Magnetization dynamics in the inertial regime: nutation predicted at short time scales

Abstract: The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized Landau-Lifshitz-Gilbert equation that includes inertial terms, and the corresponding Fokker-Planck equation, are then derived in the framework of mesoscopic non-equilibrium thermodynamics theory. A typical relaxation time $\tau$ is introduced describing the relaxation of the magnetization acceleration from the inertial regime towards the precession regime defined by a constant Larmor frequency. For time scales larger than $\tau$, the usual Gilbert equation is recovered. For time scales below $\tau$, nutation and related inertial effects are predicted. The inertial regime offers new opportunities for the implementation of ultrafast magnetization switching in magnetic devices.