Thin convex shells in Micromagnetics
Giovanni Di Fratta · arXiv (Cornell University) · 2016
Micromagnetic distributions of the vortex and onion type have been widely studied in the context of planar structures. Recently a significant interest to nanomagnets with curved shape has appeared. In particular, spherical shells are currently of great interest due to their capability to support skyrmion solutions which can be stabilized by curvature effects only, in contrast to the planar case where the intrinsic Dzyaloshinsky-Moriya interaction is required. It is well established that the effects of the demagnetizing field operator can be reduced to an effective easy-surface anisotropy for planar thin shells whose thickness is much less than the size of the system. The result has later been extended to surfaces whose closure is diffeomorphic to the closed unit disk of $\mathbb{R}^2$. The aim of the paper is to perform a rigorous $\Gamma$-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.