Influence of the magnetic dipole interaction on the properties of magnetic vortices in particles of small size

Abstract

Two type of plaquette systems are proposed for modeling a vortex in an easy-plane two-dimensional Heisenberg ferromagnet with the dipole–dipole interaction of the magnetic moments of the lattice taken into account. The first plaquette describes a system with the boundary spins fixed in the easy plane perpendicular to the “surface” of the magnet, while in the second plaquette the boundary spins are fixed parallel to the “surface.” The properties of static vortex ordering of the magnetization and the transformation of the spectra of eigenmodes of the plaquettes upon a change in the parameters of the easy-plane exchange anisotropy and dipole–dipole interaction are investigated. It is shown that the region of stability of the various vortex solutions on the plane of the anisotropy and dipole–dipole interaction parameters is substantially different for these two plaquettes. The differences between the results obtained for the dynamics and structure of the vortex solutions with the dipole interaction taken into account and those obtained in a treatment including only the exchange interaction are analyzed.