Nonequilibrium Extension of the Landau-Lifshitz-Gilbert Equation for Magnetic Systems

TL;DR

This paper extends the Landau-Lifshitz-Gilbert equation to non-equilibrium quantum magnetic systems using the invariant operator method, capturing nonadiabatic dynamics and radiation-spin interactions.

Contribution

It introduces a quantum theoretical framework for magnetization dynamics out of equilibrium, incorporating radiation-spin interactions via the invariant operator method.

Findings

The magnetization still obeys the Landau-Lifshitz-Gilbert equation out of equilibrium.

The invariant operator parameter and magnetization satisfy the quantum Liouville equation.

The approach models nonadiabatic and radiation effects in quantum spin systems.

Abstract

Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of the invariant operator and the magnetization defined with respect to the density operator, both satisfying the quantum Liouville equation, still obey the Landau-Lifshitz-Gilbert equation.