Correlation effects in the stochastic Landau-Lifshitz-Gilbert equation

We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of the magnetic moments is additionally subjected to an uniaxial anisotropy and is driven by a multiplicative coupled stochastic field with a finite correlation time tau. The mean value for the spin-wave components offers that the spin-wave dispersion relation and its damping is strongly influenced by the deterministic Gilbert damping parameter alpha, the strength of the stochastic forces D and its temporal range tau. The spin-spin-correlation function can be calculated in the low-correlation time limit by deriving an evolution equation for the joint probability function. The stability analysis enables us to find the phase diagram within the alpha-D plane for different values of tau where damped spin-wave solutions are stable. Even for zero deterministic Gilbert damping the magnons offer a finite lifetime. We detect a parameter range where the deterministic and the stochastic damping mechanism are able to compensate each other leading to undamped spin waves. The onset is characterized by a critical value of the correlation time. An enhancement of tau leads to an increase in the oscillations of the correlation function.