Orbital degrees of freedom as origin of magnetoelectric coupling in magnetite

A microscopic understanding of magnetoelectricity, i.e. the coupling between magnetic (electric) properties and external electric (magnetic) fields, is a crucial milestone for future generations of electrically-controlled spintronic devices. Here, we focus on the first magnetoelectric known to mankind: magnetite. By means of a joint approach based on phenomenological Landau theory and density-functional simulations, we show that magnetoelectricity in charge-/orbital-ordered Fe3O4 in the non-centrosymmetric Cc structure is driven by the interplay between a peculiar orbital-order and on-site spin-orbit coupling. The excellent agreement with available experiments confirms our theoretical picture, pointing to magnetite as a prototype of a novel category of magnetoelectrics where ferroelectric polarization can be induced, tuned or switched via a magnetic field.