Chaos in Spin-Wave Instabilities

Parametric excitation of spin-waves with high microwave power causes spin-wave instability where number of spin-waves grows exponentially with time beyond thermal level. Above the spin-wave instability threshold, auto-oscillations of magnon number which include cascade of period-doubling bifurcations, chaos, periodic window and period-halving have been experimentally observed. From experimental time-series data, return maps, fractal dimensions, positive Lyapunov exponents, phase space portraits of strange attractors and two-dimensional Poincaré sections are obtained. A theoretical model of chaos due to nonlinear four-magnon interaction under parallel pumping is given. Numerical solutions display a rich variety of periodic and chaotic trajectories. A multi-fractal structure, singularity spectrum f(α), is numerically studied for two modes model which includes a microwave cavity mode.