We put forward the concept of a bulk Rashba effect emerging in a multiferroic material, such as an antiferromagnetic system with a polar crystal structure. According to symmetry considerations, while time-reversal and space-inversion symmetries are both broken, there exist specific spin flipping operations that relate opposite spin sites in the magnetic crystal structure. As a consequence, at certain high-symmetry points in the momentum space, the magnetic point group allows the spin angular momentum to be locked to the linear momentum, a typical feature of the Rashba effect. In such a case, spin-splitting effects induced by spin-orbit coupling can arise, similar to what happens in non-magnetic Rashba systems. As a prototypical example, ab-initio calculations of antiferromagnetic BiCoO3 in the polar structure reveal that a large Rashba-like band- and spin- splitting occurs at the conduction band bottom, having a large weight from Bi-p orbital states. Moreover, we show that the spin texture of such a multiferroic can be modulated by applying a magnetic field. In particular, an external in-plane magnetic field is predicted not only to induce spin-canting, but also a distortion of the energy isocontours and a shift of the spin-vortex (centered on the high-symmetry point and characteristic of Rashba effect) along a direction perpendicular to the applied field.
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