Spin-current driven Dzyaloshinskii-Moriya interaction in multiferroic BiFeO3 from first principles

The electrical control of magnons opens up new ways to transport and process information for logic devices. In magnetoelectrical multiferroics, the Dzyaloshinskii-Moriya (DM) interaction directly allows for such control and hence is of major importance. We determine the origin and the strength of the (converse) spin-current DM interaction in the $R3c$ bulk phase of multiferroic ${\mathrm{BiFeO}}₃$ based on density functional theory. Our data support only the existence of one DM interaction contribution originating from the spin-current model. By exploring the magnon dispersion in the full Brillouin zone, we show that the exchange is isotropic, but the DM interaction and anisotropy prefer any propagation and any magnetization direction within the full (111) plane. Our work emphasizes the significance of the asymmetric potential induced by the spin current over the structural asymmetry induced by the anionic octahedron in multiferroics such as ${\mathrm{BiFeO}}₃$.