Langevin-dynamics study of the dynamical properties of small magnetic particles

The stochastic Landau-Lifshitz-Gilbert equation of motion for a classical m agnetic moment is numerically solved (properly observing the customary inte rpretation of it as a Stratonovich stochastic differential equation), in or der to study the dynamics of magnetic nanoparticles. The corresponding Lang evin-dynamics approach allows for the study of the fluctuating trajectories of individual magnetic moments, where we have encountered remarkable pheno mena in the overbarrier rotation process, such as crossing-back or multiple crossing of the potential barrier, rooted in the gyromagnetic nature of th e system. Concerning averaged quantities, we study the linear dynamic respo nse of the archetypal ensemble of noninteracting classical magnetic moments with axially symmetric magnetic anisotropy. The results are compared with different analytical expressions used to model the relaxation of nanopartic le ensembles, assessing their accuracy. It has been found that, among a num ber of heuristic expressions for the linear dynamic susceptibility, only th e simple formula proposed by Shliomis and Stepanov matches the coarse featu res of the susceptibility reasonably. By comparing the numerical results wi th the asymptotic formula of Storonkin {Sov. Phys. Crystallogr. 30, 489 (19 85) [Kristallografiya 30, 841 (1985)]}, the effects of the intra-potential- well relaxation modes on the low-temperature longitudinal dynamic response have been assessed, showing their relatively small reflection in the suscep tibility curves but their dramatic influence on the phase shifts. Compariso n of the numerical results with the exact zero-damping expression for the t ransverse susceptibility by Garanin, Ishchenko, and Panina {Theor. Math. Ph ys. (USSR) 82, 169 (1990) [Teor. Mat. Fit. 82, 242 (1990)]}, reveals a siza ble contribution of the spread of the precession frequencies of the magneti c moment in the anisotropy field to the dynamic response at intermediate-to -high temperatures. [S0163-1829 (98)00446-9].