Chiral Skyrmion and Skyrmionium States Engineered by the Gradient of Curvature

Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose an alternative mechanism to stabilize chiral Neel skyrmion states relying on the gradient of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers +/- 1 and a skyrmionium state with a winding number 0. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii-Moriya interaction. The latter emerges due to the gradient of the local curvature at the bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables us to reduce the magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii-Moriya interaction.