In curved geometries,a lot of novel curvaturedriven effects are discovered due to the curvature-induced effective anisotropy and Dzyaloshinskii-Moriya interaction.Curvature effect also provides means to modify conventional results and launch new functionalities in study of magnetic skyrmions.Magnetic skyrmions are particle-like spin textures with topological protections.It has been found in several magnetic materials and has been one of the research hotspots in magnetism and spintronics as the carriers of information.BothDzyaloshinskii-Moriya interaction and anisotropy have significant effects on the formation and stability of magnetic skyrmions.The magnetic skyrmions in curved geometries show some novel characteristics,and the study in this field may promote the development of magnetic skyrmions.This article provides a review of the present state of the research on skyrmions in curved geometries including curved nanotracks,thin films with curved defect,nanotubes,spherical and hemispherical shells.The reviewmainly covers three aspects,the formation and stability of skyrmions,the shape and size of skyrmions,and the dynamical behaviors of skyrmions in curved geometries.
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