Electric Polarization in a Nanosized, Two-Layer, Ferromagnetic Film with Combined Uniaxial and Cubic Anisotropy in the Layers

The average electric polarization arising in a two-layer, nanosized, ferromagnetic film with a combined uniaxial and cubic anisotropy and a vortical distribution of magnetization is studied numerically. Allowance for the cubic anisotropy leads to a multifold increase in the average electric polarization in samples with a positive constant of cubic anisotropy and a significant decrease in samples with a negative constant of cubic anisotropy. Analysis of the hysteresis of the average electric polarization in a magnetic field perpendicular to the film revealed striking differences in the field dependences in films with different cubic anisotropy. If the cubic anisotropy is positive, then the maxima of the average polarization curves shift to the region of low magnetic fields upon an increase in the anisotropy constant. The intensity of the maxima becomes larger, and the hysteresis practically disappears. For films with a negative constant of cubic anisotropy, the maxima of the average polarization curves shift to the region of high fields upon an increase in this constant and the intensity of the maxima becomes significantly smaller.