Electric-field-switchable magnets:: The case of BaNiF4

We show, using the antiferromagnetic ferroelectric BaNiF4 as a model system, that the "weak" magnetic order arising from a polar structural distortion in a ferroelectric magnet due to the Dzyaloshinskii-Moriya interaction can be switched by an electric field. We calculate the magnitude of the resulting magnetic order parameter in BaNiF4 using first-principles techniques, and we show that it is one to two orders of magnitude larger than the converse effect of "weak ferroelectricity" resulting from noncentrosymmetric magnetic ordering. Our work points the way toward the design of multiferroic devices, in which the magnetoelectric domain state can be fully controlled by both electric and magnetic fields.