Radiation-spin interaction, Gilbert damping, and spin torque.

Magnetization relaxation processes, which are represented by the Gilbert damping term and the spin torque term in the Landau-Lifshitz-Gilbert (LLG) equation, are described by the radiation-spin interaction (RSI), where the radiation field is produced by magnetization precessional motion itself. It is shown that the LLG equation including the Gilbert damping term and the spin torque term is derived from the spin Hamiltonian containing the RSI. The derivation of the LLG equation is given in a self-consistent method. It is also shown that, according to RSI, the magnitude of the magnetization vector deviates from the magnetization saturation with the order of O(alpha(2)), where alpha is the Gilbert damping parameter.