Butterfly curves and critical modes for second-order spin-wave instability processes in yttrium iron garnet films

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Abstract
Combined Brillouin light-scattering (BLS) and microwave pumping techniques were used to measure the second-order spin-wave instability threshold microwave field amplitudes and characterize the critical modes for ferromagnetic resonance (FMR) saturation in 4.15 μm-thick yttrium iron garnet films at 8.47 GHz with the static magnetic field in-plane. To the best of our knowledge, this work represents the first BLS measurements for second-order FMR saturation processes in ferrite materials. Several new results were obtained: (1) A new type of butterfly curve for second-order processes. (2) Strong scattering from modes at low wave numbers in the 104 rad/cm range. (3) An observed in-plane propagation direction for these low wave number modes at 90° to the in-plane static field direction. These results differ significantly from the behavior expected from the bulk sample instability theories of Suhl and Schlömann, which predict critical modes at wave numbers and propagation directions in the 105–106 rad/cm and 0° ranges, respectively, and a sharp cusplike response centered at FMR. These results indicate that significant modifications of the bulk theory, which take into account the real modes supported by the film, are needed to realistically model second-order instability processes in films.