Chaos and Multi-Fractal in Nonlinear Spin Dynamics

参数激励下的自旋波系统是研究非线性非平衡自旋动力学系统的一个很好的例子。当微波功率远高于Suhl不稳定性阈值时，系统变得不稳定，自旋波个数随时间变化。观察到了规则和不规则的自振现象，即倍周期分叉、准周期混沌和间歇性混沌。由于微观量子理论很好地理解了磁学，所以它是混沌理论研究的一个很好的例子。研究了分维、返回映射、Lyapunov指数、奇异吸引子和f(α)谱随磁场和驱动微波功率的变化。表征混沌奇异吸引子多重分形结构的F(α)谱，在混沌开始时(临界区)观察到，与倍周期通向混沌的理论普适谱非常吻合。在混沌区观察到的光谱与在临界区观察到的光谱不同，在交叉区同时观察到临界区和混沌区的光谱。微观模型哈密顿量的数值模拟给出了类似的f(α)谱的分叉现象，通过环面观察到了从准周期到混沌的转变和锁相。用庞加莱映射和层流周期长度分布研究了在自振开始上方观察到的间歇性混沌。在调制泵浦下观察到Arnold舌态和锁频状态，从理论和实验上研究了参激自旋波的非线性辐射衰减。

A spin-wave system under parametric excitation provides a good example of nonlinear and nonequilibrium spin dynamics system. Spin-wave pairs grow far above the thermal levels under parametric excitation ehich is performed by parallel and perpendicular pumping When microwave power is increased well above the threshold of Suhl instability, the system becomes unstable and the number of spin-wave varies with time. Many types of regular and irregular auto-oscillations are observed, that is, period-doubling bifurcation, qeasi-periodic and intermittency chaos. Since magnetism is well understood by microsscopic quantum theory, it is one of excellent examples of theoretical research of chaos.Fractal dimensions, return maps, Lyapunov exponents, strange attractor and f(alpha) spectra are studied as a function of magnetic field and driving microwave power. f(alpha) spectra, which characterize the multi-fractal structure of chaotic strange attractor, observed at the onset of chaos (critical regime)are in excellent agreement with the theoretical universal spectra of period-doubling route to chaos. The spectra observed in chaotic regime is different from one in critical regime and both spectra of critical and chaotic regimes are observed in the crossover region. Numerical simulation by microscopic model Hamiltonian gives similar bifurcation phenomena of f(alpha) spectra.Transition from quasiperiodicity to chaos through a torus and phase locking is observed. Intermittency chaos observed just above the onset of auto-oscillations was studied by Poincare maps and distribution of laminar period lengths. Arnold's tongue and frequency-locked state are observed under modulated pumping field Nonlinear radiation damping of parametrically excited spin-waves are theoretically and experimentally studied.