Chaos in Magnetic Crystals

在<CuCl_4>9 GHz抽运频率和氦温下，研究了铁磁&lt;（CH_3NH_3）_2&gt;（MACC）和钇铁石榴石（YIG）的平行抽运实验。在自旋波不稳定性阈值以上，检测到频率为1-100 kHz的磁振子振幅的自振荡。从磁性晶体反射的调幅微波由隧道二极管检测，该二极管提供快速的频率响应，并通过数字存储器和信号分析仪记录在计算机文件中。随着抽运功率的增加，观察到了倍周期、混沌和周期窗口，用时间延迟法从混沌振荡的实验时间序列数据中构造了三维相空间的相图。得到了确定的一维返回映射。相空间轨迹的庞加莱截面呈二维片状，并表现出奇异吸引子的拉伸和保持效应。通过使用经验返回映射，得到MACC和YIG的李雅普诺夫指数分别为0.43和0.34。正的李雅普诺夫指数表示吸引子内附近轨迹的平均指数发散率，它会导致对初始条件的敏感依赖，从而导致混沌行为。随着轨道的演化，奇异吸引子不断地重复拉伸和折叠，形成分形结构。用相关积分法计算了奇异吸引子的分形维数，MACC为2.3，YIG为2.0。研究了混沌的功率谱、Kolmogorov熵和不变测度等混沌特性。

Parallel pumping experiments in ferromagnetic <(CH_3NH_3)_2> <CuCl_4> (MACC) and yttrium-iron-garnet(YIG) are studied at the pumping frequencies of 9 GHz band and the Helium temperatures. Above the spin-wave instability threshold, auto-oscillations of magnon amplitude with a frequency of 1-100 kHz are detected. Amplitude modulated microwave reflected from magnetic crystals is detected by a tunnel diode which offers fast frequency response and recorded in computer files through a digital memory and a signal analyzer. As the pumping power is increased, period-doubling, chaos and periodic windows are observed.Phase portraits in three-dimensional phase space are constructed from experimental time series data of chaotic oscillations by means of time delay method. Definite one-dimensional return maps are obtained. The Poincare sections of the phase space trajectories are two-dimensional sheet-like and exhibit the stretching and holding effect which are characteristics of a strange attractor. By using empirical return maps Lyapunov exponents are obtained as 0.43 for MACC and 0.34 for YIG. A positive Lyapunov exponent indicates the average rate of exponential divergence of nearby trajectories within the attractor and it causes sensitive dependence on initial conditions and therefore chaotic behavior. Infinitely repeated stretching and folding with the evolution of trajectories causes a fractal structure to the strange attractor. Fractal dimension of strange attractors are calculated by the method of correlation integral as 2.3 for MACC and 2.0 for YIG. Other chaotic characteristics such as power spectra, Kolmogorov entropy and invariant measure are also studied.