Curvilinear Magnetic Shells

In this chapter, we extend the discussion of curvature effects in magnetism towards the description of geometrically curved magnetic thin shells. A self-consistent micromagnetic framework of curvilinear magnetism describes the impact of curvature–induced effects, driven by both local and nonlocal interactions, on the statics and dynamics of magnetic textures in extended curved thin shells. In particular, we focus on the effects in magnetic thin films with in-plane and out-of-plane easy axis of magnetization on spherical, cone-, bump-, and indentation-like objects. The special interest will be addressed to skyrmions in curved magnetic films. Statics of skyrmions as well as their magnetization dynamics will be considered. We provide an overview of relevant experimental methods, which allow fabricating these geometrically curved extended thin films including nanosphere lithography, ion beam induced surface patterning and also chemical synthesis approaches to realize metal and oxide hollow nanostructures with a tunable morphology. We anticipate that the strong theoretical background on the fundamental understanding of the curvature effects in geometrically curved magnetic shells and the availability of the fabrication methods to produce these architectures will stimulate experimental activities targeting the validation of the exciting theoretical predictions including curvature–induced skyrmions, pinning of chiral domain walls on local bends and exploring novel nonlocal chiral symmetry breaking effects.