Dipolar induced magnetic anisotropy and magnetic topological defects in ultrathin films

A Taylor expansion of the spin field enables us to obtain a local representation of dipole-dipole interactions in the plane. The magnetic anisotropy induced by the lattice symmetry by means of the dipolar interaction is analyzed for a hexagonal lattice. The reduction of the divergence of higher terms of the dipolar Hamiltonian leads to a set of nonlinear equations on the partial derivatives of the spin field. Topological defects are shown to be approximate solutions of these equations and are classified according to their validity and occurrence frequency. Because of dipolar interactions, this result is shown to be general for two-dimensional lattices observed on a large scale.