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Topologically stable structures include vortices in a wide variety of matter,such as skyrmions in ferro- and antiferromagnets, and hedgehog point defects inliquid crystals and ferromagnets. These are characterized by integer-valuedtopological quantum numbers. In this context, closed surfaces are a prominentsubject of study as they form a link between fundamental mathematical theoremsand real physical systems. Here we perform an analysis on the topology andstability of equilibrium magnetization states for a thin spherical shell witheasy-axis anisotropy in normal directions. Skyrmion solutions are found for arange of parameters. These magnetic skyrmions on a spherical shell have twodistinct differences compared to their planar counterpart: (i) they aretopologically trivial, and (ii) can be stabilized by curvature effects, evenwhen Dzyaloshinskii-Moriya interactions are absent. Due to its specifictopological nature a skyrmion on a spherical shell can be simply induced by auniform external magnetic field.

Topologically stable magnetization states on a spherical shell: curvature stabilized skyrmions