Influence of randomness and retardation on the FMR-linewidth

The theory predicts that the spin-wave lifetime $\tau_L$ and the linewidth of ferromagnetic resonance $\Delta B$ can be governed by random fields and spatial memory. To that aim the effective field around which the magnetic moments perform a precession is superimposed by a stochastic time dependent magnetic field with finite correlation time. The magnetization dynamics is altered by inclusion of a spatial memory effect monitoring a non-local interaction of size $\xi$. The underlying Landau-Lifshitz-Gilbert equation (LLG) is modified accordingly. The stochastic LLG is equivalent to a Fokker-Planck equation which enables to calculate the mean values of the magnetization vector. Within the spin-wave approximation we present an analytical solution for the excitation energy and its damping. The lifetime and the linewidth are analyzed depending on the strength of the random field $D$ and its correlation time $\tau_c$ as well as the retardation strength $\Gamma_0$ and the size $\xi$. Whereas $\tau_L$ decreases with increasing $D$, retardation strength $\Gamma_0$ and $\tau_c$, the lifetime is enhanced for growing width $\xi$ of the spatial retardation kernel. In the same manner we calculate the experimentally measurable linewidth $\Delta B$ is increased strongly when the correlation time $\tau_c$ ranges in the nanosecond interval.