Magnon-driven stochastic spin Hall nano-oscillators

The recent demonstration of pure spin current-induced spin-transfer torque arising from the spin Hall effect (SHE) represents an efficient route to controlling the magnetization dynamics in magnetic nanostructures. In a ferromagnet /heavy metal bilayer, a pure spin current is generated when a longitudinal charge current passes through the HM and induces a transverse spin current due to the strong spin-orbit coupling in the HM [1, 2]. The conversion of the charge current density (JC) to pure spin current density (JS) is characterized by the spin Hall angle (θSHA) in these bilayers. The pure spin current may be sufficient to excite perpetual self-oscillations in the magnetization, which can further induce spin waves in these systems. This is of particular interest for spintronics applications and has led to a new class of microwave devices called spin Hall nano-oscillators (SHNOs) [3,4]. Generating higher spin current densities through a higher θSHA is necessary to improve the performance of SHNOs and to avoid higher charge current densities. So far, studies have focused on different HMs with various spin-orbit coupling strengths to generate higher spin current---for example, the β-phase of W, Ta, or NixCu1-x. In this work, we demonstrate the compositional effect on the magnetodynamic and auto-oscillations properties of Ni100-xFex/Pt (x= 10 to 40) nanoconstriction based spin Hall nano-oscillators [5].The devices are fabricated from Ni100-xFex(5) /Pt (6) bilayer (thicknesses in nanometers) deposited in a high vacuum magnetron sputtering chamber where Ni-Fe alloys were co-sputtered under the same conditions and from pure Ni and Fe targets, where the composition was established by varying the respective plasma powers. Two kinds of spin Hall devices were fabricated from each film: (1) 8 x 16 μm2 rectangular stripes and (2) nanoconstriction-based SHNOs with a width of 140 nm.We first discuss the ST-FMR spectra measured on rectangular stripes to determine the variation of the magnetodynamics with the Fe content. We measure an increase in the magnetization (μ0Ms) and a decrease in the Gilbert damping. In addition to that, we measure a reduction of the impact of spin-torque on the ST-FMR linewidth with the dc current (μ0ΔH/ I) as Fe content increases Fig. 1(a). This is translated into a reduction in the spin Hall angle with the increase of Fe content as shown in Fig. 1(b). The reduction in the spin Hall angle can be correlated primarily to the compositional effect: the spin Hall angle scales inversely proportional with the saturation magnetization. Note that the observed variation of spin Hall angle with increasing Fe content is also qualitatively consistent with the decrease of damping as a function of the Fe content, and can be well explained in terms of the spin transport model Ref. [6]. The suppression of spin pumping due to increased μ0Ms should result in lowering the effective spin mixing conductance and therefore spin-torque efficiency, which can be seen as a monotonic decrease of spin Hall angle with increasing Fe content in Fig. 1(b).Next, we turn to discuss the compositional effect on the characteristics of auto-oscillations in nanoconstriction-based SHNOs. We record the generated microwave power spectral density (PSD) as a function of a direct current (I) under an in-plane magnetic field μ0H = 0.05 T using a spectrum analyzer and a low noise amplifier with a +33 dB gain. The spectral characteristics of the auto-oscillations i.e. frequency, power, and linewidth were extracted from the PSD. It is interesting to note that the onset auto-oscillation frequency differs between devices, i.e. the onset frequency shifts up for Fe-rich devices due to higher magnetization. The integrated power varies with the dc current, showing a bell shape of amplitude around 1 pico-watt. A qualitative comparison between the power of devices shows that Fe-rich devices have lower output power. This is understood as the readout of devices depends on AMR and as the AMR drops in Fe-rich devices the power follows. Finally, the measured auto-oscillations have linewidths around 50 MHz.The threshold current for auto-oscillations, (Ith), is extracted from plots of p-1 vs. I, [7] as shown in the inset of Fig. 1(c). For Fe-rich devices, higher currents are required to excite auto-oscillations. The enhancement in threshold current densities for Fe-rich devices is a direct consequence of the reduction in the spin Hall angle.Our experimental results show that the dominant compositional effect is from the magnetization that plays a central role in determining the characteristics of the spin Hall devices. **

Pure spin currents produced by the spin Hall effect(SHE) in a nonmagnetic heavy metal has the potential to drive ultra-fast, energy-efficient spintronic devices such as spin Hall nano-oscillators(SHNOs)[1-3], spin-orbit torque based magnetic random access memory(SOT-MRAM), and spin logic devices[4,5]. One key challenge in such emerging devices remains to reduce their high current densities(Jc) and energy consumption to drive magnetization switching and auto oscillations in the adjacent ferromagnets. Efforts have been made to increase the SOT efficiency(ζSOT) by choosing suitable material combinations and/or use oxygen incorporation[6]. However, the increased ζSOT is observed at the expense of an equivalent increase in the longitudinal resistivity(ρ), which essentially cancels out any reduction in the power consumption. A more successful direction is instead to alloy elements, which are in themselves already good SOT material[7].Here, we demonstrate such alloying of W with Ta to obtain a simultaneous increase of both the ζSOT and the spin Hall conductivity(σSH), which in turn substantially reduces the Jc in W100-xTax(5nm)/CoFeB(tCFB=1.4 to 2 nm)/MgO(2nm) SHNOs. First, we performed STFMR measurements on microbars (6 ×18 µm2, 6 ×12 µm2) to determine their magnetodynamical properties such as current induced ζSOT and σSH. The ζSOT varies from maximum ~ -0.57(x=10%) to ~-0.18(x = 50%) as compared to pure β-W, ~-0.36(x=0). Thanks to a reduced resistivity of W100-xTax, the increased ζSOT is accompanied with a significant increase of the σSH of about ~140% as compared to pure β-W. Finally, we investigated the alloying effect on the auto-oscillation threshold current(Ith) densities by fabricating SHNOs of different widths varying from 10nm to 150nm on a 4 × 14 µm2 mesa[1] and observed about 40% reduction in Ith (at x=12%) as compared to pure β-W measured. The trade-off between ζSOT, ρ, and σSH demonstrates the promising aspects of a W-Ta alloying approach for energy-efficient operation of emerging spintronic devices  Fig.1: (a) Variation of ρ(blue) and σSH(red) vs. W100-xTax alloy composition. (b-c) Power spectral densities showing a 40% reduction in the SHNO Ith for two SHNOs with identical constriction width of 50nm.

Spin Hall nano-oscillators (SHNOs) have the unique ability to convert a direct current input to microwave signals by means of spin Hall effect and spin orbit torque [1]. The generated microwave signals depend on several factors inherent to having a flow of direct current such as the current density, Oersted fields, Joule heating and naturally the magnetic state in a given device geometry. In addition, other factors such as frequency locking or synchronisation onto an external microwave source can contribute to the microwave output of a given SHNO [2-5]. The interplay of all these factors affects the agility of the magnetisation auto-oscillations of an SHNO. We report the study of SHNOs while subject to current pulses as well as RF pulses, measured using time resolved micro-focused Brillouin light scattering (micro-BLS). The SHNOs under test consist of a double-disk constriction of NiFe(5 nm)/Pt(7 nm). First, we discuss how few-nanosecond pulses can still efficiently induce magnetisation auto-oscillations, thereby demonstrating that both the onset and outset of the auto-oscillations occur within a sub-nanosecond timescale. Then, we proceed to showing how auto-oscillations can be affected by external microwave pulses. Various degrees of enhancement (injection-locking) or suppression of the auto-oscillation signal can be achieved by choice of the frequency and the amplitude of the external microwave signal. The knowledge of the agility or the response to either intended or unwanted parasitic external excitations is paramount for SHNOs to be able to operate on very short time-scale with well defined responses in, for example, the context neuromorphic computing [6].

Synchronization of large spin Hall nano-oscillators (SHNO) arrays is an appealing approach toward ultra-fast non-conventional computing based on nanoscale coupled oscillator networks [1]. However, for large arrays, interfacing to the network, tuning its individual oscillators, their coupling, and providing built-in memory units for training purposes, remain substantial challenges. Here, we address all these challenges using memristive gating of W/CoFeB/MgO/AlOx based SHNOs. We use this type of stack as their substantial perpendicular magnetic anisotropy (PMA) can generate both localized and propagating spin waves [2]. In its high resistance state (HRS), the memristor modulates the perpendicular magnetic anisotropy (PMA) at the CoFeB/MgO interface purely by the applied electric field, which leads to both a voltage-controlled SHNO frequency and a voltage-controlled threshold current [3]. In its low resistance state (LRS), and depending on the voltage polarity, the memristor adds/subtracts a current Im to/from the SHNO drive. The operation in this LRS also affects the SHNO auto-oscillation mode and frequency, which can be tuned up to 28~MHz/V. This tuning allows us to reversibly turn on/off mutual synchronization in chains of four SHNOs and turn the chain into different partially synchronized states [4]. Memristor gating is, therefore, an efficient approach to input, tune, and store the state of the SHNO array for any non-conventional computing paradigm, all in one platform. Examples include SHNO based Ising Machines [5,6] and pattern recognition using memristive-controlled SHNO chains [4], which will both be discussed in detail in the presentation.

Spin Hall nano oscillator (SHNO), a new type spintronic nano-device, can electrically excite and control spin waves in both nanoscale magnetic metals and insulators with low damping by the spin current due to spin Hall effect and interfacial Rashba effect. Several spin-wave modes have been excited successfully and investigated substantially in SHNOs based on dozens of different ferromagnetic/nonmagnetic (FM/NM) bilayer systems (e.g., FM = Py, [Co/Ni], Fe, CoFeB, Y3Fe5O12; NM = Pt, Ta, W). Here, we will review recent progress about spin-wave excitation and experimental parameters dependent dynamics in SHNOs. The nanogap SHNOs with in-plane magnetization exhibit a nonlinear self-localized bullet soliton localized at the center of the gap between the electrodes and a secondary high-frequency mode which coexists with the primary bullet mode at higher currents. While in the nanogap SHNOs with out of plane magnetization, besides both nonlinear bullet soliton and propagating spin-wave mode are achieved and controlled by varying the external magnetic field and current, the magnetic bubble skyrmion mode also can be excited at a low in-plane magnetic field. These spin-wave modes show thermal-induced mode hopping behavior at high temperature due to the coupling between the modes mediated by thermal magnon mediated scattering. Moreover, thanks to the perpendicular magnetic anisotropy induced effective field, the single coherent mode also can be achieved without applying an external magnetic field. The strong nonlinear effect of spin waves makes SHNOs easy to achieve synchronization with external microwave signals or mutual synchronization between multiple oscillators which improve the coherence and power of oscillation modes significantly. Spin waves in SHNOs with an external free magnetic layer have a wide range of applications from as a nanoscale signal source of low power consumption magnonic devices to spin-based neuromorphic computing systems in the field of artificial intelligence.

Since the advent of spin-torque nano-oscillators (STNOs) {1}, mutual synchronization of two or more STNOs has been of intense interest as it not only improves both the microwave signal power and the signal quality factor (Q-factor) appealing to communication technology but can also be used directly for neuromorphic computing due to the tunable magnetic nature of the interaction between STNOs. Thanks to the spin Hall effect, a new class of spintronic oscillators known as spin Hall nano-oscillators (SHNOs) has emerged. Compared to STNOs, they rely on the current flowing in-plane, which makes their fabrication easier and allow for a large number of SHNOs to synchronize in both chains and arrays. {5,6}In this work, we explore mutual synchronization in nano-constriction (NC) based SHNO chains and demonstrate robust synchronization of SHNOs for longer chains with up to 21 Oscillators [Fig. 1(a&b)]. We investigate both NiFe(4 nm)/Pt(5 nm) {6,7} and W(5 mm)/CoFeB(1.4 nm)/MgO(2 nm) {8,9} SHNOs. We report that the robust mutual synchronization can deliver an enhanced output power and significantly lower linewidth (Fig. 2(a&b)). A sub-MHz linewidth [Fig. 2(b), as low as 300 kHz for NiFe/Pt] can be achieved for 21 synchronized oscillators. The high-frequency operation results in a very high quality factor (Q=f/△f) of >30,000 for NiFe/Pt and >25000 for W/CoFeB/MgO, which is the highest reported in chains. A linear decrease in linewidth and increase in output power (up to in-phase synchronization) is observed with the number of oscillators [Fig. 2(c)]. The low current and low field operation of these oscillators along with wide frequency tunability (2-28 GHz) with both current and magnetic fields, make these oscillators ideal candidates for various spintronic applications.   Robust mutual synchronization of spin Hall nano-oscillator chains

Spin Hall nano-oscillators (SHNOs) are emerging spintronic oscillators with significant potential for technological applications, including microwave signal generation, and unconventional computing. Despite their promising applications, SHNOs face various challenges, such as high energy consumption and difficulties in growing high-quality thin film heterostructures with clean interfaces. Here, single-layer topological magnetic Weyl semimetals open a possible solution as they possess both intrinsic ferromagnetism and a large spin-orbit coupling due to their topological properties. However, producing such high-quality thin films of magnetic Weyl semimetals that retain their topological properties and Berry curvature remains a challenge. We address these issues with high-quality single-layer epitaxial ferromagnetic Co2MnGa Weyl semimetal thin film-based SHNOs. We observe a giant spin Hall conductivity, σSHC = (6.08 ± 0.02) × 105 (ℏ/2e) Ω-1 m-1, which is an order of magnitude higher than previous reports. Theoretical calculations corroborate the experimental results with a large intrinsic spin Hall conductivity due to presence of a strong Berry curvature. Further, self spin-orbit torque driven magnetization auto-oscillations are demonstrated for the first time, at an ultralow threshold current density of Jth = 6.2 × 1011 A m-2. These findings indicate that magnetic Weyl semimetals have tremendous application potential for developing energy-efficient spintronic devices.

Oscillator-based data-classification schemes have been proposed recently using the Kuramoto model which predicts synchronization behaviour of coupled oscillators through a general framework neglecting underlying physics [1,2]. Here we propose hardware implementation of a Kuramoto-model-based data-classification scheme through an array of dipole-coupled uniform-mode spin Hall nano-oscillators (SHNOs) [2,3].Using micromagnetic simulations on 'mumax3' software [4], which actually capture physics of SHNOs, we first study how synchronization range between two uniform-mode SHNOs (150 nm diameter) varies with physical distance between them (Fig. 1b). Thus we correlate the coupling constant in Kuramoto model (Fig. 1a) with dipole-coupling strength between two SHNOs in 'mumax3' (Fig. 1b) .Using this correlation, we generate a synchronization map for a two-input-two-output dipole-coupled uniform-mode SHNO system through micromagnetics (Fig. 2a). Red circles show frequency values of input oscillators (F1,F2) for which the two output oscillators are synchronized, and black circles show (F1,F2) for which they are not. These data points coincide with pink region showing sync. and grey region showing de-sync., obtained from Kuramoto model (Fig. 2a). Thus we establish here that synchronization behaviour of SHNOs obtained from physics-based modeling (micromagnetics) is consistent with that obtained from Kuramoto model, where underlying physics of SHNOs is ignored. This shows that a Kuramoto-model-based data classification scheme [2] can indeed be implemented on an array of SHNOs.Next we show, through micromagnetics, classification of data from a popular data set (Fisher's Iris [5]) using an array of uniform-mode SHNOs. While distinguishing flowers in Iris of Setosa type from Virginica type, output oscillators synchronize for Setosa and desynchronize for Virginica (Fig. 2b). The obtained accuracy is 98.67%  Fig. 1. For a two-oscillator system, coupling constant in Kuramoto model (a) is correlated with distance between two SHNOs in micromagnetics (b) using the synchronization-range values.  Fig. 2. Synchronization map of the two-input-two-output oscillator system in (a) (details in text) used for data classification from Iris set (b)

Spin Hall nano-oscillators (SHNOs) exploiting current-driven magnetization auto-oscillation have recently received much attention because of their potential for neuromorphic computing. Widespread applications of neuromorphic devices with SHNOs require an energy-efficient method of tuning oscillation frequency over broad ranges and storing trained frequencies in SHNOs without the need for additional memory circuitry. While the voltage-driven frequency tuning of SHNOs has been demonstrated, it was volatile and limited to megahertz ranges. Here, we show that the frequency of SHNOs is controlled up to 2.1 GHz by an electric field of 1.25 MV/cm. The large frequency tuning is attributed to the voltage-controlled magnetic anisotropy (VCMA) in a perpendicularly magnetized Ta/Pt/[Co/Ni]n/Co/AlOx structure. Moreover, the non-volatile VCMA effect enables cumulative control of the frequency using repetitive voltage pulses which mimic the potentiation and depression functions of biological synapses. Our results suggest that the voltage-driven frequency tuning of SHNOs facilitates the development of energy-efficient neuromorphic devices.

Spin Hall nano oscillators (SHNOs) have attracted much attention in recent years due to their great potential for applications in neuromorphic computation. However, the output power of SHNOs is very low and an external magnetic field is required to generate microwave signal continuously, which hinders the further development of SHNOs. In order to solve the two problems, we propose a new-type SHNO based on the giant magnetoresistance (GMR) effect, while retaining the advantage of the simple fabrication process of the conventional oscillator. The huge magnetoresistance ratio provided by the GMR effect can increase the power of this novel oscillator by several orders of magnitude. In addition, by designing the magnetization easy axis of the free and reference layers in the GMR film layers, this novel oscillator can operate effectively without the need of and external magnetic field. Furthermore, we have preliminarily investigated the feasibility of electrical synchronization in the field of SHNOs from the perspective of microspin simulation and found that parallel connection can provide stronger coupling strength compared with series connection. Our research solves the core problems that currently hinder the further development of SHNOs, facilitating the realization and application of large-scale synchronized array of SHNOs.

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. GHz spin Hall nano-oscillators (SHNOs) are a particularly attractive technology for building fast, energy-efficient, and scalable Ising machines; however, electrical coupling mechanisms which allow for full programmability among different oscillator nodes have not yet been fully demonstrated in such a network. Here, we develop a general analytical framework that can describe injection locking of SHNOs with arbitrary oscillation orbits at both the fundamental frequency and harmonics. With this compact analytical framework, we integrate the SHNO into a Verilog-A device model that can emulate the oscillator’s injection locking behavior in circuit simulations, where the dynamics of coupled oscillator networks are simulated together with conventional electronic components (Fig. 1). While our abstract circuit simulations achieve similar accuracy as full micromagnetic simulations, the device model we developed leads to more than 100 times improvement in simulation efficiency and allows us to evaluate the performance using realistic circuits.Using circuit-level simulations, we further study the effects of phase noise and scalability in networks of up to hundreds of coupled oscillators to show that the SHNO-based Ising machine can be operated robustly at room temperature. Compared with existing technologies, SHNO networks exhibit orders of magnitude improvement in time, space, and energy efficiency (Table 1). Our results provide analytical tools and design insights that will be useful for the realization of a CMOS-integrated SHNO Ising machine.  Fig. 1: (a) Electrical coupling circuit linking two SHNOs in the oscillator-based Ising machine. (b) Phases of oscillators in a 4-node coupled network solving the Ising model in circuit simulations (HSPICE) using our abstract device model and in micromagnetic simulations (MuMax3).  Table 1: Comparison of speed, energy, and space metrics between the SHNO Ising machine and existing technologies. Values are standardized to a 100-node network.

Spin Hall nano-oscillators (SHNOs) are emerging spintronic devices for microwave signal generation and oscillator-based neuromorphic computing combining nano-scale footprint, fast and ultra-wide microwave frequency tunability, CMOS compatibility, and strong non-linear properties providing robust large-scale mutual synchronization in chains and two-dimensional arrays. While SHNOs can be tuned via magnetic fields and the drive current, neither approach is conducive to individual SHNO control in large arrays. Here, we demonstrate electrically gated W/CoFeB/MgO nano-constrictions in which the voltage-dependent perpendicular magnetic anisotropy tunes the frequency and, thanks to nano-constriction geometry, drastically modifies the spin-wave localization in the constriction region resulting in a giant 42% variation of the effective damping over four volts. As a consequence, the SHNO threshold current can be strongly tuned. Our demonstration adds key functionality to nano-constriction SHNOs and paves the way for energy-efficient control of individual oscillators in SHNO chains and arrays for neuromorphic computing.

Oscillator-based data-classification schemes have been proposed recently using the Kuramoto model, which tries to capture the synchronization behavior of coupled oscillators without considering the underlying physics of the oscillation and the coupling. In this paper, we propose the hardware implementation of a Kuramoto-model-based data-classification scheme through an array of dipole-coupled uniform-mode spin Hall nano-oscillators (SHNOs). Using micromagnetic simulations, which capture the underlying physics of operation of the SHNOs, we first study the variation of synchronization range between two uniform-mode SHNOs as a function of the physical distance between them. Thus we correlate the coupling constant in the Kuramoto model with the dipole-coupling strength between two SHNOs, which our micromagnetic simulation takes into account. Next, we generate the synchronization map for the two-input–two-output dipole-coupled uniform-mode SHNO system through micromagnetics and show that it matches with the one predicted by the Kuramoto model. Thus, we demonstrate here that the synchronization behavior of SHNOs obtained from micromagnetics-based modeling is consistent with that obtained from the Kuramoto model, which ignores the underlying physics of the SHNOs. This suggests that the Kuramoto-model-based data classification scheme can indeed be implemented physically on an array of SHNOs. To verify our claim, we show, through micromagnetic simulation, binary classification of data from a popular machine-learning data set (Fisher’s Iris data set) using an array of uniform-mode SHNOs.

We demonstrate low-operational-current W/Co20Fe60B20/MgO spin Hall nano-oscillators (SHNOs) on highly resistive silicon (HiR-Si) substrates. Thanks to a record high spin Hall angle of the β-phase W (θSH = −0.53), a very low threshold current density of 3.3 × 107 A/cm2 can be achieved. Together with their very wide frequency tunability (7–28 GHz), promoted by a moderate perpendicular magnetic anisotropy, HiR-Si/W/CoFeB based SHNOs are potential candidates for wide-band microwave signal generation. Their CMOS compatibility offers a promising route towards the integration of spintronic microwave devices with other on-chip semiconductor microwave components.

We demonstrate highly efficient spin Hall nano-oscillators (SHNOs) based on NiFe/β-W bilayers. Thanks to the very high spin Hall angle of β-W, we achieve more than a 60% reduction in the auto-oscillation threshold current compared to NiFe/Pt bilayers. The structural, electrical, and magnetic properties of the bilayers, as well as the microwave signal generation properties of the SHNOs, have been studied in detail. Our results provide a promising path for the realization of low-current SHNO microwave devices with highly efficient spin-orbit torque from β-W.