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

We show that the metastable skyrmion on a plane can be stabilized by removing a disk of radius ρ0 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 ρ0(1+√(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 α→π/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