Parametric excitation of Walker modes in ferromagnetic spheres

In numerous previous studies the parametric instabilities generally known as the subsidiary absorption and the parallel pumped instability have been studied using spin plane waves and neglecting boundary conditions. In this study the parametric coupling to the true spherical modes is explored. It is found that certain pairs of these modes may become excited when the pumping exceeds the Suhl threshold. Selection rules for these mode pairs are obtained. Numerical results are obtained for the coupling coefficients and compared with spin-wave results. Certain deviations from the spin-wave theory are found to persist even for high-order modes. Analysis is also carried out for ``retrograde pumping,'' a variation of perpendicular pumping which does not appear to have been previously studied.