Electric polarization in two-layer bounded ferromagnetic film

A numerical study of the ground state of a two-layer ferromagnetic bounded film is carried out. The film layers have uniaxial anisotropy easy-plane and easy-axis. All calculations were carried out for films with parameters of ferrites-garnets - Materials that admit a magnetoelectric effect. The ground state was calculated using a three-dimensional micromagnet modeling package OOMMF for rectangular films of different sizes. It was shown that in a film, along with a homogeneous ground state, the vortex distribution of the magnetization is realized. For the vortex distribution, the electric polarization is calculated. It was found that the component of the electric polarization vector of the film perpendicular to the film plane is nonzero. This is due to the presence of the vortex core. The change in the electric polarization due to magnetic reversal of the film by an external magnetic field is studied. It is shown that as the field increases, the polarization modulus also increases to certain field values, and then decreases to zero. As the transverse dimensions of the film decrease, the magnitude of the maximum of the electric polarization increases.