Dancing Skyrmions: collective coordinate dynamics of magnetic skyrmions

Chiral magnets exhibit 2-dimensional localised topological soliton excitations coined magnetic skyrmions that are used in spintronic devices.

In this talk, I will focus on their rather unintuitive first order dynamics given by the Landau–Lifshitz–Gilbert equation. I will reframe known and unknown results about breathing solutions of excited skyrmions in a more geometric way, using a finite number of collective coordinates. I will show the correct even dimensional sub-space has a complex structure that links conjugate pairs of excitations. Dynamics is then approximated as a metriplectic flow (combination of gradient and symplectic flow) on this sub-space.

Finally, I will then use this approach to consider their more complicated current driven dynamics. In particular, we can show that the conjugate pairs that couple to the current depend intrinsically on the skyrmions symmetry and topology. This is based on ongoing work in collaboration with Bernd Schroers at the University of Edinburgh.