We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional classical, ferromagnetic, anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local-field term of the Landau-Lifshitz equations, and Langevin-like additive noise both have the same effect on vortex dynamics ͑within a very plausible assumption consistent with the collective coordinate approach͒. This is a nontrivial result, as multiplicative and additive noises usually modify the dynamics quite differently. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics. ͓S0163-1829͑99͒03917-X͔

Using a discrete model of 2-dimensional easy-plane classical ferromagnets, we propose that a rotating magnetic field in the easy plane can switch a vortex from one polarization to the opposite one if the amplitude exceeds a threshold value, but the backward process does not occur. Such switches are indeed observed in computer simulations.

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.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

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.

In the two-dimensional anisotropic classical Heisenberg model with XY symmetry there are nonplanar vortices which exhibit a localized structure of the z components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory ͑1969͒. The result is compared with Langevin dynamics simulations for the full many-spin model. ͓S0163-1829͑99͒09909-9͔