We report a first-principles study of the recently predicted $Pmc{2}_1$ phase of the multiferroic $\mathrm{BiFeO}{}_3$ material, revealing a novel magnetoelectric effect that makes it possible to control magnetism with an electric field. The effect can be viewed as a two-step process: Switching the polarization first results in the change of the sense of the rotation of the oxygen octahedra, which in turn induces the switching of the secondary magnetic order parameter. The first step is governed by an original trilinear-coupling energy between polarization, octahedral tilting, and an antiferroelectric distortion. The second step is controlled by another trilinear coupling, this one involving the predominant and secondary magnetic orders as well as the oxygen octahedral tilting. In contrast with other trilinear-coupling effects in the literature, the present ones occur in a simple $AB{\text{O}}_3$ perovskite and involve a large polarization.

• Received 30 May 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.057202