Skyrmions on a sphere shell

Skyrmions, as small electronic spin-structures, provide a window into strongly interacting many electron systems. The existence of these spin-textures has been studied in quantum Hall (QH) ferromagnets, in which the kinetic energy of the electrons is quenched by the strong external magnetic field. The large angular momentum (l) single particle states on the surface of a sphere are similarly degenerate in energy as a function of their z component (m) for fixed (l). This makes electrons on a sphere an interesting system for studying spin textures. Using Hartree-Fock theory, we initially force a skyrmionic texture on the system by applying a small “scaffolding” field that couples to the spins to produce a texture and investigate the stability of the spin-structure as the field goes to zero. We study the dependence of the skyrmion stability on the number of electrons, the choice of interactive potential, and material parameters.