Electronic ferroelectricity induced by charge and orbital orderings.

After the revival of the magnetoelectric effect which took place in the early 2000s, the interest in multiferroic materials displaying simultaneous presence of spontaneous long-range magnetic and dipolar order has motivated an exponential growth of research activity, from both the experimental and theoretical perspectives. Within this context, and relying also on the rigorous formulation of macroscopic polarization as provided by the Berry-phase approach, it has been possible to identify new microscopic mechanisms responsible for the appearance of ferroelectricity. In particular, it has been realized that electronic spin, charge and orbital degrees of freedom may be responsible for the breaking of the space-inversion symmetry, a necessary condition for the appearance of electric polarization, even in centrosymmetric crystal structures. In view of its immediate potential application in magnetoelectric-based devices, many efforts have been made to understand how magnetic orderings may lead to ferroelectric polarization, and to identify candidate materials. On the other hand, the role of charge and orbital degrees of freedom, which have received much less attention, has been predicted to be non-negligible in several cases. Here, we review recent theoretical advances in the field of so-called electronic ferroelectricity, focusing on the possible mechanisms by which charge- and/or orbital-ordering effects may cause the appearance of macroscopic polarization. Generally, a naive distinction can be drawn between materials displaying almost localized electrons and those characterized by a strong covalent character and delocalized electrons. As for the latter, an intuitive understanding of basic mechanisms is provided in the framework of tight-binding model Hamiltonians, which are used to shed light on unusual charge/orbital effects in half-doped manganites, whereas the case of magnetite will be thoroughly discussed in light of recent progress pointing to an electronic origin of its proposed ferroelectric and magnetoelectric properties.