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

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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 ρ/dt ≠ 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.