Nonuniform Magnetoelectric Effect in a Nano-Sized Ferromagnetic Film with Surface Anisotropy

A numerical study of the ground state of a ferromagnetic finite film has been performed. The film is characterized by the uniaxial easy-plane bulk magnetic anisotropy and easy-axis surface anisotropy. All calculations were performed for films with parameters of ferrite garnets. The ground state of nano-sized rectangular films (nanocolumns) differing in the cross dimensions is calculated using OOMMF three-dimensional micromagnetic simulation software. The electric polarization is calculated for the vortex magnetization distribution for the ground state. It was found that, in the case of surface anisotropy, the polarization vector component of the film, which is perpendicular to the film plane, is nonzero. A change in the electric polarization upon magnetization of film in an external magnetic field is studied. As the magnetic field increases, the polarization module is also shown to increase to certain values of the field and, after that, decreases to zero. As the cross dimensions of film decreases and the surface anisotropy constant increases, the electric polarization of a nanocolumn increases.