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In this article we review and discuss a mechanism for coupling betweenelectric polarization and magnetization that can ultimately lead toelectric-field switchable magnetization. The basic idea is that a ferroelectricdistortion in an antiferromagnetic material can "switch on" theDzyaloshinskii-Moriya interaction which leads to a canting of theantiferromagnetic sublattice magnetizations, and thus to a net magnetization.This magnetization M is coupled to the polarization P via a trilinear freeenergy contribution of the form P(M x L), where L is the antiferromagneticorder parameter. In particular, we discuss why such an invariant is present inR3c FeTiO_3 but not in the isostructural multiferroic BiFeO_3. Finally, weconstruct symmetry groups that in general allow for this kind offerroelectrically-induced weak ferromagnetism.

Electric-field switchable magnetization via the Dzyaloshinskii-Moriya interaction: FeTiO_3 versus BiFeO_3