Magnon Theory of Domain Wall Wavefronts and the Ballistic Diffusive Crossover in the Classical Anisotropic Landau Lifshitz Spin Chain
Abstract
We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau--Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic t1/3 broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at Δc=1/7, corresponding to γc≃ 1.047. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.
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BibTeX
@misc{sarkar2026magnon,
title = {{Magnon Theory of Domain Wall Wavefronts and the Ballistic Diffusive Crossover in the Classical Anisotropic Landau Lifshitz Spin Chain}},
author = {Akash Sarkar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13474},
eprint = {2609.13474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13474},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magnon Theory of Domain Wall Wavefronts and the Ballistic Diffusive Crossover in the Classical Anisotropic Landau Lifshitz Spin Chain
AU - Akash Sarkar
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.13474
UR - https://arxiv.org/abs/2609.13474
AB - We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau--Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic t^1/3 broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at Δ_c=1/7, corresponding to γ_c≃ 1.047. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.
ER -