Parametric spin-wave excitation in a fine-grained polycrystalline garnet

A study has been made of the effects of the inherent losses $\Delta H_{k_{in}}$ in the anisotropy field and of the pumping frequency on the dependence of the spin-wave excitation threshold on the grain size $l$ for substituted yttrium-aluminum garnets. It is shown that the minimum threshold is proportional to $\sqrt{\Delta H_{k_{in}}^2+(A/l)^2}$ where A is the parameter dependent on the material and pumping frequency. The effects of the grain size on the threshold increase as the pumping frequency decreases. As the anisotropy field decreases, one finds an appreciable effect of the grain size on the threshold only for $l\le 2$ $\mu$m.