Analytical description of magnetization relaxation to equilibrium

Approximate analytical expressions are obtained for the magnetization relaxation to equilibrium in a thin film element with in-plane anisotropy subject to a constant external field applied along the easy axis. First, exact analytical solutions are obtained for the constant-energy motions taking place in the limit case where the damping constant is zero. Then a separate equation is derived and solved for the slow relaxation to equilibrium of the system energy. Final expressions for the magnetization relaxation are obtained by using the ensuing time-dependent energy in the solutions for the undamped dynamics.