Magnetic vortex-like excitations on a sphere

TL;DR

This paper investigates magnetic vortex-like excitations on spherical and curved surfaces, revealing unique core structures, interactions with surface geometry, and potential pinning effects, advancing understanding of magnetic phenomena on curved geometries.

Contribution

It introduces vortex solutions on spherical surfaces with two cores and analyzes their interactions with various curved geometries, a novel exploration of magnetic excitations on non-flat surfaces.

Findings

Vortices on a sphere have two cores with same charge, resulting in zero net vorticity.

Vortex behavior is influenced by surface geometry, being attracted or repelled by features like cones or hemispheres.

Spherical harmonics solutions provide insight into coreless magnetic configurations.

Abstract

We study magnetic vortex-like solutions lying on the spherical surface. The simplest cylindrically symmetric vortex presents two cores (instead of one, like in open surfaces) with same charge, so repealing each other. However, the net vorticity is computed to vanish in accordance with Gauss theorem. We also address the problem of a flat plane in which a conical, a pseudospherical and a hemispherical segments were incorporated. In this case, if we allow the vortex to move without appreciable deformation in this support, then it is attracted by the conical apex and by the pseudosphere as well, while it is repealed by the hemisphere. This suggests that such surfaces could be viewed as pinning and depinning geometries for those excitations. Spherical harmonics coreless solutions are discussed within some details.