General Form of Magnetization Damping: Magnetization dynamics of a spin system evolving nonadiabatically and out of equilibrium

TL;DR

This paper develops a quantum theory for magnetization dynamics out of equilibrium, deriving a general damping equation that extends the Landau-Lifshitz-Gilbert model to non-adiabatic conditions using the Lewis-Riesenfeld invariant method.

Contribution

It introduces a new dynamical equation for magnetization that includes non-equilibrium effects and generalizes existing damping models for quantum spin systems.

Findings

Damping term reduces to Gilbert form for radiation-spin interaction.

Results depend on correlation functions in spin-spin exchange interaction.

Provides a framework for non-adiabatic magnetization dynamics analysis.

Abstract

Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical invariant method is employed along with the Liouville-von Neumann equation for the density matrix. We derive a dynamical equation for magnetization defined with respect to the density operator with a general form of magnetization damping that involves the non-equilibrium contribution in addition to the Landau-Lifshitz-Gilbert equation. Two special cases of the radiation-spin interaction and the spin-spin exchange interaction are considered. For the radiation-spin interaction, the damping term is shown to be of the Gilbert type, while in the spin-spin exchange interaction case the results depend on a coupled chain of correlation functions.