Stabilization of half-skyrmions: Heisenberg spins on a non-simply connected manifold

Abstract

We show that the metastable skyrmion on a plane can be stabilized by removing a disk of radius ${\ensuremath{\rho}}_{0}$ at the origin. This renders the plane non-simply connected but provides a characteristic length for stabilizing the half-skyrmion which is centered at a radius ${\ensuremath{\rho}}_{0}(1+\sqrt{2}).$ We obtain exact solutions for the half-skyrmion and half-skyrmion lattice and demonstrate that these solutions are a limiting case of Heisenberg spins on (i) a truncated cone with half-angle $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}\ensuremath{\pi}/2$ and (ii) an annulus. We also discuss skyrmions in the presence of a perpendicular external magnetic field which may have relevance for polarized electrons, especially in the quantum Hall effect and quantum antidots.