Effective Linewidth due to Porosity and Anisotropy in Polycrystalline Yittrium Iron Garnet and Ca-V-Substituted Yittrium Iron Garnet at 10 GHz

The field dependence of the uniform-precession relaxation rate or an effective linewidth $\Delta H_{\mathrm{eff}}$ can provide detailed information concerning the relaxation in polycrystals. Determinations of $\Delta H_{\mathrm{eff}}$ versus static field $H_0$ have been made as a function of porosity in polycrystalline yttrium iron garnet (YIG) and as a function of anisotropy in polycrystalline calcium-vanadium-substituted YIG (YCVF). The experimental results were obtained from microwave susceptibility data taken on spherical samples at room temperature and 10 GHz. Porosity in the YIG ranged from 21 to $\Delta H_{\mathrm{eff}}$ is small, on the order of a few Oe, and field-independent. Near resonance, $\Delta H_{\mathrm{eff}}$ increases sharply and exhibits a peak. The size and symmetry of the peak are functions of porosity and anisotropy. In general, $\Delta H_{\mathrm{eff}}$ peaks at fields above the field $H_{\mathrm{res}}$ for resonance in the porous materials. The magnitude of the peak increases and the curve broadens considerably with increasing porosity. For the YCVF materials, $\Delta H_{\mathrm{eff}}$ peaks below $H_{\mathrm{res}}$ for the low-anisotropy samples, and above for the high-anisotropy samples. The effective linewidth increases and the curves broaden with increasing anisotropy. The experimental results can be explained on the basis of two-magnon scattering from inhomogeneities related to porosity and the anisotropy in randomly oriented crystallites. The increase in $\Delta H_{\mathrm{eff}}$ near resonance is due to coupling of the uniform-precession mode at the driving frequency to degenerate long-wavelength spin waves. Far from resonance, degenerate long-wavelength modes no longer exist, so that $\Delta H_{\mathrm{eff}}$ is small and field-independent. The differences in the symmetry of the $\Delta H_{\mathrm{eff}}$ peak for the different materials can be explained by differences in the coupling to the degenerate modes. The broadening of the peaks with increasing porosity and anisotropy arises from secondary scattering interactions which do not involve the uniform precession. Theoretical curves obtained from calculations which include secondary scattering are in good agreement with the data.