``Smoke Rings'' in Ferromagnets

TL;DR

This paper demonstrates that bulk ferromagnets can support stable, propagating magnetic vortex rings with unique topological properties, expanding understanding of non-linear magnetic excitations.

Contribution

It introduces the concept of magnetic vortex rings in ferromagnets, analyzing their properties and topological invariants through analytical and numerical methods.

Findings

Existence of propagating magnetic vortex rings in ferromagnets.

Identification of a sequence of vortex rings distinguished by the Hopf invariant.

Analytical and numerical characterization of energies, velocities, and structures.

Abstract

It is shown that bulk ferromagnets support propagating non-linear modes that are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These are circular loops of {\it magnetic} vorticity which travel at constant velocity parallel to their axis of symmetry. The topological structure of the continuum theory has important consequences for the properties of these magnetic vortex rings. One finds that there exists a sequence of magnetic vortex rings that are distinguished by a topological invariant (the Hopf invariant). We present analytical and numerical results for the energies, velocities and structures of propagating magnetic vortex rings in ferromagnetic materials.