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 a surface anisotropy. The effects of lattice pinning leads to appearance of a set of metastable configurations. 
V. E. Kireev, B. A. Ivanov