Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation

TL;DR

This study investigates the real-time dynamics and relaxation mechanisms of a classical spin coupled to conduction electrons in one dimension, revealing limitations of the Landau-Lifschitz-Gilbert equation and the breakdown of weak-coupling theory.

Contribution

It provides a detailed numerical analysis of spin relaxation beyond the LLG equation, highlighting retardation effects, energy conservation, and the inapplicability of Gilbert damping in 1D systems.

Findings

Retardation effects cause spin relaxation through dispersive wave emission.

Weak J regime is well described by LLG, but full dynamics differ quantitatively.

Gilbert damping concept is ill-defined in one-dimensional systems.

Abstract

The real-time dynamics of a classical spin in an external magnetic field and locally exchange coupled to an extended one-dimensional system of non-interacting conduction electrons is studied numerically. Retardation effects in the coupled electron-spin dynamics are shown to be the source for the relaxation of the spin in the magnetic field. Total energy and spin is conserved in the non-adiabatic process. Approaching the new local ground state is therefore accompanied by the emission of dispersive wave packets of excitations carrying energy and spin and propagating through the lattice with Fermi velocity. While the spin dynamics in the regime of strong exchange coupling J is rather complex and governed by an emergent new time scale, the motion of the spin for weak J is regular and qualitatively well described by the Landau-Lifschitz-Gilbert (LLG) equation. Quantitatively, however, the full quantum-classical hybrid dynamics differs from the LLG approach. This is understood as a breakdown of weak-coupling perturbation theory in J in the course of time. Furthermore, it is shown that the concept of the Gilbert damping parameter is ill-defined for the case of a one-dimensional system.