Dynamics of skyrmions in ferromagnets and antiferromagnets
Stavros Komineas (Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece)

We study ferromagnets with a Dzyaloshinskii-Moriya interaction and easy-axis anisotropy. Our analysis is based on an important link between topology and dynamics which is established through the construction of unambiguous conservation laws. In particular, we study the motion of a topological skyrmion with skyrmion number Q=1 and a non-topological skyrmionium with Q=0 under the influence of an applied field gradient (which plays the role of a force). The Q=1 skyrmion undergoes Hall motion perpendicular to the direction of the field gradient with a drift velocity proportional to it. In contrast, the non-topological Q=0 skyrmionium is accelerated in the direction of the field gradient, thus exhibiting ordinary Newtonian motion.

We derive a sigma-model for the micromagnetic structure in antiferromagnets. This is Lorentz invariant showing that the dynamics of solitons is radically different than that in ferromagnets. However, when an homogeneous external field is applied a link between topology and dynamics, similar but not identical to ferromagnets, is again established.