Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission

The non-equilibrium dynamics of domain wall initial states in a classical anisotropic Heisenberg chain exhibits a striking coexistence of apparently linear and non-linear behaviours: the propagation and spreading of the domain wall can be captured quantitatively by \textit{linear}, i.e. non-interacting, spin wave theory absent its usual justifications; while, simultaneously, for a wide range of easy-plane anisotropies, emission can take place of stable topological solitons -- a process and objects intrinsically associated with interactions and non-linearities. The easy-axis domain wall only has transient dynamics, the isotropic one broadens diffusively, while the easy-plane one yields a pair of ballistically counter-propagating domain walls which, unusually, broaden \textit{subdiffusively}, their width scaling as $t^{1/3}$.