Curvature induced stabilization of vortices on magnetic spherical sector shells

Finite element micromagnetics are used to simulate the vortex and onion states on permalloy spherical shells with different curvatures. To distinguish between the effects of size and curvature (covaried in the typical semi-spherical or crescent shaped caps) a family of spherical sectors where the volume is varied at constant curvature is considered. This family is parametrized by intersecting cone angle. Permalloy is chosen as a typical case of an easy-surface magnet in which the demagnetization field bounds the magnetization to follow the curvature of the surface. The thickness of the shell is set to 3 nm, i.e. comparable to the exchange length, so that the local magnetization does not vary along the thickness of the shell. It is found that as the curvature increases the vortex states become favorable down to smaller sizes. This is mainly due to the increased exchange energy cost of the onion states at larger curvatures. Furthermore, it is found that at larger curvatures, stronger in-plane fields are required to destabilize the vortex states and turn them into onion states.