Spin-transfer Torque Oscillators Research Articles

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.

Spin Transfer Torque Oscillation in Orthogonal Magnetization Disks

We numerically demonstrated the spin transfer torque oscillation (STO) in a magnetic orthogonal configuration by introducing a 90° magnetic coupling. In our model, the multilayer consists of a top layer with in-plane magnetic anisotropy, a nonmagnetic spacer, and a bottom layer with perpendicular magnetic anisotropy. The advantage of utilizing the orthogonal configuration is the high efficiency of spin transfer torque but it is difficult to stabilize STO. By introducing 90° magnetic coupling into the trilayer of FePt/spacer/Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">90</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> , or Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> or Ni, a stable STO in an orthogonal configuration was realized. When the top layer was Ni with low levels of saturation magnetization, a small damping constant, and a small anisotropy, it exhibited high frequency and low amplitude. This indicates the possibility of controlling the STO frequency. Moreover, the STO frequency was increased by enhancing the 90° coupling. The combination of the orthogonal magnetization structure and 90° magnetic coupling is an effective approach to obtain a stable spin transfer torque oscillator with high frequency.

Terahertz spin-transfer torque oscillator based on a synthetic antiferromagnet

Bloch-Bloembergen-Slonczewski equation is adopted to simulate magnetization dynamics in spin-valve based spin-transfer torque oscillator with synthetic antiferromagnet acting as a free magnetic layer. High frequency up to the terahertz scale is predicted in synthetic antiferromagnet spin-transfer torque oscillator with no external magnetic field if the following requirements are fulfilled: antiferromagnetic coupling between synthetic antiferromagnetic layers is sufficiently strong, and the thickness of top (bottom) layer of synthetic antiferromagnet is sufficiently thick (thin) to achieve a wide current density window and frequency window. Additionally, the transverse relaxation time of the free magnetic layer should be sufficiently larger compared with the longitudinal relaxation time. Otherwise, stable oscillation cannot be sustained or scenarios similar to regular spin valve-based spin-transfer torque oscillator with relatively low frequency will occur. Our calculations pave a new way for exploring THz spintronics devices.

Spin–transfer torque oscillator in magnetic tunneling junction with short–wavelength magnon excitation

Bloch–Bloembergen–Slonczewski (BBS) equation is established by extending Bloch–Bloembergen equation, and it is used to study magnetization oscillation in the free magnetic layer of a magnetic tunneling junction. Since both short–wavelength magnon excitation and spin–transfer torque are taken into account in the BBS equation, it is distinguished from Landau–Lifshitz–Gilbert–Slonczewski equation. The macro–spin BBS model predicts that the transverse relaxation time in free magnetic layer should be long enough, as compared with the longitudinal relaxation time, to achieve stable magnetization oscillation for spin–transfer torque oscillator application. Moreover, field–like torque favors the tolerance of fast transverse relaxation, which makes magnetic tunneling junction a better choice than spin valve for the spin–transfer torque oscillator application.

Micromagnetic Model Analysis of Spin-Transfer Torque Oscillator and Write Heads for Microwave-Assisted Magnetic Recording

A micromagnetic model analysis was used to investigate spin-transfer torque oscillators (STOs) and magnetic write heads for microwave-assisted magnetic recording (MAMR). Our goal was to propose STOs, the Gilbert damping constant of the write head, and write head configurations that allow the STO element to operate at a low injected current density J. First, we derived the write head field and field generation layer rotations for various models with various main pole (MP) widths and MP throat heights. Second, we used the write head model and tried to reduce J by optimizing the Gilbert damping constant of the write head. Then, we used various STOs and write head structures and derived STO fields, clockwise and counterclockwise components, and FGL angles versus J. Finally, we performed media recording simulations and noted some challenges in the MAMR simulations.

Simulation of stress-modulated magnetization precession frequency in Heusler-based spin torque oscillator

We investigated stress-modulated magnetization precession frequency in Heusler-based spin transfer torque oscillator by combining micromagnetic simulations with phase field microelasticity theory, by encapsulating the magnetic tunnel junction into multilayers structures. We proposed a novel method of using an external stress to control the magnetization precession in spin torque oscillator instead of an external magnetic field. The stress-modulated magnetization precession frequency can be linearly modulated by externally applied uniaxial in-plane stress, with a tunable range 4.4–7.0GHz under the stress of 10MPa. By comparison, the out-of-plane stress imposes negligible influence on the precession frequency due to the large out-of-plane demagnetization field. The results offer new inspiration to the design of spin torque oscillator devices that simultaneously process high frequency, narrow output band, and tunable over a wide range of frequencies via external stress.

Synchronization of spin-transfer torque oscillators by spin pumping, inverse spin Hall, and spin Hall effects

We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.

Dynamic control of metastable remanent states in mesoscale magnetic elements

The formation of the vortex-antivortex-vortex (v-av-v) metastable remanent states in elongated magnetic elements have been systematically investigated using micromagnetic modeling. It is demonstrated that the v-av-v magnetization pattern can be effectively stabilized by exciting the single vortex state with an external RF field. Furthermore, we show that a set of different polarity combinations of the vortex cores can be achieved by adjusting the frequency and amplitude of the excitation field. The corresponding dynamic response in time- and frequency-domain has also been presented. Owing to the diversity of the collective modes with different vortex-antivortex combinations, this system may open promising perspectives in the area of spin transfer torque oscillators.

Model Analysis of Tilted Spin-Torque Oscillator With Magnetic Write Head for Shingled Microwave-Assisted Magnetic Recording

A model analysis was used to investigate a spin-transfer torque oscillator (STO) and magnetic write head for shingled microwave-assisted magnetic recording, where the interactions between STO and write head were included. The magnetic head had a tilted main pole (MP)-trailing shield (TS) gap with respect to the medium surface. The STO was placed in the tilted gap and off-center with respect to the MP center axis. The head structure allowed stable STO oscillation due to the lower in-plane field on the STO and large magnetic head field and high field gradient in the cross-track direction due to the wide pole. An off-centered STO in the MP-TS tilted gap had a stable oscillation at the cost of a slight reduction in oscillation amplitude.

High-Frequency Vortex-Based Spin Transfer Nano-Oscillators

Spin transfer torque oscillators based on magnetic vortex precession can deliver output powers large enough for practical applications. In addition they do not require discrete electronic components, such as capacitors or inductors, to tune the oscillation frequency. At the current stage, this oscillation frequency is still too low and can be increased only by trading off the output power. Here, we present our experimental results on nanocontact oscillators, which are, amongst the spintronic oscillators, those that can deliver the largest power. Based on the analysis of our experimental results, we propose a new device geometry and numerically demonstrate that an increase of the frequency, up to a useful range for practical applications, can be obtained without trading off output power.

Higher order vortex gyrotropic modes in circular ferromagnetic nanodots

Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50–100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators.

Injection locking at zero field in two free layer spin-valves

This paper predicts the possibility to achieve synchronization (via injection locking to a microwave current) of spin-transfer torque oscillators based on hybrid spin-valves composed by two free layers and two perpendicular polarizers at zero bias field. The locking regions are attained for microwave frequency near 0.5f0, f0, and 2f0, where f0 is the input oscillator frequency. Those properties make this system promising for applications, such as high-speed frequency dividers and multipliers, and phase-locked-loop demodulators.

Frequency-tunable perpendicular spin torque oscillator

We present an experimental study on the frequency tunability of a perpendicular spin transfer torque oscillator with a perpendicularly magnetized (Co/Pd)5 reference electrode and a Co/(Pd/Co)4 composite oscillating layer of a giant magnetoresistive stack. A current-perpendicular-to-plane magnetoresistance ratio of 2.55% is obtained for the stack. Spin transfer torque induced steady oscillation with a narrow line-width has been obtained with direct current injection. As the injected dc current level is varied from 4.5 to 8.5 mA under a small constant applied field, the oscillation frequency increases from 5 to 6.2 GHz and back to 5.8 GHz. The oscillation with the narrowest linewidth occurs at the injection current magnitude at which the highest oscillation amplitude is also obtained. Micromagnetic modeling suggests that a nanomagnet above its critical single domain size is subjected to higher order spin wave generation at large current density. The spatial inhomogenity created across the nanomagnet can account for the drop in its oscillation frequency at relatively large injection currents.

Large amplitude magnetization dynamics and the suppression of edge modes in a single nanomagnet

Large amplitude magnetization dynamics of a single square nanomagnet have been studied by time-resolved Kerr microscopy. Experimental spectra revealed that only a single mode was excited for all bias field values. Micromagnetic simulations demonstrate that at larger pulsed field amplitudes the center mode dominates the dynamic response while the edge mode is almost completely suppressed. Controlled suppression of edge modes in a single nanomagnet has potential applications in the operation of nanoscale spin transfer torque oscillators and bistable switching devices for which the amplitude of the magnetization trajectory is often large and a more uniform dynamic response is desirable.