Solitary wave excitations of skyrmion strings in chiral magnets

Chiral magnets possess topological line excitations where the magnetization within each cross section forms a skyrmion texture. We study analytically and numerically the low-energy, nonlinear dynamics of such a skyrmion string in a field-polarized cubic chiral magnet, and we demonstrate that it supports solitary waves. These waves are in general nonreciprocal, i.e., their properties depend on the sign of their velocity v , but this nonreciprocity diminishes with decreasing | v | . An effective field-theoretical description of the solitary waves is derived that is valid in the limit v → 0 and gives access to their profiles and their existence regime. Our analytical results are quantitatively confirmed with micromagnetic simulations for parameters appropriate for the chiral magnet FeGe. Similarities with solitary waves found in vortex filaments of fluids are pointed out.