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We analyze the Landau-Lifshitz-Gilbert equation when the precession motion ofthe magnetic moments is additionally subjected to an uniaxial anisotropy and isdriven by a multiplicative coupled stochastic field with a finite correlationtime $\tau$. The mean value for the spin wave components offers that thespin-wave dispersion relation and its damping is strongly influenced by thedeterministic Gilbert damping parameter $\alpha$, the strength of thestochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlationfunction can be calculated in the low correlation time limit by deriving anevolution equation for the joint probability function. The stability analysisenables us to find the phase diagram within the $\alpha-D$ plane for differentvalues of $\tau$ where damped spin wave solutions are stable. Even for zerodeterministic Gilbert damping the magnons offer a finite lifetime. We detect aparameter range where the deterministic and the stochastic damping mechanismare able to compensate each other leading to undamped spin-waves. The onset ischaracterized by a critical value of the correlation time. An enhancement of$\tau$ leads to an increase of the oscillations of the correlation function.

Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation