Spin Hall Oscillator Research Articles

Nonlinear dynamics of a spin-Hall nano-oscillator based on the canted antiferromagnet.

The theory of the nonlinear dynamics of a canted antiferromagnet-based (AFM) spin-Hall oscillator with weak ferromagnetism caused by the strong Dzyaloshinskii-Moriya interaction between magnetic sublattices is rigorously studied. The AFM oscillator's frequency tuning is carried out both due to a DC spin-polarized current flowing through the normal metal layer and an external permanent magnetic field. A feature of the operation of this oscillator is the presence of a hysteresis region between the subcritical (damping) and overcritical (self-oscillating) regimes. We show that it is necessary to reduce an effective easy-plane anisotropy field of the AFM or choose antiferromagnetic material with a smaller exchange field between magnetic sublattices to get a smaller hysteresis region. The action of an external permanent magnetic field on an antiferromagnet leads to the presence of two stable equilibrium states, and the self-oscillating regime is characterized by two-mode generation. We find the conditions for the absence of two-mode generation on the "current density-magnetic field strength" plane. We believe that our results can be helpful for the practical development of a sub-THz frequency tunable oscillator based on the AFM with weak ferromagnetism.

Stochastic generation in a Josephson-like antiferromagnetic spin Hall oscillator driven by a pure AC current

We numerically demonstrate that a pure time-harmonic bias AC current of a specific amplitude τf and angular frequency ωf can excite the chaotic magnetization dynamics in a Josephson-like antiferromagnetic (AFM) spin Hall oscillator (SHO) with biaxial magnetic anisotropy of an AFM layer. The nature of such a stochastic generation regime in a Josephson-like AFM SHO could be explained by the random hopping of the working point of the SHO between several quasi-stable states under the action of an applied AC current. We reveal that depending on the ωf/τf ratio several stochastic generation regimes interspersed with regular generation regimes can be achieved in an AFM SHO, which can be used in spintronic random signal sources and various nano-scale random signal devices, including the spintronic p-bit device considered in this work. The obtained results are important for the development and optimization of spintronic devices capable of generating and processing (sub-)THz-frequency random signals, which are promising for ultra-fast probabilistic computing, cryptography, secure communication, etc.

Evaluation of Memory Capacity and Time Series Prediction Using a Spin Hall Oscillator as Reservoir

Spintronic devices, such as spin Hall oscillators and spin transfer torque oscillators, have become popular candidates for use as the reservoir in the reservoir computing architecture. The memory capacity of a reservoir quantifies the amount of information retained at any given time, indicating its significance for different reservoir computing tasks. In this work, we consider a spin Hall oscillator, consisting of a bilayer structure of platinum/permalloy, as the reservoir. Using micromagnetic simulations, we evaluate the change in memory capacity of the spin Hall oscillator system as the magnetization dynamics varies from transient state oscillations to limit cycle oscillations. We also perform a three-bit parity task to study the performance of the oscillator in carrying out a nonlinear task. A time series prediction task, namely the NARMA2 task, is also performed. The results of both tasks confirm a correlation between the evaluated memory capacity of the reservoir and its efficiency in performing temporal tasks. The best performance in reservoir computing tasks is observed when the output magnetization dynamics of the oscillator consists of both transient state and limit cycle oscillations.

Classification tasks using input driven nonlinear magnetization dynamics in spin Hall oscillator

The inherent nonlinear magnetization dynamics in spintronic devices make them suitable candidates for neuromorphic hardware. Among spintronic devices, spin torque oscillators such as spin transfer torque oscillators and spin Hall oscillators have shown the capability to perform recognition tasks. In this paper, with the help of micromagnetic simulations, we model and demonstrate that the magnetization dynamics of a single spin Hall oscillator can be nonlinearly transformed by harnessing input pulse streams and can be utilized for classification tasks. The spin Hall oscillator utilizes the microwave spectral characteristics of its magnetization dynamics for processing a binary data input. The spectral change due to the nonlinear magnetization dynamics assists in real-time feature extraction and classification of 4-binary digit input patterns. The performance was tested for the classification of the standard MNIST handwritten digit data set and achieved an accuracy of 83.1% in a simple linear regression model. Our results suggest that modulating time-driven input data can generate diverse magnetization dynamics in the spin Hall oscillator that can be suitable for temporal or sequential information processing.

Delayed Antiferromagnetic Spin Hall Oscillator as Random THz Signal Source

Delayed Antiferromagnetic Spin Hall Oscillator as Random THz Signal Source

Ising Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks that provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. Here we propose using an electrically coupled array of gigahertz spin Hall nano-oscillators to realize such a network. By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, we explicitly show the mapping between the coupled oscillators' properties and the Ising model. We integrate our analytical model into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillators in circuit simulators. With this abstract model, we analyze the performance of the spin Hall oscillator network at the circuit level using conventional electronic components and considering phase noise and scalability. Our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency.

Theory of the electric field controlled antiferromagnetic spin Hall oscillator and detector

A theory of an electrically controlled terahertz-frequency auto-oscillator is developed here within the framework of the antiferromagnetic sigma model. The structure is based on a trilayer heterostructure: a piezoelectric ceramic, NiO-based antiferromagnet (AFM), and a heavy metal. The authors demonstrate that the frequency of the AFM resonance of the layered structure in a passive subcritical regime can be controlled by the external electric field applied to the piezoelectric, by choosing a proper piezoelectric material, and by the magnitude of the electric current flowing in the heavy metal.

Dimensional crossover in spin Hall oscillators

Auto-oscillations of magnetization driven by direct spin current have been previously observed in multiple quasi-zero-dimensional (0D) ferromagnetic systems such as nanomagnets and nanocontacts. Recently, it was shown that pure spin Hall current can excite coherent auto-oscillatory dynamics in quasi-one-dimensional (1D) ferromagnetic nanowires but not in quasi-two-dimensional (2D) ferromagnetic films. Here we study the 1D to 2D dimensional crossover of current-driven magnetization dynamics in wire-based Pt/$\mathrm{Ni}_{80}\mathrm{Fe}_{20}$ bilayer spin Hall oscillators via varying the wire width. We find that increasing the wire width results in an increase of the number of excited auto-oscillatory modes accompanied by a decrease of the amplitude and coherence of each mode. We also observe a crossover from a hard to a soft onset of the auto-oscillations with increasing the wire width. The amplitude of auto-oscillations rapidly decreases with increasing temperature suggesting that interactions of the phase-coherent auto-oscillatory modes with incoherent thermal magnons plays an important role in suppression of the auto-oscillatory dynamics. Our measurements set the upper limit on the dimensions of an individual spin Hall oscillator and elucidate the mechanisms leading to suppression of coherent auto-oscillations with increasing oscillator size.

Dipole-dominated dissipative magnetic solitons in quasi-one-dimensional spin-torque oscillators

It is well-known that a spin-transfer torque caused by a dc electric current can excite in a two-dimensional ferromagnetic film exchange-dominated magnetic solitons, often called “spin-wave bullets”, under the condition of a negative nonlinear shift of spin wave frequency. In this work, we demonstrate that in a quasi-one-dimensional (1D) case, e.g., in a nanowire spin-Hall oscillator, it is possible to excite a stable dissipative magnetic soliton, which is dominated by the dipole-dipole interaction. This dissipative magnetic soliton can be described in the framework of a 1D Ginzburg-Landau auto-oscillator model, and has the shape similar to that of the exchange-dominated spin wave bullet, but with a different spatial localization law. The influence of the dipolar interaction makes possible the stabilization of a dissipative soliton in a relatively large (micron-sized) active area of the oscillator, which is in a sharp contrast with the two-dimensional case, where the excitation of a stable spin-wave bullet was observed only in relatively small active areas having typical sizes of the order of 100 nm. The characteristics and possible applications of these dipole-dominated spin wave bullets are discussed.

Out-of-Plane Auto-Oscillation in Spin Hall Oscillator With Additional Polarizer

The theoretical investigation on magnetization dynamics excited by the spin Hall effect in metallic multilayers having two ferromagnets is discussed. The relaxation of the transverse spin in one ferromagnet enables us to manipulate the direction of the spin-transfer torque excited in another ferromagnet, although the spin-polarization originally generated by the spin Hall effect is geometrically fixed. Solving the Landau-Lifshitz-Gilbert-Slonczewski equation, the possibility to excite an out-of-plane auto-oscillation of an in-plane magnetized ferromagnet is presented. An application to magnetic recording using microwave-assisted magnetization reversal is also discussed.

Injection locking of multiple auto-oscillation modes in a tapered nanowire spin Hall oscillator

Spin Hall oscillators (SHO) are promising candidates for the generation, detection and amplification of high frequency signals, that are tunable through a wide range of operating frequencies. They offer to be read out electrically, magnetically and optically in combination with a simple bilayer design. Here, we experimentally study the spatial dependence and spectral properties of auto-oscillations in SHO devices based on Pt(7 nm)/Ni80Fe20(5 nm) tapered nanowires. Using Brillouin light scattering microscopy, we observe two individual self-localized spin-wave bullets that oscillate at two distinct frequencies (5.2 GHz and 5.45 GHz) and are localized at different positions separated by about 750 nm within the SHO. This state of a tapered SHO has been predicted by a Ginzburg-Landau auto-oscillator model, but not yet been directly confirmed experimentally. We demonstrate that the observed bullets can be individually synchronized to external microwave signals, leading to a frequency entrainment, linewidth reduction and increase in oscillation amplitude for the bullet that is selected by the microwave frequency. At the same time, the amplitude of other parasitic modes decreases, which promotes the single-mode operation of the SHO. Finally, the synchronization of the spin-wave bullets is studied as a function of the microwave power. We believe that our findings promote the realization of extended spin Hall oscillators accomodating several distinct spin-wave bullets, that jointly cover an extended range of tunability.

Self-feedback electrically coupled spin-Hall oscillator array for pattern-matching operation

An oscillator array has been proposed for associative memory, in which the synchronization of multiple oscillators is utilized for pattern-matching operations. An input pattern is represented by a set of frequency shifts of the oscillators and the matching result is attributed to the degree of synchronization. Here, we propose an electrically coupled spin-Hall oscillator (SHO) array in which multiple SHOs exhibit synchronization by interacting with each other through self-feedback spin torques. We numerically demonstrate the pattern matching functionality of the proposed SHO array.

Synchronization of Spin Hall Oscillators With Magnetodipolar Coupling

We have found that the stacked spin Hall oscillator (SHO) based on the spin Hall effect and anisotropy magnetoresistance is synchronized via magnetodipolar interaction calculated with consideration of the shape of the SHO. Employing a macrospin simulation approach, we have obtained the boundary separating the synchronized and nonsynchronized states as a function of the difference in the natural frequency between two SHOs. We have also found that the emitted microwave power is enhanced by synchronization of a larger number of SHOs. It is anticipated that the results will be tested with existing experimental techniques.

Dynamic Feedback in Ferromagnet-Spin Hall Metal Heterostructures.

In ferromagnet-normal-metal heterostructures, spin pumping and spin-transfer torques are two reciprocal processes that occur concomitantly. Their interplay introduces a dynamic feedback effect interconnecting energy dissipation channels of both magnetization and current. By solving the spin diffusion process in the presence of the spin Hall effect in the normal metal, we show that the dynamic feedback gives rise to (i)a nonlinear magnetic damping that is crucial to sustain uniform steady-state oscillations of a spin Hall oscillator at large angles and (ii)a frequency-dependent spin Hall magnetoimpedance that reduces to the spin Hall magnetoresistance in the dc limit.

Exchange magnon induced resistance asymmetry in permalloy spin-Hall oscillators

We investigate magnetization dynamics in a spin-Hall oscillator using a direct current measurement as well as conventional microwave spectrum analysis. When the current applies an anti-damping spin-transfer torque, we observe a change in resistance which we ascribe mainly to the excitation of incoherent exchange magnons. A simple model is developed based on the reduction of the effective saturation magnetization, quantitatively explaining the data. The observed phenomena highlight the importance of exchange magnons on the operation of spin-Hall oscillators.