Stochastic Magnetization Dynamics Driven by a Jump-Noise Process

Abstract

An approach to modeling thermal noise effects in stochastic magnetization dynamics using a jump-noise process is presented. The damping term present in classical Landau-Lifshitz and Landau-Lifshitz-Gilbert equations is shown to result from the average of the jump-noise process in the presented stochastic Landau-Lifshitz equation approach. A numerical technique for solving the Landau-Lifshitz equation driven by a jump-noise process based on the Monte Carlo method is introduced and the results obtained from this method are shown. The drawback of using the Monte Carlo approach is discussed as well as the introduction of an averaging method to model stochastic magnetization dynamics on energy graphs. This averaging technique takes advantage of the difference in time-scale between the precessional motion and thermal effects in the stochastic Landau-Lifshitz model. By averaging over precessional trajectories, a stochastic magnetization dynamics equation on graphs is obtained. This averaging technique is demonstrated to be consistent with Monte Carlo results through numerical simulations. Application of the averaging technique to self-oscillations in magnetization dynamics due to the spin-transfer torque phenomenon is investigated and numerical results are presented. Finally, the power spectral density for magnetization dynamics on energy graphs is calculated. Numerical results for the power spectral density are studied and analyzed.