Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert (LLG) equation, the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H k. The evolution of three-component magnetization is solved analytically under the condition of H = nH k (n = 3, 1 and 0). It is found that with an increase of H or a decrease of the initial polar angle of magnetization, the relaxation time decreases and the angular frequency of magnetization increases. For comparison, the analytical solution for H k = 0 is also given. When the magnetization becomes stable, the angular frequency is proportional to the total effective field acting on the magnetization. The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization, but also can be used as a standard model to test the numerical calculation of LLG equation.