Abstract

Curved thin films are currently of great interest due to their capability to support spontaneous skyrmion solutions, i.e., chiral spin textures observable in a stable state even when no spin-orbit coupling mechanism, in the guise of Dzyaloshinskii-Moriya interaction (DMI), is considered. The evidence of these states sheds light on the role of the geometry in magnetism: chiral spin-textures can be stabilized by curvature effects only, in contrast to the planar case for which the DMI is required. In addition to fundamental reasons, the interest in these geometries is triggered by recent advances in the fabrication of magnetic spherical hollow nanoparticles, which lead to artificial materials with unexpected characteristics and numerous applications ranging from logic devices to biomedicine.
In this talk, after a brief overview of the existing literature on the micromagnetics of curved thin films, we will focus on the investigation of magnetic skyrmions in spherical thin films. The question will lead to a sharp Poincaré-type inequality that allows for a precise characterization of the global minimizers of the micromagnetic energy functional on the 2-sphere.