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

In this paper 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) over right arrow M is coupled to the polarization (P) over right arrow P via a trilinear free energy contribution of the form (P) over right arrow (M) over right arrow (L) over right arrow where (L) over right arrow 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 ferroelectrically-induced weak ferromagnetism.