To superspace and beyond

The significance of an algorithm developed by H. T. Stokes & B. J. Campbell [Acta Cryst. (2017), A73, 4-13] is discussed. The algorithm promises to be a key tool for understanding the structure-property relationships of the many technologically important materials that display incommensurate modulations in their atomic and/or magnetic structure

First-principles investigation of the magnetoelectric properties of Ba7Mn4O15

Type-II multiferroics, in which the magnetic order breaks inversion symmetry, are appealing for both fundamental and applied research due their intrinsic coupling between magnetic and electrical orders. Using first-principles calculations we study the ground state magnetic behaviour of Ba7Mn4O15 which has been classified as a type-II multiferroic in recent experiments. Our constrained moment calculations with the proposed experimental magnetic structure shows the spontaneous emergence of a polar mode giving rise to an electrical polarisation comparable to other known type-II multiferroics. When the constraints on the magnetic moments are removed, the spins self-consistently relax into a canted antiferromagnetic ground state configuration where two magnetic modes transforming as distinct irreducible representations coexist. While the dominant magnetic mode matches well with the previous experimental observations, the second mode is found to possess a different character resulting in a non-polar ground state. Interestingly, the non-polar magnetic ground state exhibits a significantly strong linear magnetoelectric coupling comparable to the well-known multiferroic BiFeO3, suggesting strategies to design new linear magnetoelectrics

Hybrid Local-Order Mechanism for Inversion Symmetry Breaking

Using classical Monte Carlo simulations, we study a simple statistical mechanical model of relevance to the emergence of polarisation from local displacements on the square and cubic lattices. Our model contains two key ingredients: a Kitaev-like orientation-dependent interaction between nearest neighbours, and a steric term that acts between next-nearest neighbours. Taken by themselves, each of these two ingredients is incapable of driving long-range symmetry breaking, despite the presence of a broad feature in the corresponding heat capacity functions. Instead each component results in a "hidden" transition on cooling to a manifold of degenerate states, the two manifolds are different in the sense that they reflect distinct types of local order. Remarkably, their intersection---\emph{i.e.} the ground state when both interaction terms are included in the Hamiltonian---supports a spontaneous polarisation. In this way, our study demonstrates how local ordering mechanisms might be combined to break global inversion symmetry in a manner conceptually similar to that operating in the "hybrid" improper ferroelectrics. We discuss the relevance of our analysis to the emergence of spontaneous polarisation in well-studied ferroelectrics such as BaTiO$_3$ and KNbO$_3$.Comment: 8 pages, 8 figure

Improper Ferroelectric Polarisation in a Perovskite driven by Inter-site Charge Transfer and Ordering

It is of great interest to design and make materials in which ferroelectric polarisation is coupled to other order parameters such as lattice, magnetic and electronic instabilities. Such materials will be invaluable in next-generation data storage devices. Recently, remarkable progress has been made in understanding improper ferroelectric coupling mechanisms that arise from lattice and magnetic instabilities. However, although theoretically predicted, a compact lattice coupling between electronic and ferroelectric (polar) instabilities has yet to be realised. Here we report detailed crystallographic studies of a novel perovskite Hg$^{\textbf{A}}$Mn$^{\textbf{A'}}_{3}$Mn$^{\textbf{B}}_{4}$O$_{12}$ that is found to exhibit a polar ground state on account of such couplings that arise from charge and orbital ordering on both the A' and B-sites, which are themselves driven by a highly unusual Mn$^{A'}$-Mn$^B$ inter-site charge transfer. The inherent coupling of polar, charge, orbital and hence magnetic degrees of freedom, make this a system of great fundamental interest, and demonstrating ferroelectric switching in this and a host of recently reported hybrid improper ferroelectrics remains a substantial challenge.Comment: 9 pages, 7 figure

Electronic Orders in the Verwey Structure of Magnetite

Electronic structure calculations of the Verwey ground state of magnetite, Fe3O4, using density functional theory with treatment of on-site Coulomb interactions (DFT+U scheme) are reported. These calculations use the recently-published experimental crystal structure coordinates for magnetite in the monoclinic space group Cc. The computed density distribution for minority spin electron states close to the Fermi level demonstrates that charge order and Fe2+-orbital order are present at the B-type lattice sites to a first-approximation. However, Fe2+/Fe3+ charge differences are diminished through weak bonding interactions of the Fe2+-states to specific pairs of neighboring iron sites that create linear, three-B-atom trimeron units that may be regarded as 'orbital molecules'. Trimerons are ordered evenly along most Fe atom chains in the Verwey structure, but more complex interactions are observed within one chain.Comment: 13 pages, 4 figures. Changes for version 2: Fig. 4 and corresponding discussion extende

Pressure-dependent phase transitions in hybrid improper ferroelectric Ruddlesden-Popper oxides

The temperature-dependent phase transitions in Ruddlesden-Popper oxides with perovskite bilayers have been under increased scrutiny in recent years due to the so-called hybrid improper ferroelectricity that some chemical compositions exhibit. However, little is currently understood about the hydrostatic pressure dependence of these phase transitions. Herein we present the results of a combined high-pressure powder synchrotron x-ray diffraction experiment and abinitio study on the bilayered Ruddlesden-Popper phases Ca3Mn2O7 and Ca3Ti2O7. In both compounds we observe a first-order phase transition, that in combination with our density functional theory calculations, we can confidently assign as being between polar A21am and nonpolar Acaa structures. Interestingly, we show that while the application of pressure ultimately favors a nonpolar phase, as is commonly observed for proper ferroelectrics, regions of response exist where pressure actually acts to increase the polar mode amplitudes. The reason for this can be untangled by considering the varied response of octahedral tilts and rotations to hydrostatic pressure and their trilinear coupling with the polar instability

Charge order at the frontier between the molecular and solid states in Ba3NaRu2O9

We show that the valence electrons of Ba3NaRu2O9, which has a quasi-molecular structure, completely crystallize below 210 K. Using an extended Hubbard model, we show that the charge ordering instability results from long-range Coulomb interactions. However, orbital ordering, metal-metal bonding and formation of a partial spin gap enforce the magnitude of the charge separation. The striped charge order and frustrated hcp lattice of Ru2O9 dimers lead to competition with a quasi-degenerate charge-melted phase under photo-excitation at low temperature. Our results establish a broad class of simple metal oxides as models for emergent phenomena at the border between the molecular and solid states.Comment: Minor changes, with supporting information. To appear in Phys. Rev. Let