Observation of period doubling and chaos in spin-wave instabilities in yttrium iron garnet

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 \ensuremath{\approx}16 kHz corresponds to the lowest spherical dimensional resonance of a packet of spin waves of small wave vector and long lifetime (\ensuremath{\approx} ${10}^{3}$ 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.