ISSN:
1434-6036
Keywords:
PACS. 05.40.+j Fluctuation phenomena, random processes, and Brownian motion - 75.10.Hk Classical spin models - 75.30.-m Intrinsic properties of magnetically ordered materials
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100510050653
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