here not only deepen our understanding of the electronic properties and structural and magnetic ordering transitions under high pressure of square lattice antiferromagnets AMoOPO4Cl (A = K, Rb), but also push the boundaries of knowledge by recognizing the role of nonmagnetic ions P 3s in magnetic exchange coupling.

Resonant x-ray diffraction measurements in charge ordered kagome superconductors KV3Sb5and RbV3Sb5

We report on (resonant) x-ray diffraction experiments on the normal state properties of kagome-lattice superconductors KV3Sb5and RbV3Sb5. We have confirmed previous reports indicating that the charge density wave (CDW) phase is characterized by a doubling of the unit cell in all three crystallographic directions. By monitoring the temperature dependence of Bragg peaks associated with the CDW phase, we ascertained that it develops gradually over several degrees, as opposed to CsV3Sb5, where the CDW peak intensity saturates promptly just below the CDW transition temperature. Analysis of symmetry modes indicates that this behavior arises due to lattice distortions linked to the formation of CDWs. These distortions occur abruptly in CsV3Sb5, while they progress more gradually in RbV3Sb5and KV3Sb5. In contrast, the amplitude of the mode leading to the crystallographic symmetry breaking fromP6/mmmtoFmmmappears to develop more gradually in CsV3Sb5as well. Diffraction measurements close to the V K edge and the Sb L1edge show no sensitivity to inversion- or time-symmetry breaking, which are claimed to be associated with the onset of the CDW phase. The azimuthal angle dependence of the resonant diffraction intensity observed at the Sb L1edge is associated with the difference in the population of unoccupied states and the anisotropy of the electron density of certain Sb ions.

The anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in hafnia

The anti-symmetric and anisotropic symmetric exchange interactions between two magnetic dipole moments - responsible for intriguing magnetic textures (e.g., magnetic skyrmions) - have been discovered since last century, while their electric analogues were either hidden for a long time or still not known. It is only recently that the anti-symmetric exchange interactions between electric dipoles was proved to exist (with materials hosting such an interaction being still rare) and the existence of anisotropic symmetric exchange interaction between electric dipoles remains ambiguous. Here, by symmetry analysis and first-principles calculations, we identify hafnia as a candidate material hosting the non-collinear dipole alignments, the analysis of which reveals the anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles in this material. Our findings can hopefully deepen the current knowledge of electromagnetism in condensed matter, and imply the possibility of discovering novel states of matter (e.g., electric skyrmions) in hafnia-related materials.

Alterferroicity with seesaw-type magnetoelectricity

Primary ferroicities like ferroelectricity and ferromagnetism are essential physical properties of matter. Multiferroics, with coexisting multiple ferroic orders in a single phase, provide a convenient route to magnetoelectricity. Even so, the general trade-off between magnetism and polarity remains inevitable, which prevents practicable magnetoelectric cross-control in the multiferroic framework. Here, an alternative strategy, i.e., the so-called alterferroicity, is proposed to circumvent the magnetoelectric exclusiveness, which exhibits multiple but noncoexisting ferroic orders. The natural exclusion between magnetism and polarity, as an insurmountable weakness of multiferroicity, becomes a distinct advantage in alterferroicity, making it an inborn rich ore for intrinsic strong magnetoelectricity. The general design rules for alterferroic materials rely on the competition between the instabilities of phononic and electronic structures in covalent systems. Based on primary density functional theory calculations, Ti-based trichalcogenides are predicted to be alterferroic candidates, which exhibit unique seesaw-type magnetoelectricity. This alterferroicity, as an emerging branch of the ferroic family, reshapes the framework of magnetoelectricity, going beyond the established scenario based on multiferroicity.

Investigations on the polymorphism of K4CaSi6O15 at elevated temperatures

In the present study, single crystals and polycrystalline material of K4CaSi6O15 were prepared from solid-state reactions between stoichiometric mixtures of the corresponding oxides/carbonates. Heat capacity (C p) measurements above room temperature using a differential scanning calorimeter indicated that two thermal effects occurred at approximately T 1 = 462 K and T 2 = 667 K, indicating the presence of structural phase transitions. The standard third-law entropy of K4CaSi6O15 was determined from low-temperature C p's measured by relaxation calorimetry using a Physical Properties Measurement System and amounts to S°(298K) = 524.3 ± 3.7 J·mol-1·K-1. For the 1st transition, the enthalpy change ΔH tr1 = 1.48 kJ·mol and the entropy change ΔS tr1 = 3.25 J·mol-1·K-1, whereas ΔH tr2 = 3.33 kJ·mol-1 and ΔS tr2 = 5.23 J·mol-1·K-1 were determined for the 2nd transition. The compound was further characterized by in-situ single-crystal X-ray diffraction between ambient temperature and 1063 K. At 773 K, the high-temperature phase stable above T 2 has the following basic crystallographic data: monoclinic symmetry, space group P21/c, a = 6.9469(4) Å, b = 9.2340(5) Å, c = 12.2954(6) Å, β = 93.639(3)°, V = 787.13(7) Å3, Z = 2. It belongs to the group of interrupted framework silicates and is based on tertiary (Q3-type) [SiO4]-tetrahedra. Together with the octahedrally coordinated Ca-cations, a three-dimensional mixed polyhedral network structure is formed, in which the remaining K-ions provide charge balance by occupying voids within the net. The intermediate temperature modification stable between T 1 and T 2 shows a (3+2)-dimensional incommensurately modulated structure that is characterized by the following q-vectors: q1 = (0.057, 0.172, 0.379), q2 = (-0.057, 0.172, -0.379). The crystal structures of the high- and the previously studied ambient temperature polymorph (space group Pc) are topologically equivalent and show a group-subgroup relationship. The index of the low- in the high-symmetry group is six and involves both, losses in translation as well as point group symmetry. The distortion is based on shifts of the different atom species and tilts of the 4- and 6-fold coordination polyhedra. Actually, for some of the oxygen atoms, the displacements exceed 0.5 Å. A more detailed analysis of the distortions relating to both structures has been performed using mode analysis, which revealed that the primary distortion mode transforms according to the Λ1 irreducible representation of P21/c. However, other modes with smaller distortion amplitudes are also involved.

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.

New High-Performance Piezoelectric: Ferroelectric Carbon-Boron Clathrate

High-performance piezoelectrics have been extensively reported with a typical perovskite structure, in which a huge breakthrough in piezoelectric constants is found to be more and more difficult. Hence, the development of materials beyond perovskite is a potential means of achieving lead-free and high piezoelectricity in next-generation piezoelectrics. Here, we demonstrate the possibility of developing high piezoelectricity in the nonperovskite carbon-boron clathrate with the composition of ScB_{3}C_{3} using first-principles calculations. The robust and highly symmetric B-C cage with mobilizable Sc atom constructs a flat potential valley to connect the ferroelectric orthorhombic and rhombohedral structures, which allows an easy, continuous, and strong polarization rotation. By manipulating the cell parameter b, the potential energy surface can be further flattened to produce an extra-high shear piezoelectric constant d_{15} of 9424  pC/N. Our calculations also confirm the effectiveness of the partial chemical replacement of Sc by Y to form a morphotropic phase boundary in the clathrate. The significance of large polarization and high symmetric polyhedron structure is demonstrated for realizing strong polarization rotation, offering the universal physical principles to aid the search for new high-performance piezoelectrics. This work takes ScB_{3}C_{3} as an example to exhibit the great potential for realizing high piezoelectricity in clathrate structure, which opens the door to developing next-generation lead-free piezoelectric applications.

Ferroelectricity in layered bismuth oxide down to 1 nanometer

Atomic-scale ferroelectrics are of great interest for high-density electronics, particularly field-effect transistors, low-power logic, and nonvolatile memories. We devised a film with a layered structure of bismuth oxide that can stabilize the ferroelectric state down to 1 nanometer through samarium bondage. This film can be grown on a variety of substrates with a cost-effective chemical solution deposition. We observed a standard ferroelectric hysteresis loop down to a thickness of ~1 nanometer. The thin films with thicknesses that range from 1 to 4.56 nanometers possess a relatively large remanent polarization from 17 to 50 microcoulombs per square centimeter. We verified the structure with first-principles calculations, which also pointed to the material being a lone pair-driven ferroelectric material. The structure design of the ultrathin ferroelectric films has great potential for the manufacturing of atomic-scale electronic devices.

γ-BaFe2O4: a fresh playground for room temperature multiferroicity

Multiferroics, showing the coexistence of two or more ferroic orderings at room temperature, could harness a revolution in multifunctional devices. However, most of the multiferroic compounds known to date are not magnetically and electrically ordered at ambient conditions, so the discovery of new materials is pivotal to allow the development of the field. In this work, we show that BaFe2O4 is a previously unrecognized room temperature multiferroic. X-ray and neutron diffraction allowed to reveal the polar crystal structure of the compound as well as its antiferromagnetic behavior, confirmed by bulk magnetometry characterizations. Piezo force microscopy and electrical measurements show the polarization to be switchable by the application of an external field, while symmetry analysis and calculations based on density functional theory reveal the improper nature of the ferroelectric component. Considering the present findings, we propose BaFe2O4 as a Bi- and Pb-free model for the search of new advanced multiferroic materials.

Charge Density Wave in Kagome Lattice Intermetallic ScV_{6}Sn_{6}

Materials hosting kagome lattices have drawn interest for the diverse magnetic and electronic states generated by geometric frustration. In the AV_{3}Sb_{5} compounds (A=K, Rb, Cs), stacked vanadium kagome layers give rise to unusual charge density waves (CDW) and superconductivity. Here we report single-crystal growth and characterization of ScV_{6}Sn_{6}, a hexagonal HfFe_{6}Ge_{6}-type compound that shares this structural motif. We identify a first-order phase transition at 92 K. Single crystal x-ray and neutron diffraction reveal a charge density wave modulation of the atomic lattice below this temperature. This is a distinctly different structural mode than that observed in the AV_{3}Sb_{5} compounds, but both modes have been anticipated in kagome metals. The diverse HfFe_{6}Ge_{6} family offers more opportunities to tune ScV_{6}Sn_{6} and explore density wave order in kagome lattice materials.

Bi2CoO2F4-A Polar, Ferrimagnetic Aurivillius Oxide-Fluoride

Aurivillius oxides have been a research focus due to their ferroelectric properties, but by replacing oxide ions by fluoride, divalent magnetic cations can be introduced, giving Bi₂ MO₂F₄ (M = Fe, Co, and Ni). Our combined experimental and computational study on Bi₂CoO₂F₄ indicates a low-temperature polar structure of P2₁ ab symmetry (analogous to ferroelectric Bi₂WO₆) and a ferrimagnetic ground state. These results highlight the potential of Aurivillius oxide-fluorides for multiferroic properties. Our research has also revealed some challenges associated with the reduced tendency for polar displacements in the more ionic fluoride-based systems.

Refining perovskite structures to pair distribution function data using collective Glazer modes as a basis

Structural modelling of octahedral tilts in perovskites is typically carried out 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 the development of constraints for modelling pure octahedral tilts and implementation of the constraints in diffpy-CMI, a powerful package to analyse pair distribution function (PDF) data. The model in the program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, providing an intuitive picture of the tilting. The model has many fewer refinable variables than the unconstrained space group fits and provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO₃ which has the known Glazer tilt system α⁺β^-β^-. The Glazer model fits comparably to the corresponding space-group model Pnma below r = 14 Å and becomes progressively worse than the space-group model at higher r due to non-rigid distortions in the real material.

Pressure–Temperature Phase Diagram of Multiferroic TbFe2.46Ga0.54(BO3)4

The pressure–temperature phase diagram of the multiferroic TbFe2.46Ga0.54(BO3)4 was studied for hydrostatic pressures up to 7 GPa and simultaneously with temperatures up to 400 K by the Raman spectroscopy technique. The structural phase transition from the R32 phase to the P3121 phase was determined by observing the condensation of soft modes and the appearance of new lines. An increase in pressure leads to an increase in the temperature of the structural phase transition. These phases are stable over the entire investigated temperature and pressure range. No other phases have been found.

Strong Nonlinearity Induced by Coaxial Alignment of Polar Chain and Dense [BO3 ] Units in CaZn2 (BO3 )2

Discovery of new efficient nonlinear optical (NLO) materials with large second-order nonlinearity for the short-wave ultraviolet spectral region (λ_PM ≤266 nm, PM=phase-matching) is still very challenging. Herein, a new beryllium-free borate CaZn₂ (BO₃ )₂ with Sr₂ Be₂ B₂ O₇ (SBBO) double-layered like configuration was rationally designed, which not only preserves the structural merits but also eliminates the limitations of the SBBO crystal. CaZn₂ (BO₃ )₂ shows a large PM second harmonic generation (SHG) reponse of 3.8×KDP, which is 38 times higher than that of its barium analogue. This enhancement mainly originates from the ¹ [Zn₂ O₆ ]_∞ polar chains with a large net dipole moment and [BO₃ ] units with a high NLO active density. Our findings show the great significance of the [ZnO₄ ] tetrahedra introduced strategy to design beryllium-free SBBO-type NLO crystals and also verify the feasibility of using simple non-isomorphic substitution to induce giant second-order nonlinearity enhancement.

Structural and Electronic Effect Driven Distortions in Visible Light Absorbing Polar Materials ATa2V2O11 (A = Sr, Pb)

Complex vanadates of tantalum(V), such as ATa₂V₂O₁₁ (A = Sr, Pb), are rare and underrated materials, which have potential application domains that could be substantially expanded, mitigating the existing controversy on their atomic and electronic organization. Herein, we present a thorough structural examination combining synchrotron powder X-ray diffraction-aided distortion mode analysis with computational methods to study hettotypes of SrTa₂V₂O₁₁ (STVO) and PbTa₂V₂O₁₁ (PTVO). Being distinct from the perovskite family due to the presence of [VO₄] groups, both compounds are polar dielectric materials with certain similarities to SBT and PBT Aurivillius phases. Applying the model of anions of metallic matrices to the analysis of electron localization functions calculated on top of as-established equilibrium structures helps retrace the effects in the Sr and Pb surroundings on the respective crystal packings of STVO and PTVO.

Lattice dynamics of BaFe2Se3

This paper presents a study of the lattice dynamics in BaFe₂Se₃. We combined first-principle calculations, infrared measurements and a thorough symmetry analysis. Our study confirms thatPnmacannot be the space group of BaFe₂Se₃, even at room temperature. The phonons assignment requiresPmto be the BaFe₂Se₃space group, not only in the magnetic phase, but also in the paramagnetic phase at room temperature. This is due to a strong coupling between a short-range spin-order along the ladders, and the lattice degrees of freedom associated with the Fe-Fe bond length. This coupling induces a change in the bond-length pattern from an alternated trapezoidal one (as inPnma) to an alternated small/large rectangular one. Out of the two patterns, only the latter is fully compatible with the observed block-type magnetic structure. Finally, we propose a complete symmetry analysis of the BaFe₂Se₃phase diagram in the 0-600 K range.

Study of the Temperature- and Pressure-Dependent Structural Properties of Alkali Hydrido-closo-borate Compounds

In this work, we report on the structural properties of alkali hydrido-closo-(car)borates, a promising class of solid-state electrolyte materials, using high-pressure and temperature-dependent X-ray diffraction experiments combined with density functional theory (DFT) calculations. The mechanical properties are determined via pressure-dependent diffraction studies and DFT calculations; the shear moduli appear to be very low for all studied compounds, revealing their high malleability (that can be beneficial for the manufacturing and stable cycling of all-solid-state batteries). The thermodiffraction experiments also reveal a high coefficient of thermal expansion for these materials. We discover a pressure-induced phase transition for K₂B₁₂H₁₂ from Fm3̅ to Pnnm symmetry around 2 GPa. A temperature-induced phase transition for Li₂B₁₀H₁₀ was also observed for the first time by thermodiffraction, and the crystal structure determined by combining experimental data and DFT calculations. Interestingly, all phases of the studied compounds (including newly discovered high-pressure and high-temperature phases) may be related via a group–subgroup relationship, with the notable exception of the room-temperature phase of Li₂B₁₀H₁₀.

Herein, we study the pressure and temperature dependencies of alkali hydrido-closo-borates in extracting the mechanical properties of this class of compounds that have a promising future as solid electrolytes. In our research, we have discovered and determined two new high-pressure and high-temperature crystal structures.

Preparation, characterization and DFT+U study of the polar Fe3+-based phase Ba5Fe2ZnIn4S15 containing S= 5/2 zigzag chains

The polar magnetic chalcogenide phase Ba5Fe2ZnIn4S15 was synthesized and its structure solved from single crystal XRD. It is the first member with a 3d magnetic metal (Fe3+) in the Pb5ZnGa6S15-type...

The Exploration of New Infrared Nonlinear Optical Crystals Based on Polymorphism of BaGa4S7

Balancing the key performance metrics, such as, large second harmonic generation (SHG) response and wide band gap is an extremely important but intractable challenge for the development of infrared (IR)...

DFT-Guided Crystal Structure Redetermination and Lattice Dynamics of the Intermetallic Actinoid Compound UIr

UIr has been discussed as a rare example of a noncentrosymmetric, ferromagnetic superconductor crystallizing in the acentric PdBi structure type (P2₁, mP16). Here we present a new structure model for UIr. By means of single-crystal and powder X-ray diffraction we find UIr to crystallize in the centrosymmetric space group P2₁/c, in line with previous ab initio calculations. The discrepancy with the previous noncentrosymmetric model in space group P2₁ is explained by the occurrence of twinning. The observed twinning hints toward a high-temperature displacive phase transition of UIr to the CrB structure type (Cmcm, oS8): we discuss the lattice dynamics corresponding to this transition by crystallographic symmetry mode analysis and by density functional theory (DFT). We find that spin-orbit coupling is essential to understand this phase transition. We apply our theoretical considerations for a critical judgment of the structure models of UPt and NpIr that have been reported to crystallize isotypically with UIr. We confirm that UPt is isotypic to UIr (P2₁/c), whereas we predict NpIr to crystallize in the CrB structure type. Our report on the centrosymmetric crystal structure of UIr has an effect on all those theoretical models that investigated potentially novel superconducting coupling mechanisms of this compound on the basis of the noncentrosymmetric structure model.

Neutron diffraction study of the monoclinic - tetragonal phase transition in NdNbO4 and NdTaO4

Phase transition and high-temperature properties of NdNbO₄ and NdTaO₄ were studied in situ using powder neutron diffraction methods. Both oxides undergo a reversible phase transition from a monoclinic I2/a phase at low temperatures to a tetragonal I4₁/a phase at high temperatures. The phase transition has been investigated through analysis of the spontaneous strains and symmetry distortion modes. Well below the transition temperature, T_c, the thermal evolution of the lattice parameters and symmetry modes suggest the transition is continuous, although a small discontinuity in both the spontaneous strains and symmetry distortion modes shows the transition is strictly first order. Analysis of the refined structures reveals that the Nb and Ta cations are best described as having a distorted 6-coordinate arrangement in the monoclinic structure, with four short and two long bonds. Breaking of the two long bonds at high temperatures, resulting in a transformation of the Nb(Ta) coordination to a regular tetrahedron, is believed to be responsible for the first order nature of the transition.

Aluminum Amidinates: Insights into Alkyne Hydroboration

The mechanism of the aluminum-mediated hydroboration of terminal alkynes was investigated using a series of novel aluminum amidinate hydride and alkyl complexes bearing symmetric and asymmetric ligands. The new aluminum complexes were fully characterized and found to facilitate the formation of the (E)-vinylboronate hydroboration product, with rates and orders of reaction linked to complex size and stability. Kinetic analysis and stoichiometric reactions were used to elucidate the mechanism, which we propose to proceed via the initial formation of an Al-borane adduct. Additionally, the most unstable complex was found to promote decomposition of the pinacolborane substrate to borane (BH3), which can then proceed to catalyze the reaction. This mechanism is in contrast to previously reported aluminum hydride-catalyzed hydroboration reactions, which are proposed to proceed via the initial formation of an aluminum acetylide, or by hydroalumination to form a vinylboronate ester as the first step in the catalytic cycle.

Mode Crystallography Analysis through the Structural Phase Transition and Magnetic Critical Behavior of the Lacunar Spinel GaMo4Se8

In the lacunar spinels, with the formula AB₄X₈, transition-metal ions form tightly bound B₄ clusters resulting in exotic physical properties such as the stabilization of Néel-type skyrmion lattices, which hold great promise for energy-efficient switching devices. These properties are governed by the symmetry of these compounds with distortion of the parent noncentrosymmetric F4̅3m space group to the polar R3m, with recent observation of a coexisting Imm2 low-temperature phase. In this study, through powder neutron diffraction, we further confirm that a metastable Imm2 coexists with the R3m phase in GaMo₄Se₈ and we present its structure. By applying the mode crystallography approach to the distortions together with anisotropic microstrain broadening analysis, we postulate that the formation origin of the minority Imm2 phase stems from the high compressive stress observed in the R3m phase. Bond valence sum analysis also suggests a change in electronic configuration in the transition to Imm2 which could have implications on the electrical properties of the compound. We further establish the nature of the magnetic phase transition using critical exponent analysis obtained from single-crystal magnetization measurements which shows a mixture of tricritical mean-field and 3D Heisenberg behavior [β = 0.22(4), γ = 1.19(1), and δ = 6.42(1)]. Magnetoentropic mapping performed on a single crystal reveals the signature of a positive entropy region near the magnetic phase transition which corresponds to the skyrmion phase field observed in a polycrystalline sample.

Effect of B-Site Order-Disorder in the Structure and Magnetism of the New Perovskite Family La2MnB'O6 with B' = Ti, Zr, and Hf

In this work, we report the synthesis as well as the structural and magnetic characterization of the three perovskites La₂MnB'O₆ (B' = Ti, Zr, and Hf). Interestingly, only La₂MnTiO₆ crystallizes in the monoclinic double perovskite space group P2₁/n, with a complete rocksalt order of the B-site cations, whereas La₂MnZrO₆ and La₂MnHfO₆ crystallize in the orthorhombic simple perovskite space group Pbnm, with complete disorder in the B site. Moreover, the magnetic susceptibility at low temperatures shows clear antiferromagnetic transitions below 10 K for the three compounds, but only the Ti-based perovskite has long-range magnetic ordering. The latter compound has an antiferromagnetic type-II structure described by the P_S-1 magnetic space group, while the other two have a spin-glass behavior below the transition temperature due to both spin disorder and competing superexchange interactions in the systems. This is the first time that two of the three studied compounds were synthesized (B' = Zr and Hf) and the first time that the whole series is described in thorough detail using symmetry-adapted refinements and magnetic crystallography.

Group Theory Analysis to Study Phase Transitions of Quasi-2D Sr3Hf2O7

We present an ab-initio study performed in the framework of density functional theory, group-subgroup symmetry analysis and lattice dynamics, to probe the octahedral distortions, which occur during the structural phase transitions of the quasi-2D layered perovskite Sr3Hf2O7 compound. Such a system is characterized by a high-temperature I4/mmm centrosymmetric structure and a ground-state Cmc21 ferroelectric phase. We have probed potential candidate polymorphs that may form the I4/mmm → Cmc21 transition pathways, namely Fmm2, Ccce, Cmca and Cmcm. We found that the band gap widths increase as the symmetry decreases, with the ground-state structure presenting the largest gap width (∼5.95 eV). By probing the Partial Density of States, we observe a direct relation regarding the tilts and rotations of the oxygen perovskite cages as the transition occurs; these show large variations mostly of the O p-states which contribute mostly to the valence band maximum. Moreover, by analyzing the hyperfine parameters, namely the Electric Field Gradients and asymmetric parameters, we observe variations as the transition occurs, from which it is possible to identify the most plausible intermediate phases. We have also computed the macroscopic polarization and confirm that the Cmc21 phase is ferroelectric with a value of spontaneous polarization of 0.0478 C/m2. The ferroelectricity of the ground-state Cmc21 system arises due to a second order parameter related to the coupling of the rotation and tilts of the O perovskite cages together with the Sr displacements.

Toward the Coordination Fingerprint of the Edge-Sharing BO4 Tetrahedra

The K₃Sb₄BO₁₃ (KSBO) material undergoes an uncommon symmetry increase upon cooling, from triclinic symmetry at room temperature to monoclinic symmetry at low temperature. The first-order phase transition is accompanied by shrinkage of the unit cell, resulting in the transformation of every pair of head-to-tail triangular BO₃ groups into one B₂O₆ unit featuring unique edge-sharing BO₄ tetrahedra. This is the first material with B₂O₆ units formed through temperature lowering and exhibiting a B-O anionic framework composed uniquely of isolated edge-sharing BO₄ tetrahedra. Several techniques including single-crystal X-ray diffraction experiments, Raman and ¹¹B magic-angle-spinning NMR spectroscopies, and, for the first time, B K-edge electron energy loss spectroscopy were used to evidence the rare and discrete B₂O₆ units. The complete transformation of BO₃ units into B₂O₆ units makes the KSBO compound the perfect candidate to extract information about B₂O₆ units whose signal can be unambiguously assigned.

Relation among Oxygen Stoichiometry, Structure, and Co Valence and Spin State in Single-Layer La2-xAxCoO4±δ (A = Ca, Sr) Perovskites

We have investigated the role of oxygen stoichiometry and structural properties in the modulation of Co valence and spin state in single-layer La_2-xA_xCoO_4±δ (A = Sr, Ca; 0 ≤ x ≤ 1) perovskites as well as the interplay between their local structural properties and the magnetic and charge-ordering phenomena. We show the results of high angular resolution powder X-ray diffraction and Co K-edge X-ray absorption and emission spectroscopy experiments on polycrystalline and single-crystal samples. The different doping-induced changes in the Co valence and spin state by Ca (or Sr) substitution can be understood in terms of the evolving oxygen stoichiometry. For Ca doping, the interstitial oxygen excess around the La/Ca atoms in underdoped samples is rapidly lost upon increasing the Ca content. The creation of oxygen vacancies leads to the stabilization of a mixed-valence Co^2.5+ independently of the Ca content. In contrast, Sr substitution leads to almost stoichiometric samples and a lower oxygen vacancy concentration, which allows higher mixed-valence states for Co up to Co^2.9+. The Co mixed-valence state along the two series is fluctuating between two valence states, Co^2.4+ as in La₂CoO_4.2 and Co^2.9+ as in LaSrCoO_3.91, that become periodically ordered for the charge-ordered phases around the half-doping. The X-ray emission derived spin states agree well with the Co fluctuating mixed-valence state derived from X-ray absorption spectroscopy on consideration of a distribution of high-spin Co²⁺ and low-spin Co³⁺. Furthermore, there is no quenching of the orbital contribution for the high-spin Co²⁺, as concluded from a comparison with macroscopic magnetization measurements. Doping holes are mainly located in the ab plane and have a strong oxygen 2p character. The major lattice distortions, which are different for Sr and Ca doping, occur along the c axis, where changes in the oxygen stoichiometry take place. Moreover, charge-order transitions are clearly shown from the anomalous increase of the c lattice parameter with an increase in the temperature above 500 K but there is no signature for a temperature-dependent spin-state transition.

Enhanced stability in CH3NH3PbI3 hybrid perovskite from mechano-chemical synthesis: structural, microstructural and optoelectronic characterization

Among the hybrid organic-inorganic perovskites MAPbX₃ (MA: methyl-ammonium CH₃-NH₃⁺, X = halogen), the triiodide specimen (MAPbI₃) is still the material of choice for solar energy applications. Although it is able to absorb light above its 1.6 eV bandgap, its poor stability in humid air atmosphere has been a major drawback for its use in solar cells. However, we discovered that this perovskite can be prepared by ball milling in a straightforward way, yielding specimens with a superior stability. This fact allowed us to take atomic-resolution STEM images for the first time, with sufficient quality to unveil microscopic aspects of this material. We demonstrated full Iodine content, which might be related to the enhanced stability, in a more compact PbI₆ framework with reduced unit-cell volume. A structural investigation from neutron powder diffraction (NPD) data of an undeuterated specimen was essential to determine the configuration of the organic MA unit in the 100-298 K temperature range. A phase transition is identified, from the tetragonal structure observed at RT (space group I4/mcm) to an orthorhombic (space group Pnma) phase where the methyl-ammonium organic units are fully localized. Our NPD data reveal that the MA changes are gradual and start before reaching the phase transition. Optoelectronic measurements yield a photocurrent peak at an illumination wavelength of 820 nm, which is redshifted by 30 nm with respect to previously reported measurements on MAPbI₃ perovskites synthesized by crystallization from organic solvents.

Spin phonon coupling in Mn doped HoFeO3 compounds exhibiting spin reorientation behaviour

An investigation has been carried out on the spin phonon coupling in a series of isostructural polycrystalline orthorhombic (Space group Pnma) compounds HoFe_1-X Mn _X O₃ (x  ⩽  0.6) exhibiting spin reorientation below Néel temperature (T _N), using magnetization, neutron diffraction, and Raman scattering techniques. Mn doping leads to an anomalous increase in the spin reorientation temperature (T _SR), shifting it close to room temperature from T _SR ~ 60 K for x  =  0 sample, and concomitant lowering of T _N. The T _SR is absent in samples for x  ⩾  0.5. The magnetic structure undergoes a transition at T _SR from Γ₄  →  Γ₁ in the Mn doped compounds as against Γ₄  →  Γ₂ observed in HoFeO₃ sample. In the region T  <  T _N an anomalous softening of Raman phonon modes viz., B _2g(5) and B _3g(3), identified with the stretching motion and breathing mode, respectively, of Fe/Mn-O₆ octahedra, is observed in compounds exhibiting spin-reorientation behaviour, indicating a spin-phonon coupling in these compounds. A quadratic correlation between the deviation of phonon frequency and variation of antiferromagnetic moment (Δω [Formula: see text] M ²) is observed in these compounds. The temperature evolution of the M2+  mode obtained from the analysis of neutron diffraction data based on symmetry adapted mode decomposition of the Pnma structure further corroborates the mode softening observation.

A new tilt and an old twist on the nickel arsenide structure-type: synthesis and characterisation of the quaternary transition-metal cyanamides A2MnSn2(NCN)6 (A = Li and Na)

In this work, we describe the synthesis and structure of the quaternary transition-metal cyanamides Na2MnSn2(NCN)6 and Li2MnSn2(NCN)6. These phases crystallise isotypically in layered structures, with P3[combining macron]1m symmetry, that comprise hexagonal close-packed arrays of NCN2- anions with metal cations in 5/6 of the octahedral holes, thereby reflecting low-symmetry modifications of the hierarchical [NiAs]-type MNCN structure. The distinct coordination requirements of the metal cations template an ordered decoration across the octahedral sites with corundum-like [Sn2(NCN)3]2+ layers alternating with [A2Mn(NCN)3]2- layers which resemble a portion of the Li2Zr(NCN)3 structure. This motif is also mirrored in the form of the NCN2- anions which adopt N-C[triple bond, length as m-dash]N2- cyanamide shapes with clear single- and triple-bond character. Distortion-mode analysis reveals the importance of K1 octahedral twist and K2 cyanamide tilt displacements in stabilising these phases, the latter of which is only accessible because of the extended nature of the NCN2- anion. These are the first examples of non-binary transition-metal cyanamides to be discovered and this study highlights how the additional flexibility of the NCN2- anion affords a novel structure-type not observed in oxide chemistry.