Improper ferroelectricity (trimerization) in the hexagonal manganites RMnO 3 leads to a network of coupled structural and magnetic vortices that induce domain wall magnetoelectricity and magnetization (M), neither of which, however, occurs in the bulk. Here we combine first-principles calculations, group-theoretic techniques and microscopic spin models to show how the trimerization not only induces a polarization (P) but also a bulk M and bulk magnetoelectric (ME) effect. This results in the existence of a bulk linear ME vortex structure or a bulk ME coupling such that if P reverses so does M. To measure the predicted ME vortex, we suggest RMnO 3 under large magnetic field. We suggest a family of materials, the hexagonal RFeO 3 ferrites, also display the predicted phenomena in their ground state.

Materials that exhibit simultaneous order in their electric and magnetic ground states hold promise for use in next-generation memory devices in which electric fields control magnetism. Such materials are exceedingly rare, however, owing to competing requirements for displacive ferroelectricity and magnetism. Despite the recent identification of several new multiferroic materials and magnetoelectric coupling mechanisms, known single-phase multiferroics remain limited by antiferromagnetic or weak ferromagnetic alignments, by a lack of coupling between the order parameters, or by having properties that emerge only well below room temperature, precluding device applications. Here we present a methodology for constructing single-phase multiferroic materials in which ferroelectricity and strong magnetic ordering are coupled near room temperature. Starting with hexagonal LuFeO3-the geometric ferroelectric with the greatest known planar rumpling-we introduce individual monolayers of FeO during growth to construct formula-unit-thick syntactic layers of ferrimagnetic LuFe2O4 (refs 17, 18) within the LuFeO3 matrix, that is, (LuFeO3)m/(LuFe2O4)1 superlattices. The severe rumpling imposed by the neighbouring LuFeO3 drives the ferrimagnetic LuFe2O4 into a simultaneously ferroelectric state, while also reducing the LuFe2O4 spin frustration. This increases the magnetic transition temperature substantially-from 240 kelvin for LuFe2O4 (ref. 18) to 281 kelvin for (LuFeO3)9/(LuFe2O4)1. Moreover, the ferroelectric order couples to the ferrimagnetism, enabling direct electric-field control of magnetism at 200 kelvin. Our results demonstrate a design methodology for creating higher-temperature magnetoelectric multiferroics by exploiting a combination of geometric frustration, lattice distortions and epitaxial engineering.

The natural mineral azurite Cu(3)(CO(3))(2)(OH)(2) is a frustrated magnet displaying unusual and controversially discussed magnetic behavior. Motivated by the lack of a unified description for this system, we perform a theoretical study based on density functional theory as well as state-of-the-art numerical many-body calculations. We propose an effective generalized spin-1/2 diamond chain model which provides a consistent description of experiments: low-temperature magnetization, inelastic neutron scattering, nuclear magnetic resonance measurements, magnetic susceptibility as well as new specific heat measurements. With this study we demonstrate that the balanced combination of first principles with powerful many-body methods successfully describes the behavior of this frustrated material.

Using first-principles density functional calculations, we study the electronic and magnetic properties of the ferromagnetic insulating double perovskite compound La2NiMnO6, which has been reported to exhibit an interesting magnetic field sensitive dielectric anomaly as a function of temperature. Our study reveals the existence of very soft infrared active phonons that couple strongly with spins at the Ni and Mn sites through modification of the superexchange interaction. We suggest that these modes are the origin for the observed dielectric anomaly in La2NiMnO6.

Despite several reports on the surface phase transformations from a layered to a disordered spinel and a rock-salt structure at the surface of the Ni-rich cathodes, the precise structures and compositions of these surface phases are unknown. The phenomenon, in itself, is complex and involves the participation of several contributing factors. Of these factors, transition metal (TM) ion migration toward the interior of the particle and hence formation of TM-densified surface layers, triggered by oxygen loss, is thermodynamically probable. Here, we simulate the thermodynamic phase equilibria as a function of TM ion content in the cathode material in the context of lithium nickel oxides, using a combined approach of first-principles density functional calculations, the cluster expansion method, and grand canonical Monte Carlo simulations. We developed a unified lattice Hamiltonian that accommodates not only rock-salt like structures but also topologically different spinel-like structures. Also, our model provides a foundation to investigate metastable cation compositions and kinetics of the phase transformations. Our investigations predict the existence of several Ni-rich phases that were, to date, unknown in the scientific literature. Our simulated phase diagrams at finite temperature show a very low solubility range of the prototype spinel phase. We find a partially disordered spinel-like phase with far greater solubility that is expected to show very different Li diffusivity compared to that of the prototype spinel structure.