Langevin dynamic simulation of spin waves in a micromagnetic model

A Langevin dynamic (LD) model of thermally excited magnetization fluctuations is applied to the study of a linear chain of coupled spins representing a simple micromagnetic model system. It is shown that thermal activation gives rise to correlated magnetization fluctuations (spin waves) as a result of the collective response of the coupled system to the random thermal perturbations included in the LD approach. Two regimes are defined. In the ferromagnetic resonance regime the thermal perturbations result in small amplitude linear fluctuations that show classical spin-wave behavior, with characteristics of both exchange and magnetostatic modes. In the regime close to magnetization reversal, nonlinear effects result in complex spectra and dispersion relations. However, even in this regime correlated fluctuations exist that have the characteristics of the candidate eigenmodes of magnetization reversal. With the increase of magnetization fluctuation amplitude, the complex interplay of nonlinearities leads to spin-wave instabilities and subsequently chaotic behavior. Finally, at the nucleation itself the chaotic behavior is supressed and the energy is transfered into the main reversal mode. Thus, although thermal effects can be relatively small, their presence in establishing the reversal mode is a central factor in the magnetization reversal process itself.