Dimension reduction for the micromagnetic energy functional on curved thin films

Abstract

Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature e ects only, in contrast to the planar case where the intrinsic Dzyaloshinsky-Moriya interaction is required.The aimof the paper is to performa $\Gamma$-development analysis of the micromagnetic energy functional, when the shell is generated, like in the case of a sphere, by a bounded and convex smooth surface.