Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence of spin transport

Oleksandr Gamayun, Yuan Miao, Enej Ilievski

Published 2019-01-25Version 1

We investigate the dynamics of spin in the axially anisotropic Landau--Lifshitz field theory with a magnetic domain wall initial condition. Employing the analytic scattering technique, we obtain the exact scattering data and reconstruct the time-evolved profile. We identify three qualitatively distinct regimes of spin transport, ranging from ballistic expansion in the easy-plane regime, absence of transport in the easy-axis regime and log-modified diffusion for the isotropic interaction. Our results are in perfect qualitative agreement with those found in the anisotropic quantum Heisenberg spin-$1/2$ chain, indicating a remarkable classical-quantum correspondence of macroscopic spin transport.