Abstract
Excitation of chaotic magnetization dynamics in nanomagnets is of great interest because it bridges the condensed matter physics and nonlinear science and has a potential to emerging technologies such as neuromorphic computing. However, it has been difficult to observe and identify chaos in spintronics devices because the excitation of chaos requires dynamics in a large-dimensional phase space, according to the Poincar\'e-Bendixson theorem. An efficient way to overcome this issue is using feedback, which enables the dynamical degrees of freedom to be increased even in a single device. Here, we experimentally demonstrate the excitation of chaos in a vortex spin-torque oscillator by utilizing a feedback circuit. The radio-frequency current emitted by the oscillator flows in the feedback circuit and is converted into an oscillating magnetic field. The oscillating field generates a torque acting on the vortex and modulates its dynamics, resulting in chaotic dynamics which can be tuned by electrical means.
Highlights
Chaos is deterministic but unpredictable nonlinear dynamics with high sensitivity to the initial state
We have experimentally investigated the existence of chaos in a vortex spin-torque oscillators (STOs) with a feedback circuit
The appearance of a multipeak structure indicates that the dynamical trajectory changes from a simplified circular one to complex orbit due to modulation or chaos
Summary
Chaos is deterministic but unpredictable nonlinear dynamics with high sensitivity to the initial state. Chaos occurs in a phase space larger than two dimensions, according to the Poincaré-Bendixson theorem [2,32] Additional factors, such as periodic signal, are necessary to increase the number of degrees of freedom. The number of the experimental investigations on the dynamical systems with time delay had been limited because the time scales in the proposed systems were slow and the implementation of long time delay was required [35] It took approximately 20 years to perform the experiment of MackeyGlass system [36] after its proposal [34]. The feedback effect makes the number of degrees of freedom uncountably infinite in principle, and highly nonlinear (complex) dynamics can be excited [35]. These results indicate that spintronics devices are suitable to investigate the complex dynamics caused by the feedback effect experimentally.
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