Evolution of the antiferromagnetism vector of a multiferroic BiFeO$_3$ during switching its ferroelectric polarization

The evolution of the antiferromagnetism vector of multiferroic BiFeO$_3$ during switching of its ferroelectric polarization by an electric field has been studied by numerical simulation in the framework of the phenomenological model for the magnetic anisotropy energy. Optimal variants have been found for the cut of electrosensitive BiFeO$_3$ layer, the deformation induced by a substrate, and the direction of applying electric field for the development of prototypes of new-generation marnetoresistive memory.