BaNiF4: an electric field-switchable weak antiferromagnet

We show that in the antiferromagnetic ferroelectric BaNiF4 the Dzyaloshinskii-Moriya interaction leads to a small canting of the magnetic moments, away from the easy axis, resulting in a noncollinear magnetic structure. The canting corresponds to an additional "weak" antiferromagnetic order parameter whose orientation is determined by the polar structural distortion and can be reversed by switching the ferroelectric polarization with an electric field. Our results point the way to a more general coupling mechanism between structural distortions and magnetic order parameters in magnetoelectric multiferroics which can be exploited in the design of electric field-switchable magnets.