Spin-torque Nano-oscillators Research Articles

Spin-torque nano-oscillators and their applications

Spin-torque nano-oscillators (STNOs) have emerged as an intriguing category of spintronic devices based on spin transfer torque to excite magnetic moment dynamics. The ultra-wide frequency tuning range, nanoscale size, and rich nonlinear dynamics have positioned STNOs at the forefront of advanced technologies, holding substantial promise in wireless communication, and neuromorphic computing. This review surveys recent advances in STNOs, including architectures, experimental methodologies, magnetodynamics, and device properties. Significantly, we focus on the exciting applications of STNOs, in fields ranging from signal processing to energy-efficient computing. Finally, we summarize the recent advancements and prospects for STNOs. This review aims to serve as a valuable resource for readers from diverse backgrounds, offering a concise yet comprehensive introduction to STNOs. It is designed to benefit newcomers seeking an entry point into the field and established members of the STNOs community, providing them with insightful perspectives on future developments.

Microwave artificial neurons based on magnetic tunnel junction nano-oscillators for image recognition and denoising

We report a microwave artificial neuron based on magnetic tunnel junction spin torque nano-oscillator (STNO). Based on STNO neurons, the three-layer full connected artificial neural network (ANN) are constructed to recognize handwritten digit with a produced accuracy of up to 90.95%. To address noise inherent in real circuits leads to poor recognition accuracy, we harness the frequency mutation characteristics of the STNO output near the critical threshold current for denoising handwritten digits corrupted by noise. Before and after denoising using the aforementioned ANN, the recognition accuracy is improved from 55.98% to 88.76%.

Spin-torque vortex-oscillator with modified saturation magnetization in ferromagnetic nanodots

Recent years have seen greater interest in manipulating vortex states in magnetic nanostructures for non-volatile memory and logic networks. We show how reducing saturation magnetization locally in ferromagnetic thick nanodot vortex-based spin-torque nano-oscillators modulates their frequency using micromagnetic simulations. When a spin-polarized current and a static in-plane magnetic field are applied to the vortex core of an isolated thick nanodot, the uniform gyrotropic modes and the first higher-order gyrotropic mode resonate at different frequencies in various saturation magnetization areas. The intensity of the first higher-order mode gets almost suppressed in areas with modified saturation magnetization. With linewidths ranging from 25 to 70 MHz with the considered dimensions, these small spin-torque vortex-oscillator devices made of thick Permalloy nanodots seem promising for use in gigahertz signal processing. Our study suggests that locally modifying saturation magnetization may be a cost-effective technique to build dense oscillator and array networks for neuromorphic computing without lithographical fabrication stages.

Circular motion of noncollinear spin textures in Corbino disks: Dynamics of Néel- versus Bloch-type skyrmions and skyrmioniums

Magnetic skyrmions are nanoscale magnetic whirls that can be driven by currents via spin torques. They are promising candidates for spintronic devices such as the racetrack memory, where a motion along the uniform current is typically desired. However, for spin torque nano-oscillators in Corbino disks, the goal is to achieve a circular motion, perpendicular to the radially applied current. As we show, based on analytical calculations and micromagnetic simulations, Bloch skyrmions engage in a circular motion with frequencies in the MHz range when driven by spin-orbit torques. In contrast, Néel skyrmions get stuck at the edges of the disk. Our analysis reveals that the antagonistic dynamics between Bloch- and Néel-type magnetic textures arise from their helicity. Furthermore, we find that skyrmioniums, which are topologically trivial variations of skyrmions, move even faster and allow an increase in the current density without being pushed toward the edges of the disk. When driven by spin-transfer torques instead, Bloch and Néel skyrmions no longer exhibit different dynamics. Instead, they move along a circular trajectory due to the skyrmion Hall effect caused by their topological charge. Consequently, the topologically trivial skyrmioniums inevitably become trapped at the disk edge in this scenario. To provide a comprehensive understanding, our paper also examines currents applied tangentially, further enriching our insights into skyrmion dynamics and appropriate current injection methods for skyrmion-based devices. Published by the American Physical Society 2024

Sparse reservoir computing with vertically coupled vortex spin-torque oscillators for time series prediction

Spin torque nano-oscillators possessing fast nonlinear dynamics and short-term memory functions are potentially able to achieve energy-efficient neuromorphic computing. In this study, we introduce an activation-state controllable spin neuron unit composed of vertically coupled vortex spin torque oscillators and a V–I source circuit is proposed and used to build an energy-efficient sparse reservoir computing (RC) system to solve nonlinear dynamic system prediction task. Based on micromagnetic and electronic circuit simulation, the Mackey–Glass chaotic time series and the real motor vibration signal series can be predicted by the RC system with merely 20 and 100 spin neuron units, respectively. Further study shows that the proposed sparse reservoir system could reduce energy consumption without significantly compromising performance, and a minimal response from inactivated neurons is crucial for maintaining the system’s performance. The accuracy and signal processing speed show the potential of the proposed sparse RC system for high-performance and low-energy neuromorphic computing.

A spin-torque nano-oscillator based on interlayer-coupled meron–skyrmion pairs with a fixed orbit

In recent years, magnetic skyrmion-based spin-torque nano-oscillators (STNOs) have attracted considerable interest for their prospect in future-generation communication and spintronic technologies. However, some critical issues, which hamper their practical applications, e.g., the long start-up time and variable skyrmion gyration orbit, remain to be resolved. Here, we numerically demonstrate the realization of a fixed-orbit STNO, which is based on an interlayer-coupled meron–skyrmion (MS) pair instead of a magnetic skyrmion. In this STNO, the MS pair possesses a structurally defined, fixed orbit within a broad range of driving currents, even in the presence of random defects. The output frequency range of the STNO based on an MS pair far exceeds that of the STNO typically featuring a single skyrmion. Moreover, the output frequency of this STNO can be further elevated if more MS pairs are incorporated. Our results reveal the nontrivial dynamics of the interlayer-coupled MS pair, opening perspectives for the design and optimization of fundamental spintronic devices.

Temperature effect on a weighted vortex spin-torque nano-oscillator for neuromorphic computing

In this work, we present fabricated magnetic tunnel junctions (MTJs) that can serve as magnetic memories (MMs) or vortex spin-torque nano-oscillators (STNOs) depending on the device geometry. We explore the heating effect on the devices to study how the performance of a neuromorphic computing system (NCS) consisting of MMs and STNOs can be enhanced by temperature. We further applied a neural network for waveform classification applications. The resistance of MMs represents the synaptic weights of the NCS, while temperature acts as an extra degree of freedom in changing the weights and TMR, as their anti-parallel resistance is temperature sensitive, and parallel resistance is temperature independent. Given the advantage of using heat for such a network, we envision using a vertical-cavity surface-emitting laser (VCSEL) to selectively heat MMs and/or STNO when needed. We found that when heating MMs only, STNO only, or both MMs and STNO, from 25 to 75 °C, the output power of the STNO increases by 24.7%, 72%, and 92.3%, respectively. Our study shows that temperature can be used to improve the output power of neural networks, and we intend to pave the way for future implementation of a low-area and high-speed VCSEL-assisted spintronic NCS.

Non-isochronous exceptional point shift in coupled spin-torque nano-oscillators

This paper explores the nonlinear dynamics of mutually coupled spin-torque nano-oscillators and examines the relationship between non-isochronism and the appearance of exceptional points (EPs). We demonstrate that by manipulating the amplitudes of the driving force and the angles of the external bias magnetic field and spin-polarized current, it is possible to observe and fine-tune the position of EPs. Namely, EPs shift most significantly when the azimuth angle of the equilibrium state is approximately 90° and the system’s non-isochronism reaches its peak. The results of this investigation provide valuable insights for enhancing the performance of spintronic devices in applications such as microwave signal generation, spin-based computing, and sensing.

Tunability of Microwave Frequency Using Spin Torque Nano Oscillator by the Generated Oersted Field with Tunable Free Layer

The current-induced magnetization precession dynamics provoked by the spin transfer torque (STT) in a spin valve device i.e. tri-layer device (commonly spin torque nano oscillator (STNO)) is investigated numerically by solving the governing Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation. In this study, we have devised an STNO device made of EuO-based ferromagnetic alloy in free and fixed magnetic layers. The copper acts as a nonmagnetic spacer. Here, we have introduced the current induced Oesterd field (CIOF), which is generated when a spin-polarized current passes through the STNO device. In the device, we have tuned the free layer angle [Formula: see text] from [Formula: see text] to [Formula: see text] as an increment of [Formula: see text]. For every individual [Formula: see text] ranging from [Formula: see text] to [Formula: see text], the generated Oersted field’s strength can be altered by increasing the STNO device’s diameter. Henceforth, it is apparent that the frequency tunability is achieved in the device for all the values of [Formula: see text]. The frequency and power of the device depend entirely on the material’s saturation magnetization, which inherently reflects the current density and coherence of spin-polarized DC. From the results, it is apparent that for a particular [Formula: see text], the frequency keeps increasing with the eventual decrease in power when we increase the strength of the Oersted field from 10[Formula: see text]kA/m to 50[Formula: see text]kA/m. By doing so, the maximum frequency can be tuned up to 212[Formula: see text]GHz for [Formula: see text] with [Formula: see text] as 50[Formula: see text]kA/m. The high frequency emitted by the device acts as a linchpin ingredient, as well as a launch pad element in much of scientific and technological point of view. It paves way for a new route in the areas such as high capacity, high precision, high density as well as the sensing applications.

A ferromagnetic skyrmion-based spin-torque nano-oscillator with modified edge magnetization

Magnetic skyrmion-based spin-torque nano-oscillators (STNOs) have attracted significant interest because of their potential applications as microwave signal emitters and integrability in the existing CMOS process flow. However, the stable circular motion of the skyrmion in the nanodisk is affected by the Magnus force, which can destroy and annihilate the skyrmion at the nanodisk edge, thereby limiting the application of the maximum oscillation frequency. To overcome this problem, we investigated the influence of a modified magnetized structure at the edge of the nanodisk on the oscillation dynamics of skyrmions, in which the modified magnetized profile is acquired by local modification of the magnetic material parameters, and these skyrmions can move along the tilting magnetization formatted wall. It was found that the upper threshold for steady skyrmion oscillations can be improved by approximately two times compared to the standard structure without modified edge magnetization profiles. Based on the effective field analysis, we confirmed that the spatial distribution of the tilting moment at the edge layer changed the effective field distribution and caused a non-monotonic change in the upper threshold current with the modified region width. Our results may provide an optional route for designing future skyrmion-based STNOs with better performance in the communication and computing areas.

Magnetic droplet soliton pairs

We demonstrate magnetic droplet soliton pairs in all-perpendicular spin-torque nano-oscillators (STNOs), where one droplet resides in the STNO free layer (FL) and the other in the reference layer (RL). Typically, theoretical, numerical, and experimental droplet studies have focused on the FL, with any additional dynamics in the RL entirely ignored. Here we show that there is not only significant magnetodynamics in the RL, but the RL itself can host a droplet driven by, and coexisting with, the FL droplet. Both single droplets and pairs are observed experimentally as stepwise changes and sharp peaks in the dc and differential resistance, respectively. While the single FL droplet is highly stable, the coexistence state exhibits high-power broadband microwave noise. Furthermore, micromagnetic simulations reveal that the pair dynamics display periodic, quasi-periodic, and chaotic signatures controlled by applied field and current. The strongly interacting and closely spaced droplet pair offers a unique platform for fundamental studies of highly non-linear soliton pair dynamics.

Nonlinear dynamics of directly coupled skyrmions in ferrimagnetic spin torque nano-oscillators

Nonlinear spin torque nano-oscillators have received substantial attentions due to their important applications in microwave communication and neuromorphic computing. Here we investigate the dynamical behaviors of directly coupled skyrmion oscillators in a synthetic ferrimagnet. We demonstrate through the micromagnetic simulation and Thiele’s equation that the skyrmion oscillators can present either synchronization or frequency comb, depending on the strength of interactions between the skyrmions. The underlying physics of the transition between the two scenarios are unveiled based on a quantitative analysis of the effective potentials, which also successfully interprets the dependence of the transition on parameters. By further demonstrating the tunability of the nonlinear dynamics by the driving current of the oscillators, our work reveals the great potentials of ferrimagnetic-skyrmion-based interacting oscillators for nonlinear applications.

Driving magnetic oscillation by electric flip in Permalloy/BaTiO3 composite

In this work, the Permalloy/BaTiO3 composite with granule/matrix structure is designed. The theoretical calculation reveals coupling between electric polarization and magnetic anisotropy. As electric polarization is downward and upward in BaTiO3 matrix, the magnetizing orientation tends to be parallel and perpendicular in Permalloy granule respectively. The Landau-Lifshitz-Gilberts model further predicts magnetic oscillation driven by electric flip. Explicitly, as electric polarization flips with low frequency in BaTiO3 matrix, the magnetic moment oscillates with high frequency in Permalloy granule. It results from the anisotropy field altered periodically by polarization flip. Based on the magnetic tunneling model, the moment oscillation can output periodical voltage signal. With the Square-Root circuit, the oscillating amplitude of output voltage becomes stable. Through 4-level connection of this design, the 1.0 MHz input can drive 3.5 GHz output. This work gives a novel strategy for spin torque nano-oscillator. Compared to the spin-transfer torque method, this avenue could avoid the heat influence of current.

Spin-torque nano-oscillator based on two in-plane magnetized synthetic ferrimagnets

We report the dynamic characterization of the spin-torque-driven in-plane precession modes of a spin-torque nano-oscillator based on two different synthetic ferrimagnets: a pinned one characterized by a strong Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, which is exchange-coupled to an antiferromagnetic layer; and a non-pinned one characterized by weak RKKY coupling. The microwave properties associated with the steady-state precession of both synthetic ferrimagnets (SyFs) are characterized by high spectral purity and power spectral density. However, frequency dispersion diagrams of the damped and spin-transfer torque modes reveal drastically different dynamical behavior and microwave emission properties in both SyFs. In particular, the weak coupling between the magnetic layers of the non-pinned SyF raises discontinuous dispersion diagrams suggesting a strong influence of mode crossing. An interpretation of the different dynamical features observed in the damped and spin-torque modes of both SyF systems was obtained by solving simultaneously, in a macrospin approach, a linearized version of the Landau–Lifshitz–Gilbert equation including the spin-transfer torque term.

Sub-terahertz excitations in a synthetic antiferromagnet with perpendicular anisotropy

In this paper, micromagnetic simulations are employed to investigate terahertz (THz) magnetic excitations in a spin torque nano-oscillator (STNO) with a perpendicularly magnetized synthetic antiferromagnetic (SAF) free layer. The magnetization precession of the free layer can be finely tuned into the sub-THz range without the necessity of external magnetic fields. The excited frequency exhibits two distinctive regions, namely region-I and region-II, depending on the applied current strength. In region-I, characterized by relatively small currents, the two ferromagnetic layers are stabilized at two separate precession orbits. The frequency in this region decreases with current strength, exhibiting similar features as the Néel vector change observed in antiferromagnets. In contrast, region-II is defined by currents where the two ferromagnetic layers synchronize into the same precession orbit. The frequency increases with current, correlating with the variation in the net magnetization of the SAF layer. An analytical model is developed through the canonical transformation of Lagrange’s equation, which can describe the frequency dependence on both the applied current and the antiferromagnetic interlayer coupling strengths. The simulations and the analytical model show good agreement, offering a more profound understanding of the magnetic excitation properties in STNOs with ultrathin SAF free layers. These insights are crucial for the design of advanced terahertz spintronic devices.

Exploration of field-like torque and field-angle tunability in coupled spin-torque nano oscillators for synchronization.

We investigate the influence of field-like torque and the direction of the external magnetic field on a one-dimensional array of serially connected spin-torque nano oscillators (STNOs), having free layers with perpendicular anisotropy, to achieve complete synchronization between them by analyzing the associated Landau-Lifshitz-Gilbert-Slonczewski equation. The obtained results for synchronization are discussed for the cases of 2, 10, and 100 oscillators separately. The roles of the field-like torque and the direction of the external field on the synchronization of the STNOs are explored through the Kuramoto order parameter. While the field-like torque alone is sufficient to bring out global synchronization in the system made up of a small number of STNOs, the direction of the external field is also needed to be slightly tuned to synchronize the one-dimensional array of a large number of STNOs. The formation of complete synchronization through the construction of clusters within the system is identified for the 100 oscillators. The large amplitude synchronized oscillations are obtained for small to large numbers of oscillators. Moreover, the tunability in frequency for a wide range of currents is shown for the synchronized oscillations up to 100 spin-torque oscillators. In addition to achieving synchronization, the field-like torque increases the frequency of the synchronized oscillations. The transverse Lyapunov exponents are deduced to confirm the stable synchronization in coupled STNOs due to the field-like torque and to validate the results obtained in the numerical simulations. The output power of the array is estimated to be enhanced substantially due to complete synchronization by the combined effect of field-like torque and tunability of the field-angle.

Field-free mutual synchronization of parallel coupled spin torque nano oscillators using a free layer with first- and second-order uniaxial anisotropy

Field-free mutual synchronization of parallel coupled spin torque nano oscillators using a free layer with first- and second-order uniaxial anisotropy

Simultaneous multitone microwave emission by dc-driven spintronic nano-element

Current-induced self-sustained magnetization oscillations in spin-torque nano-oscillators (STNOs) are promising candidates for ultra-agile microwave sources or detectors. While usually STNOs behave as a monochromatic source, we report here clear bimodal simultaneous emission of incommensurate microwave oscillations in the frequency range of 6 to 10 gigahertz at femtowatt level power. These two tones correspond to two parametrically coupled eigenmodes with tunable splitting. The emission range is crucially sensitive to the change in hybridization of the eigenmodes of free and fixed layers, for instance, through a slight tilt of the applied magnetic field from the normal of the nanopillar. Our experimental findings are supported both analytically and by micromagnetic simulations, which ascribe the process to four-magnon scattering between a pair of radially symmetric magnon modes and a pair of magnon modes with opposite azimuthal index. Our findings pave the way for enhanced cognitive telecommunications and neuromorphic systems that use frequency multiplexing to improve communication performance.

Coupling-induced bistability in self-oscillating regimes of two coupled identical Spin-Torque Nano-oscillators

We consider a system of two coupled identical Spin Torque Nano-Oscillators (STNOs) with cylindrical geometry. The STNOs have free layers in the vortex magnetization configuration and fixed layer with magnetization in the out-of-plane direction. The magnetization dynamics in the two STNOs are analyzed by using a Thiele-like equation governing the dynamics of the vortex core positions. The coupling is assumed to be linear and symmetric and this enables to characterize it by a single complex parameter. We consider numerical simulations of the model as a function of the coupling strength k and phase ϕk. Depending on their values, different motions of the vortex cores are observed, e.g. periodic, and quasi-periodic. Each type of dynamics can be classified according to the symmetry property shown by the trajectories. In this respect, the transition between different types of motion corresponds to a symmetry-breaking process and we describe it as a bifurcation process. Fixing the value of the coupling constant phase, we found that there is a range of coupling constant strength in which the periodic and quasi-periodic motions coexist and both are stable. This bistability is an interesting phenomenon in connection to research on neuromorphic circuits based on STNOs.

Enhancement of microwave frequency via heterogeneous magneto resistance tilted polarizer based spin torque nano oscillator with the inclusion of Oersted field

Here, we presented a heterogeneous Magneto Resistance Tilted Polarizer-based Spin Torque Nano Oscillator [MRTP-STNO] and theoretically included Current Induced Oersted Field [CIOF] via the macro-spin domain. The dynamics of magnetization provoked by Spin Transfer Torque [STT] are studied by solving Landau-Lifshitz-Gilbert-Slonczewski [LLGS] equation. In this device, β is the independent tilt angle of the fixed layer. In contrast, θ is the angle between the free layer magnetization and the easy axis of the device, respectively. Angles β and θ can be varied from 10° to 90° as an increment of 10°. The maximum obtained frequency of the device of about 215 GHz, and PSD of 1.7 μW/mA2/GHz with CIOF as 50 kA/m. We suggest the device is an ideal candidate for ultra High-Frequency and unveils a new path for foreseeable spintronic devices.