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

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