Spin-wave instability magnon distribution for parallel pumping in yttrium iron garnet films at 9.5 GHz

Parallel-pumping spin-wave instability processes for 2-, 4.15-, and 6-μm-thick yttrium iron garnet films have been studied by microwave and Brillouin light-scattering techniques. The pump frequency was 9.5 GHz. The static and linearly polarized microwave fields were in plane. Butterfly curves of the instability threshold microwave-field amplitude vs the static field H were measured, along with companion determinations of the critical mode in-plane spin-wave polar-angle ${\mathrm{\theta }}_{\mathrm{k}}$ and in-plane wave-number k distributions vs H. The 4.15- and 6-μm-thick films show narrow distributions in the critical-mode ${\mathrm{\theta }}_{\mathrm{k}}$ values and broad distributions in the critical-mode k values which appear at threshold and extend to high power. For the 2-μm film, the critical-mode ${\mathrm{\theta }}_{\mathrm{k}}$ distribution is narrow just at the instability threshold. As the power is increased, the critical-mode ${\mathrm{\theta }}_{\mathrm{k}}$ distribution broadens and develops a bimodal character indicative of a splitting into two critical modes. These distributions also show considerable fine structure. The basic shape of the butterfly curve and the measured ${\mathrm{\theta }}_{\mathrm{k}}$ values for the 4.15- and 6-μm-thick films are in rough agreement with predictions from bulk theory, except that the measured k values are in the ${10}^4$ rad/cm range rather than near zero. These measured k distributions are quite broad and also show significant structure.