Analytical solutions of Landau–Lifshitz equation for precessional switching

A rigorous analysis of the precessional switching dynamics in uniformly magnetized particles and films is presented. Magnetization dynamics are described by the Landau–Lifshitz equation and the precessional switching is realized by applying a field pulse orthogonal to the easy axis of the particle or the film. The analysis of the switching process is based on the explicit knowledge of two integrals of motion for the magnetization dynamics and leads to closed form analytical expressions for the magnetization in terms of Jacobi elliptic functions. It is shown that switching can occur only beyond a critical field threshold. The analytical solutions are used to predict the magnetization trajectory and the switching time under external field pulses of different amplitudes and durations.