Energy loss and noise by chaotic motion of magnetic spin

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The energy loss caused by the domain-wall motion is calculated by integrating damping term. The value of the energy loss is discussed in connection with the bifurcation diagram. The energy loss jumps to a high value at the first transition to chaos. The energy loss in the periodic window is larger than the value in the neighboring chaotic region in spite of their having the same damping coefficient.A chaotic region of domain wall motion is calculated as a function of the amplitude and frequency of the external magnetic drive field. It shows an intricate pattern composed of regular and chaotic regions. An energy loss and the Lyapunov exponent of domain wall motion are calculated. A frequency at the peak of the energy loss versus frequency curve, namely a nonlinear resonance frequency, is different from a resonance frequency in the linear theory as it shifts toward a lower frequency with increasing amplitude of the external magnetic drive field. This peak shift is explained by the effect … More of the higher order term in the nonlinear restoring force. The energy loss versus frequency curve becomes irregular and the energy loss decreases in the chaotic region where the Lyapunov exponent is positive.The two-step Ott-Grebogi-Yorke (OGY) method and the prediction OGY method for controlling chaos of magnetic domain-wall motion are proposed to improve the long settling time in the original OGY method. In the two-step OGY method, a magnetic domain wall is first moved on a periodic orbit and the OGY method is used when the orbit approaches a saddle point. In the prediction OGY method, the motion of the domain wall is predicted before the OGY method is applied. An attractor in the state space can be reconstructed by using the time series of the domain-wall motion. The near future can be predicted even in the chaotic system, because the short time developments of the neighborhood system of a predictee in the attractor are not so different from each other. The settling time of the improved OGY methods is 1/5-1/30 times as long as that of the original OGY method. Less