Stoner contributions to the magnon equation of motion
Abstract
From linear response theory, we derive the equation of motion for Landau-damped magnon quasi-particles in absence of spin-orbit coupling. The derivation is based on a minimal set of assumptions, namely that the transverse magnetic susceptibility is diagonalized by one collective eigenmode per magnetic atom in the unit cell, and that the spectrum of each collective eigenmode is dominated by a single magnon resonance. The resulting equation of motion leads to a natural definition of the exchange interaction as the restoring force acting on the collective mode magnetization near equilibrium. In addition to magnetic exchange, the magnon equation of motion also contains a damping term and a dispersive quasi-particle mass, both originating from the electron-magnon coupling. The effect of these terms is illustrated for a prototypical itinerant ferromagnet, where they redshift the magnon dispersion and reduce the magnon lifetime as the magnon enters the Stoner continuum. By further assuming wave vector independence of the collective magnon subspace, the magnon equation of motion becomes atomistic with well defined magnetic sites. For real materials, one can approximate the magnon coupling constants using an arbitrary level of band theory for the dynamic transverse magnetic susceptibility.
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BibTeX
@misc{skovhus2026stoner,
title = {{Stoner contributions to the magnon equation of motion}},
author = {Thorbjørn Skovhus and Patrik Thunström},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30931},
eprint = {2608.30931},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30931},
}
RIS
TY - UNPB
TI - Stoner contributions to the magnon equation of motion
AU - Thorbjørn Skovhus
AU - Patrik Thunström
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30931
UR - https://arxiv.org/abs/2608.30931
AB - From linear response theory, we derive the equation of motion for Landau-damped magnon quasi-particles in absence of spin-orbit coupling. The derivation is based on a minimal set of assumptions, namely that the transverse magnetic susceptibility is diagonalized by one collective eigenmode per magnetic atom in the unit cell, and that the spectrum of each collective eigenmode is dominated by a single magnon resonance. The resulting equation of motion leads to a natural definition of the exchange interaction as the restoring force acting on the collective mode magnetization near equilibrium. In addition to magnetic exchange, the magnon equation of motion also contains a damping term and a dispersive quasi-particle mass, both originating from the electron-magnon coupling. The effect of these terms is illustrated for a prototypical itinerant ferromagnet, where they redshift the magnon dispersion and reduce the magnon lifetime as the magnon enters the Stoner continuum. By further assuming wave vector independence of the collective magnon subspace, the magnon equation of motion becomes atomistic with well defined magnetic sites. For real materials, one can approximate the magnon coupling constants using an arbitrary level of band theory for the dynamic transverse magnetic susceptibility.
ER -