The precession and damping of a collinear magnetization displaced from its equilibrium are described by the Landau-Lifshitz-Gilbert equation. For a noncollinear magnetization, it is not known how the damping should be described. We use first-principles scattering theory to investigate the damping in one-dimensional transverse domain walls (DWs) of the important ferromagnetic alloy Ni80Fe20 and interpret the results in terms of phenomenological models. The damping is found to depend not only on the magnetization texture but also on the specific dynamic modes of Bloch and N\'eel DWs. Even in the highly disordered Ni80Fe20 alloy, the damping is found to be remarkably nonlocal.
@article{arxiv.1404.1488,
title = {Gilbert damping in noncollinear ferromagnets},
author = {Zhe Yuan and Kjetil M. D. Hals and Yi Liu and Anton A. Starikov and Arne Brataas and Paul J. Kelly},
journal= {arXiv preprint arXiv:1404.1488},
year = {2015}
}