Spin-wave dynamics in a ferrimagnetic sphere

An experimental study is made of the interactions between spin-wave modes excited in a sphere of yttrium iron garnet by pumping the Suhl subsidiary absorption at 9.2 GHz with the dc field parallel to [111]. The dynamical behavior of the magnetization is observed under high resolution by varying two control parameters, dc field (580 Oe<H<2100 Oe) and microwave pump power (1 mW<P<200 mW). Within this parameter space quite varied behavior is found: (i) onset of the Suhl instability by excitation of a single spin-wave mode with very narrow linewidth (<0.5 G); (ii) when two or more modes are excited, interactions lead to auto-oscillations with a systematic dependence of frequency (${10}^4$–${10}^6$ Hz) on pump power these oscillations displaying period doubling to chaos; (iii) quasiperiodicity, locking, and chaos occur when three or more modes are excited; (iv) abrupt transition to wide-band power spectra (i.e., turbulence), with hysteresis; (v) irregular relaxation oscillations and aperiodic spiking behavior. A theoretical model is developed from first principles, using the plane-wave approximation and including anisotropy effects, obtaining the lowest-order nonlinear interaction terms between the excited modes. Bifurcation behavior is examined, and dynamical behavior is numerically computed and compared to the experimental data, explaining a number of features. A theory is developed regarding the nature of the experimentally observed relaxation oscillations and spiking behavior based on the interaction of ‘‘weak’’ and ‘‘strong’’ modes, and this is demonstrated in the numerical simulations.