Pseudo-symplectic numerical schemes for Landau-Lifshitz dynamics

Numerical techniques for the time integration of Landau-Lifshitz magnetization dynamics are considered. In the continuous model, such dynamics implies the conservation of magnetization amplitude and, when dissipation is neglected, even the conservation of free energy, a property which is generally corrupted by the time-discretization method. In this work, two classes of explicit schemes, based on Runge-Kutta and midpoint methods respectively, are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order $p$, but preserve magnetization amplitude and free energy to order $q>p$. Numerical tests are performed on the simulation of fast precessional switching dynamics for which an analytical solution is available.