Vortex rings in ferromagnets

TL;DR

This paper presents vortex ring solutions in three-dimensional ferromagnets modeled by the Landau-Lifshitz equation, analyzing their stability and the effects of anisotropy, with implications for both condensed matter and cosmology.

Contribution

It introduces vortex ring solutions in ferromagnets, studies their stability properties, and explores the impact of anisotropy, connecting condensed matter phenomena with cosmological vortex analogs.

Findings

Vortex rings propagate at constant speed along their axis.

Axial perturbations do not destabilize vortex rings.

Easy axis anisotropy causes instability leading to collapse.

Abstract

Vortex ring solutions are presented for the Landau-Lifshitz equation, which models the dynamics of a three-dimensional ferromagnet. The vortex rings propagate at constant speed along their symmetry axis and are characterized by the integer-valued Hopf charge. They are stable to axial perturbations, but it is demonstrated that an easy axis anisotropy results in an instability to perturbations which break the axial symmetry. The unstable mode corresponds to a migration of spin flips around the vortex ring that leads to a pinching instability and ultimately the collapse of the vortex ring. It is found that this instability does not exist for an isotropic ferromagnet. Similarities between vortex rings in ferromagnets and vortons in cosmology are noted.