Magnetoelectric and multiferroic properties of spinels

In the last two decades, significant progress has been made in combining ferroelectricity and magnetism in the same material. Usually, magnetism and ferroelectricity were thought of as independent phenomena. However, the discovery of spin-induced ferroelectricity with a strong coupling between magnetism and electric polarization is intriguing. Whether they interact non-trivially is determined by the symmetries of the crystal lattice and the appearing magnetic structure, which, in turn, depends on the nature of magnetic ions, their exchange, and anisotropic interactions, the presence of frustration, etc. Several structural families of compounds exhibiting magnetoelectric (ME) or multiferroic properties have already been reported. This paper gives an account of the richness of structure, magnetism, magnetoelectric and multiferroic properties of spinels. After presenting symmetry aspects of the crystal and magnetic structures of spinels related to these phenomena, we give several examples of magnetoelectric and multiferroic spinels explaining the relations between magnetism and electric polarization and discuss their future perspectives.