Electric-field switchable magnetization via the Dzyaloshinskii-Moriya interaction: FeTiO3 versus BiFeO3

In this article we review and discuss a mechanism for coupling between electric polarization and magnetization that can ultimately lead to electric-field switchable magnetization. The basic idea is that a ferroelectric distortion in an antiferromagnetic material can “switch on” the Dzyaloshinskii-Moriya interaction which leads to a canting of the antiferromagnetic sublattice magnetizations, and thus to a net magnetization. This magnetization ~ M is coupled to the polarization ~ P via a trilinear free energy contribution of the form ~ P · ( ~ M × ~ L), where ~ L is the antiferromagnetic order parameter. In particular, we discuss why such an invariant is present in R3c FeTiO3 but not in the isostructural multiferroic BiFeO3. Finally, we construct symmetry groups that in general allow for this kind of ferroelectricallyinduced weak ferromagnetism.