Effective anisotropy of thin nanomagnets: beyond the surface anisotropy approach

We study the effective anisotropy induced in thin nanomagnets by the nonlocal demagnetization field (dipole-dipole interaction). Assuming a magnetization independent of the thickness coordinate, we reduce the energy to an inhomogeneneous onsite anisotropy. Vortex solutions exist and are ground states for this model. We illustrate our approach for a disk and a square geometry. In particular, we obtain good agreement between spin-lattice simulations with this effective anisotropy and micromagnetic simulations.