Chaos in nanomagnet via feedback current

Abstract

Nonlinear magnetization dynamics excited by spin-transfer effect with feedback current is studied both numerically and analytically. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates the positive Lyapunov exponent for a certain range of the feedback rate, which identifies the existence of chaos in a nanostructured ferromagnet. Transient behavior from chaotic to steady oscillation is also observed in another range of the feedback parameter. An analytical theory is also developed, which indicates the appearance of multiple attractors in a phase space due to the feedback current. An instantaneous imbalance between the spin-transfer torque and damping torque causes a transition between the attractors, and results in the complex dynamics.PACS numbers:

Reduction of back switching by large damping ferromagnetic material

“…The value of the damping constant in typical ferromagnets, such as Fe, Co, Ni, and their alloys, is on the order of 10 −3 − 10 −2 , even after the effect of spin pumping [11,12] is taken into account [5,6]. Studies on threeterminal devices manipulated by spin-orbit torque [13][14][15][16][17][18][19][20][21][22][23][24], however, have revealed that the dependence of the critical current on the damping constant is weak when the easy axis of the ferromagnet is perpendicular to the film plane [25,26] or parallel to the current direction [27]; these systems are named type Z and type X, respectively, in Ref. [19].…”

“…The purpose of this study is to investigate the relation between the magnetization state manipulated by the spin-orbit torque and the magnetic damping constant by solving the Landau-Lifshitz-Gilbert (LLG) equation. We focus on the type-X system because the switching mechanism in the system is not fully understood yet, unlike the other systems [9,10,25,26]. An undesirable return of the magnetization, called back switching in this paper, occurs in a ferromagnet, where, although the spin-orbit torque brings the magnetization close to the switched state, it returns to the initial state after turning off the current.…”

“…On the other hand, we reset the initial state of the magnetization at each trial because we are interested in designing the operation conditions of memory devices. Back switching originates from the fact that the fixed point of the magnetization in the presence of current is not parallel to the easy axis of the magnetization, as discussed below, and thus, it will occur in not only type-X devices, but also type-Z devices [25,26].…”

Designing spontaneous behavioral switching via chaotic itinerancy

“…Especially, neuromorphic devices based on physical reservoir computing framework would be an excellent candidate for implementing our scheme. Sprintronics devices, for example, are recently shown to exhibit chaotic dynamics [39,40] and are actively exploited as physical reservoirs [41][42][43]. We expect that this framework would provide one of the promising application scenarios for real-world im-plementations of our scheme.…”

Effects of delayed feedback on the power spectrum of spin-torque nano-oscillators

“…A similar phenomenon can also be achieved using the spin Hall effect as a feedback mechanism [44]. Feedback in spin-torque nano-oscillators can also result in chaotic phenomena [45,46], where the time delay increases the dimensionality of the phase space thereby allowing chaos to appear even for nominally low-dimensional systems. The memory depth of a time-delay architecture for reservoir computing has also been explored in vortex-based systems [47].…”