  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 allow for such a 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 the
multiferroic BiFeO3 based on density functional theory. Our data supports only
the existence of one DM interaction contribution originating from the spin
current model. By exploring then 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 BiFeO3.
