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

Abstract

The dynamical equation for magnetization has been reconsidered by 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 nonequilibrium thermodynamics theory. A typical relaxation time $\ensuremath{\tau}$ is introduced describing the relaxation of the magnetization acceleration from the inertial regime toward the precession regime defined by a constant Larmor frequency. For time scales larger than $\ensuremath{\tau}$, the usual Gilbert equation is recovered. For time scales below $\ensuremath{\tau}$, nutation and related inertial effects are predicted. The inertial regime offers new opportunities for the implementation of ultrafast magnetization switching in magnetic devices.