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

TL;DR

This paper investigates the complex non-equilibrium behavior of domain walls in classical spin chains, revealing coexistence of linear wave propagation and non-linear soliton emission, with diverse spreading dynamics depending on anisotropy.

Contribution

It uncovers the simultaneous presence of linear spin wave behavior and non-linear soliton emission in classical spin chains, highlighting novel subdiffusive broadening of domain walls.

Findings

Easy-axis domain walls exhibit transient dynamics.

Isotropic domain walls broaden diffusively.

Easy-plane domain walls broaden subdiffusively with width scaling as t^{1/3}.

Abstract

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 $t^{1/3}$.