Dynamics of topological magnetic solitons

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.