Quantum Landau Lifshitz Gilbert equation in ferromagnetic conductors and magnetic insulators
Abstract
Understanding the microscopic origin of magnetic damping is essential for describing magnetization dynamics in nanoscale magnetic systems. In this work, we develop a microscopic framework to derive Gilbert damping terms from specific interactions in ferromagnetic conductors and magnetic insulators. In ferromagnetic conductors, magnetic damping is dominated by the s d exchange interaction between the localized magnetic moments and the itinerant electrons, which is effectively equivalent to an electronmagnon interaction. From the spin diffusion equation and the spin transfer torque therein, we obtain the corresponding quantum LLG equation. In magnetic insulators, where free electrons are absent, spin phonon interactions become the primary source of the damping.Starting from an effective spin phonon interaction and using linear response theory, we derive a quantum LLG equation with a Gilbert damping tensor analytically. Our results demonstrate that different microscopic interactions lead to qualitatively different structures of magnetic damping. Instead of being described by a universal scalar parameter, Gilbert damping can exhibit spatial dependence and tensorial characteristics determined by the underlying microscopic interactions.
Related
- Semi-analytical representation of the Gaunt-modified Landau-Lifshitz equation in a plane wave
- Magnetic Johnson noise from arbitrarily shaped conductors: experimental validation of the fluctuation-dissipation finite-element method
- Extended Landau--Lifshitz equation for nanomagnets: a path-integral derivation of surface-induced magnetization nutation
- Ferromagnetic resonance and magnetic anisotropy in YbMn6Sn6
- Geometrical Confinement of Magnetic Domains and Domain Walls on Two-Dimensional Cylindrical-Shaped Ferromagnetic Surfaces
BibTeX
@misc{zhu2026quantum,
title = {{Quantum Landau Lifshitz Gilbert equation in ferromagnetic conductors and magnetic insulators}},
author = {Ji Yang Zhu and Zheng Chuan Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32405},
eprint = {2610.32405},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32405},
}
RIS
TY - UNPB
TI - Quantum Landau Lifshitz Gilbert equation in ferromagnetic conductors and magnetic insulators
AU - Ji Yang Zhu
AU - Zheng Chuan Wang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32405
UR - https://arxiv.org/abs/2610.32405
AB - Understanding the microscopic origin of magnetic damping is essential for describing magnetization dynamics in nanoscale magnetic systems. In this work, we develop a microscopic framework to derive Gilbert damping terms from specific interactions in ferromagnetic conductors and magnetic insulators. In ferromagnetic conductors, magnetic damping is dominated by the s d exchange interaction between the localized magnetic moments and the itinerant electrons, which is effectively equivalent to an electronmagnon interaction. From the spin diffusion equation and the spin transfer torque therein, we obtain the corresponding quantum LLG equation. In magnetic insulators, where free electrons are absent, spin phonon interactions become the primary source of the damping.Starting from an effective spin phonon interaction and using linear response theory, we derive a quantum LLG equation with a Gilbert damping tensor analytically. Our results demonstrate that different microscopic interactions lead to qualitatively different structures of magnetic damping. Instead of being described by a universal scalar parameter, Gilbert damping can exhibit spatial dependence and tensorial characteristics determined by the underlying microscopic interactions.
ER -