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Ferromagnetic resonance in a polished 0. 047-cm-radius sphere of gallium-doped yttrium iron garnet is studied at 1. 3 GHz in a magnetic field of 460 G. A second-order Suhl instability is observed, owing to the nonlinear coupling of the precessing uniform magnetization with spin waves. This is detected by the onset of auto-oscillations of the magnetization. One of these modes with frequency 16 kHz corresponds to the lowest spherical dimensional resonance of a packet of spin waves of small wave vector and long lifetime (10^3 cycles). From real-time signals, spectral analysis, and return maps this mode is found to display chaotic dynamics as the driving rf field is increased: thresholds for the onset of period-doubling bifurcations, chaos, and periodic windows. Some observed return maps bear resemblance to the two-dimensional area-preserving quadratic map of H\'enon. The system has several attractors and displays "solid-state turbulence, " analogous to that in fluids.
Gibson et al. (1984) studied this question.