Dancing Skyrmions — First order dynamics of defects in condensed matter

Certain planar ferromagnetic materials exhibit topological defects in the magnetisation field coined Skyrmions, that act like particles of twisted magnetic field. While the simplest (minimal energy) Skyrmion is very symmetric, there are many possible excited states that exhibit a plethora of shapes and symmetries. The dynamics of these objects obey the first order LLG equation which essentially combines gradient and Hamiltonian flow. We will show these two competing terms naturally couple modes into pairs, resulting in excited Skyrmions exhibiting counter-intuitive breather like behaviour, where they fluctuate over extremely long time scales. We will present a simple general model that predicts this behaviour from the symmetry of the Skyrmions. We will then consider applying a current, leading to interesting excitations of these paired modes. Finally, I will emphasis the generality of this approach and how it can be systematically applied to topological solitons in many condensed matter systems such as vorticies in unconventional superconductors.

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