Gilbert damping calculation based on a second-quantization method*

Gilbert damping is a key parameter representing the energy loss in the Landau-Lifshitz-Gilbert equation, which describes the dynamics of magnetization and is crucial in micromagnetic simulations. We have developed an analytical method to calculate Gilbert damping, based on the Holstein-Primakoff transformation and the contributions from the three-particle magnon scattering process. By considering the contributions from the exchange, anisotropic, and demagnetized energies, we applied this method to calculate Gilbert dampings under different temperatures. Near the Curie temperature, the results are found to be similar with the results obtained from the coarse-graining method proposed by Feng and Visscher in 2001. This research may give useful insights into the relationship between Gilbert damping and magnons.