Dynamics of Topological Magnetic Solitons

Abstract

A direct link between the topological complexity of magnetic media and their dynamics is established through the construction of unambiguous conservation laws for the linear and angular momenta as moments of a topological vorticity. As a consequence, the dynamics of topological magnetic solitons is shown to exhibit the characteristic features of the Hall effect of electrodynamics or the Magnus effect of fluid dynamics. The main points of this program are reviewed here for both ferromagnets and antiferromagnets, while a straightforward extension to the study of superfluids is also discussed briefly.

Mechanics of a ferromagnetic domain wall

“…This article aims to provide a self-contained introduction to theory of ferromagnetic solitons. The subject has been actively researched for more than 50 years and there are a number of excellent reviews and books [1,2]. The last decades have seen new developments in the field such as the use of collective coordinates to describe the dynamics of solitons [3][4][5][6] as well as in technological applications such as soliton-based racetrack memory [7,8] A ferromagnet contains a large number of atomic magnetic dipoles that tend to line up with one another at sufficiently low temperatures.…”

Quantum Statistics of Vortices from a Dual Theory of the XY Ferromagnet

“…Up to this point, our theory of the XY ferromagnet in d = 2 + 1, recast as electrodynamics, has faithfully reproduced what is already known. The electrostatic analogy goes back to 1974 [2]; the dynamical similarity with electric charges in a background magnetic field is also not new [22][23][24]. Does this duality provide any new insights, not obvious from the original theory?…”