Chaos and strange attractors of magnons observed by parallel pumping (invited)

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Abstract
Parallel-pumping experiments in two ferromagnets, YIG and (CH3NH3)2CuCl4 (abbreviated as MACC) have been performed at a pumping frequency of 9 GHz band at liquid-helium temperatures. Above the spin-wave instability threshold, auto-oscillations of magnon number which include period-doubling and period-halving bifurcations, chaos, and periodic windows are observed. From experimental time-series data, return maps, fractal dimensions, positive Lyapunov exponents, phase space portraits of strange attractors, and two-dimensional Poincare sections are obtained. A Lyapunov exponent is one of the quantitative measures of a strange attractor. Lyapunov exponents are obtained by analyzing experimental return maps as 0.34 for YIG and 0.21 for MACC. Phase space trajectories, i.e., strange attractors, are constructed by the conventional time-delay method. The successive Poincare sections of the strange attractors exhibit the stretching and folding effects of sheets of trajectories which confirms the fractal characteristics of the strange attractors. The fractal dimensions of the attractors are obtained by the correlation integral method to be 2.0 for YIG and 2.3 for MACC.