Ferromagnetic Relaxation Caused by Interaction with Thermally Excited Magnons

The contribution of three-magnon processes to the relaxation rate of spin waves is investigated. Relaxation occurs through the confluence of two magnons (with the generation of a third magnon), and through the splitting of a magnon into two magnons. The relaxation rate due to the confluence process is approximately proportional to the wave number, whereas that due to the splitting process is approximately independent of the wave number. The latter contribution vanishes at frequencies higher than $\frac{2}{3}\left(\gamma 4\pi M\right)$ ($\gamma =\mathrm{gyromagnetic}\mathrm{ratio}$, $M=\mathrm{saturation}\mathrm{magnetization}$), and increases with decreasing frequency. The implications of the theory with respect to the observation of spin-wave instability in a rf magnetic field parallel to the dc field are discussed.