Hysteresis of the Electric Polarization in a Two-Layer Ferromagnetic Film with a Vortical Distribution of Magnetization

Hysteresis of the electric polarization of a two-layer exchange-coupled ferromagnetic film whose layers have the easy-plane and easy-axis anisotropy upon magnetization reversal is studied numerically. The magnetization reversal was carried out by a magnetic field perpendicular to the film plane from the saturation state along the easy magnetization axis. The dependences of the average electric polarization and the reduced magnetization of the film layers on the external magnetic field strength are constructed. The feasibility of sign reversal of the electric polarization in a magnetic field in films whose thickness is smaller than the transverse dimensions is found. No polarization sign reversal is observed in thicker films upon magnetization reversal.