Subsidiary-absorption spin-wave-instability processes in yttrium iron garnet thin films: Coupled lateral standing modes, critical modes, and the kink effect

Subsidiary-absorption butterfly curves of the spin-wave-instability threshold microwave-field-amplitude versus static field H, for an in-plane magnetized 1.1 mm ×2.0 mm, 7-μm-thick yttrium iron garnet film rectangle at 9.4 GHz, and with the linearly polarized microwave field perpendicular to the static field H and also in-plane, are found to show significant changes when H is changed from along the long edge to along the short edge of the rectangle. This effect is explained by a theory for the first-order spin-wave-instability threshold in magnetic films, which takes into acocunt the coupled standing spin-wave modes across the lateral dimensions of the film. This theory is a modification of a previous theory, which considered the standing modes across the film cross section only. The theory is able to reproduce the orientation effect found experimentally and give good fits to the butterfly-curve data. In contrast with previous results, it is not necessary to introduce ad hoc spin-wave angle ${\mathrm{\theta }}_{\mathit{K}}$ terms into the spin-wave linewidth to obtain these fits. The theory also yields critical-mode wave numbers in the kink region which are in the 5×${10}^4$ ${\mathrm{cm}}^{\mathrm{-}1}$ range, which agree with previous fine-structure and Brillouin light-scattering measurements. A key parameter in the analysis is a mode spacing parameter Δ${\mathrm{\omega }}_{\mathit{K}}$, which contains a factor of the form sin(2${\mathrm{\theta }}_{\mathit{K}}$)/K, where K is the mode wave number and ${\mathrm{\theta }}_{\mathit{K}}$ is the mode in-plane angle relative to H. These dependences are the key to the match with experiment. They are also general, and not limited to the thin-film geometry.