Anharmonic lattice interactions in improper ferroelectrics for multiferroic design

The design and discovery of new multiferroics, or materials that display both ferroelectricity and long-range magnetic order, is of fundamental importance for new electronic technologies based on low-power consumption. Far too often, however, the mechanisms causing these properties to arise are incompatible or occur at ordering temperatures below room temperature. One design strategy which has gained considerable interest is to begin with a magnetic material, and find novel ways to induce a spontaneous electric polarization within the structure. To this end, anharmonic interactions coupling multiple lattice modes have been used to lift inversion symmetry in magnetic dielectrics. Here we provide an overview of the microscopic mechanisms by which various types of cooperative atomic displacements result in ferroelectricity through anharmonic multi-mode coupling, as well as the types of materials most conducive to these lattice instabilities. The review includes a description of the origins of the displacive modes, a classification of possible non-polar lattice modes, as well as how their coupling can produce spontaneous polarizations. We then survey the recent improper ferroelectric literature, and describe how the materials discussed fall within a proposed classification scheme, offering new directions for the theoretical design of magnetic ferroelectrics. Finally, we offer prospects for the future discovery of new magnetic improper ferroelectrics, as well as detail remaining challenges and open questions facing this exciting new field.