Inhomogeneous states in a small magnetic disk with single-ion surface anisotropy

We investigate analytically and numerically the ground and metastable states for easy-plane Heisenberg magnets with single-ion surface anisotropy and disk geometry. The configurations with two half vortices at the opposite points of the border are shown to be preferable for strong anisotropy. We propose a simple analytical description of the spin configurations for all values of surface anisotropy. The effects of lattice pinning lead to appearance of a set of metastable configurations.