Spin Hall nano-oscillators (SHNOs) are miniaturized, ultra-broadband, microwave signal generators based on the spin Hall effect that converts a direct charge current into a transverse pure spin current, producing a spin-transfer torque into an adjacent ferromagnetic layer, which in turn excites spinwave (SW) auto-oscillations. Nano-constriction SHNOs [1] offer several advantages, thanks to their simple bilayer structure, such as significant freedom in device fabrication, material, and layout, and direct optical access to the active auto-oscillating region. SHNOs also exhibit robust frequency response [2], easy injection locking [3], and robust mutual synchronization [4]. These properties make them ideal candidates for broadband microwave signal generation, processing, and nonconventional oscillator computing.
Here we show how the controlled synchronization of SHNOs enables multiple forms of computing and demonstrations of robust mutual synchronization of two-dimensional SHNO arrays [5] (fig1.a) ranging from 2 × 2 to 8 × 8 nano-constrictions, which is observed both electrically and using micro-Brillouin light scattering microscopy (fig1.b.) Furthermore, using injection locking, we show that these SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps (fig 1.d) as ones used for neuromorphic vowel recognition [6].
SHNOs are also potentially very appealing for oscillator network based Ising machines. Ising Machines are physical systems designed to find solutions to combinatorial optimization (CO) problems by using binary spins (Ising model). One promising approach is to use interacting non-linear oscillators that have been locked in phase to a signal at double their natural frequency. We show how phase-locked spin-Hall nano-oscillators, through the injection locking of a microwave frequency at the second harmonic, show a phase binarizations, see fig.2.(a-e), and can be used as computing units in Ising machines [7].
The core functionality required for real-world implementation of SHNOs for such potential computing applications is the individual control of the oscillators through external signal, we will show that such oscillators can be externally controlled in several ways including through optical control (fig2.f) [8]. Our demonstration of optical tuning of SHNOs might open up novel optical annealing schemes applicable to Ising machines, as well as for other computing applications. Furthermore, we discuss SHNOs readout using as well different means, which opens the way for two-dimensional synchronized SHNO networks for ultra-fast neuromorphic computing. 

**References:** 

[1]. V. E. Demidov et al., Appl. Phys. Lett. 105, 172410 (2014). 
[2]. A.A. Awad et al., Appl. Phys.Lett 116, 232401 (2020). 
[3]. T. Hache et al., Appl. Phys. Lett. 114,192405 (2019). 
[4]. A. A. Awad et al., Nat.Phys. 13, 292 (2017). 
[5]. M. Zahedinejad et al., Nat. Nanotechnol. 15, 47 (2020). 
[6]. M. Romera et al., Nature 563, 230 (2018). 
[7]. A. Houshang et al., Phys. Rev. Appl. 17, 014003 (2022). 
[8]. S. Muralidhar et al., Appl. Phys. Lett. 120, 262401 (2022). 

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Synchronization of Spin Hall nano

We use nanocontact spin-torque oscillators (STNOs) to explore the applied field and current dependence of magnetic droplets. These dissipative solitons are found in
magnetic layers with perpendicular anisotropy, and they are inherently dynamic and characterized by a core of reversed spins surrounded by a precessing perimeter [1, 2, 3, 4]. The
precession frequency lies between the ferromagnetic and Zeeman resonances, but the droplet is also prone to drift which gives additional dynamics [5, 6]. Orthogonal pseudo-spin-valves
are usually used in experiments to harvest a strong magnetoresistive dynamic signal [2, 3, 5, 6], but here we use an all-perpendicular layout to study the otherwise inaccessible low field
region.
Electrical measurements reveal that the droplet transforms, freezes, into a static bubble at low fields. Figure 1 illustrates the electrical characteristics of the different states. The resistance is
similar for the droplet and the bubble (Fig. 1a), but the difference in noise level is striking (Fig. 1b) and demonstrates the bubble’s static nature. Once formed, the bubble is stable without a
sustaining current. Furthermore, the droplet-to-bubble transition is fully reversible, and the bubble can thaw back to a droplet at sufficient high field and current. The findings are
corroborated by X-ray microscopy, which images the magnetic states during the freezing. Experimental data together with simulations identify pinning as the main mechanism behind the
bubble stability. 
**References** 
[1] Hoefer et al., Theory for a dissipative droplet soliton excited by a spin torque nanocontact Phys. Rev. B 82, 054432 (2010) 
[2] Mohseni et al., Spin Torque–Generated Magnetic Droplet Solitons Science 339, 1295 (2013) 
[3] Chung et al., Spin transfer torque generated magnetic droplet solitons (invited) J. Appl. Phys 115, 172612 (2014) 
[4] Chung et al., Direct Observation of Zhang-Li Torque Expansion of Magnetic Droplet Solitons Phys. Rev. Lett. 120, 217204 (2018) 
[5] Xiao et al., Parametric autoexcitation of magnetic droplet soliton perimeter modes Phys. Rev. B 95, 024106 (2017) 
[6] Chung et al, Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators Nature Com. 7, 11209 (2016) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/bcccafe9855d49eedd92e0414da5c481.png) 
Figure 1: Phase diagrams based on the resistance and the microwave noise. (a) STNO resistance and (b) integrated (0–0.5 GHz) microwave noise level as a function of field and current. (c)
shows the noise level in (b) overlaid on the resistance in (a) displayed using a gray scale highlighting intermediate resistance levels indicative of droplets/bubbles. The parallel (P) and
antiparallel (AP) states are easily discernible in the MR-map (a) as dark blue and dark red, while both the droplet and the bubble are characterized by intermediate resistance in green–
yellow. The stark difference between the droplet and the bubble is revealed in the noise spectrum (b), where the stability of the bubble is manifested. Note however that the light-blue
flanges in (a) correspond to a different droplet regime not captured in the microwave signal presented in (b).

Freezing and thawing magnetic droplet solitons

Spintronics utilizes the spin orbit coupling (SOC) of a heavy metal layer to generate spin currents by the spin Hall effect (SHE), which can then induce spin orbit torques (SOT) to alter the magnetization of an adjacent ferromagnet. SOT can be both fast and energy-efficient and enable technological applications in spintronic devices such as spin Hall nano-oscillators (SHNOs) [1-3], SOT based magnetic random access memory(SOT-MRAM), and spin logic devices [4,5]. However, spin currents generated by SOC also exist in magnetic materials. Recent studies evidenced very large emission of spin currents and strong SOT for magnetization switching in ferrimagnets near compensation [6,7].
In the present study nearly compensated GdFeCo, and Py, are used as spin Hall layer and ferromagnetic layer, respectively. We studied the tunable behaviour of both damping-like(DL) and field-like(FL) SOT efficiencies (θDL and θFL) with respect to a Cu insertion layer in Gd26.7(FeCo)73.3 (10 nm)/Cu(1-5 nm)/Py(3 nm) stack. We performed spin transfer torque ferromagnetic resonance (ST-FMR) measurements on microbars (6 ×12 μm2) to determine the magneto dynamical properties such as current induced DL and FL SOT efficiencies. Figure 1 (a) and (b) show the ST-FMR spectra in the frequency range of 10-15 GHz, and the corresponding linewidth vs. frequency plot of Gd26.7(FeCo)73.3 (10 nm)/Cu(4 nm)/Py (3 nm); (c) and (d) show the Cu thickness dependent SOT efficiencies at f=8 GHz. The DL-SOT efficiency is found to be maximum, θDL~ 20%, at Cu (2 nm) followed by a decreasing trend at higher Cu thicknesses. However, FL-SOT efficiency shows a minimum, θFL~ 10%(-7%), up to Cu (2 nm) followed by ~-53%(48%) at Cu (5 nm) for +ve(-ve) direction of applied magnetic field. The larger value of θFL at higher Cu thickness will be useful for ultrafast current induced magnetization switching as seen in other ferrimagnetic systems. 
**References**
1. H. Mazraati et al., Low operational current spin Hall nanooscillators based on NiFe/W bilayers, Appl. Phys. Lett. 109, 242402 (2016).
2. H. Fulara et al., Spin-orbit torque–driven propagating spin waves, Sci. Adv. 5, eaax8467 (2019).
3. M. Zahedinejad et al., Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing. Nat. Nanotechnol. 15, 47–52 (2020).
4. K. Garello et al., Ultrafast magnetization switching by spin-orbit torques, Appl. Phys. Lett. 105, 212402 (2014).
5. M. Cubukcu et al., Spin-orbit torque magnetization switching of a three-terminal perpendicular magnetic tunnel junction, Appl. Phys. Lett. 104, 042406 (2014).
6. D. Céspedes-Berrocal et al., Current-induced spin torques on single GdFeCo magnetic layers, Adv. Mater., 33, 2007047(2021).
7. R. Mishra et al., Anomalous Current-Induced Spin Torques in Ferrimagnets near Compensation, Phys. Rev. Lett. 118, 167201 (2017). 
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Tunable spin orbit torques in Ferrimagnet/Ferromagnetic heterostructures

Due to their high spin polarization and easy manipulation, ferromagnetic materials dominate as the magnetically active element in spintronic devices but come with drawbacks such as large stray fields, limited scalability, and limited operational frequencies [1-3]. These shortcomings have recently inspired researchers to consider antiferromagnetic spintronics [4], as antiferromagnetic materials have no stray fields and possess ultrafast spin dynamics. However, antiferromagnets have no net magnetic moment, which leads to weak read-out signals and more difficult operation. Compensated ferrimagnets (FiMs) provide an alternative as they combine the properties of ferromagnets and antiferromagnets. In particular, FiMs can have near THz resonances as in antiferromagnets, while still having a net magnetic moment which can be used for strong read-out signals and frequency control, such as efficient tunable microwave signal output from FiM based nano-oscillators. Due to these unique properties, research in FiMs for spintronic applications is intensifying [5-7]. However, to use ferrimagnets in spintronic devices such as in spin Hall nano-oscillators (SHNOs), it is important to ensure that such films retain their advantageous properties in ultrathin films and in nano devices.
In the present study, ferrimagnetic GdFeCo thin films were grown using co-sputtering of Gd and Fe87.5Co12.5 on high resistance Si (100) substrates, and their magnetodynamic properties were studied using broadband ferromagnetic resonance measurements at room temperature. By tuning the stoichiometry of the GdFeCo films, a nearly compensated behavior is for the first time demonstrated in 2 nm thin film, as shown in Fig. 1. Values for the effective magnetization and effective Gilbert damping constant (α) of 0.02 Tesla and 0.0078±0.0002 are obtained for a 2 nm Gd24.4(FeCo)75.6 film [8], where α is comparable to the lowest value obtained in thick films [9]. The vertical dotted lines in Fig. 1 show literature values [6, 9-10] for the spin angular momentum (xa) and magnetic momentum (xm) compensation points in thick films. The composition of the films for the magnetic moment and angular momentum compensation in this work is very close to those reported in the literature.
In search of high-frequency auto-oscillations in spin Hall nano-oscillators (SHNOs), constrictions with 50-300 nm widths were also prepared using GdFeCo(2-10nm)/Pt(5nm) based stacks. Brillouing Light Scattering microscopy measurements on SHNOs show auto-oscillations in the 8 GHz range, as shown in Fig. 2 [11]. Very interestingly, different Gd compositions result in different signs of the threshold current, which indicates different signs of the effective spin-orbit torque as a function of the composition. 

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Fig. 2. (a,b) Brillouin Light Scattering Spectroscopy (BLS) vs. current of two GdFeCo based SHNOs with different Gd content, believed to operate at opposite sides of the angular momentum conpensation point (SHNO temperature > RT due to Joule heating). While thermal SWs [ferromagnetic resonace (FMR)] are seen at all currents, the Gd rich SHNO only shows auto-oscillations (AO) at negative current, and the Gd poor SHNO only shows AO at positive current. (c,d) Log plots of the BLS counts from (a,b) for the thermal spin waves SWs (green) and the AO SWs (red). While the FMR show a slight current dependence due to heating, the AO intensity shows an initially exponential increase, as expected around threshold. Insets shows the BLS spectrum profile at the highest current.

**References:** 

[1] M. Romera et al., Nature 2018, 563, 230. 
[2] M. Zahedinejad et al., Nat. Nanotechnol. 15, 47 (2020). 
[3] B. Dieny et al., Nat. Elec. 3, 446 (2020). 
[4] T. Jungwirth et al., Nat. Nanotechnol. 11, 231 (2016). 
[5] S. K. Kim et al., Nat. Mat. 21, 24 (2022). 
[6] C. Stanciu et al., Phys. Rev. B 73, 220402 (2006). 
[7] D. Cespedes-Berrocal et al., Adv. Mat. 33, 2007047 (2021). 
[8] Lakhan Bainsla et al., Adv. Funct. Mater. 32, 2111693 (2022). 
[9] D.H. Kim et al., Phys. Rev. L 122, 127203 (2019). 
[10] Y. Hirata et al., Phys. Rev. B 97, 220403 (R) (2018). 
[11] L. Bainsla, A. A. Awad, J. Åkerman et al., unpublished.

Composition dependent threshold current polarity in ferrimagnetic spin Hall nano oscillators based on GdFeCo

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

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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.

Alloying effect on auto-oscillation properties of W100-xTax/CoFeB/MgO spin Hall nano-oscillators

Self-localized spin structures can substantially enrich the scope of the field-free antiferromagnetic spintronics [1]. One of them - the domain wall (DW) is a topological soliton that bridge a connection between two ground states, similar to a link in a Josephson junction (JJ) between two superconductors. JJs are intensively investigated for decades as they promise important advantages for electronics. In particular, JJ-based qubits are already successfully realized and commercialized. We demonstrate that the DW in bi-axial AFM with the easy-axis type of primary anisotropy driven by a spin current is a close analogy of a long Josephson junction (LJJ). Thus, the dynamics of the Neel vector angle inside the DW (Josephson phase Φ) is described by a sine-Gordon type of equation, where applied spin transfer torque (STT) represents a bias current through the junction, anisotropy in a basal plane defines a plasma frequency, and characteristic speed of magnons, defined by nonhomogeneous exchange energy, corresponds to Swihart velocity. In contrast with a conventional LJJ, a DW has additional degrees of freedom, namely the position of its center X and distribution of the current along a DW. We show by micromagnetic simulations, that when the polarization of the STT is parallel to the easy axis of an AFM, the above allows to nucleate and propel a single kink-type Φ soliton [2], which is Bloch line (Fig.1) that corresponds to the Josephson vortex in LJJ, as well as their series. Withal, a weak alternate current excites Φ-type intrawall spin waves, an analog of plasma waves in LJJ, which spectrum has a bandgap, defined by the anisotropy (Fig.2). STT with a perpendicular polarization allows manipulating the X position, particularly to excite the flexural vibrations of the DW with a gapless spectrum [3] (Fig.2). The variety of possible spin transport regimes together with the possibility of DW movement or bending under the action of applied spin current, offers considerable scope for developing novel spintronics devices.

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Generation of the Bloch line, - an anlog of the Josephson vortex.

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Dispersion law for Φ (red) and X (blue) intrawall modes in easy-axis Cr2O3 antiferromagnet with the presence of in-plane anisotropy.

Spin transport in a long Josephson junction based on an antiferromagnetic domain wall.

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.

Memristor-controlled mutual synchronization of spin Hall nano-oscillator arrays for neuromorphic computing and spintronic Ising machines

Topological spin structures, such as domain walls (DW) and skyrmions, have intriguing features and can play a key role in spintronics. In both ferromagnets (FM) and antiferromagnets (AFM) a DW, driven by applied torque, behaves like a solid particle, which can be described by collective variables: DW position and the angle of the magnetic order vector, albeit the dynamic properties are dramatically different. For an AFM the DW energy as a function of its momentum is the same as that of a standard relativistic particle (Fig. 1), because of the Lorentz invariance of the AFM dynamics [1]. For FMs the gyrotropic dynamic term couples two degrees of freedom that slows down a FM DW and results in the periodic dependence of the DW energy on momentum (Fig. 1). Thus, the AFM DW is stable up to higher speeds (~10km/s in contrast to ~100m/s for FMs). We demonstrate that the DW dynamics in ferrimagnetic (FiM) materials near the spin compensation point is entirely different from the FM and AFM cases [2]. The dispersion law for FiM DWs exhibits two crossed branches with opposite group velocities (Fig. 1), where each branch contains an endpoint [3]. Driven by a field-like torque, a FiM DW accelerates to a higher speed and momentum than its FM counterpart [4] and can reach the endpoint. Wherein it falls into a region of instability, where the internal dynamics of the DW is excited, and the collective variables approach fails. We show by micromagnetic simulations that the dynamical state of a DW in this case covers a wide frequency range, far beyond the magnon bandgap of a FiM. In this way the FiM DW driven by external field-like torque acts as an efficient source of the spin waves (SW), propagating out of the DW region. We show that by varying the applied torque and spin uncompensation of a FiM one can reach three qualitatively different regimes of the excited SWs: i) frequency-comb spectrum, shown in Fig.2, ii) chaotic behavior of the DW with the broad SW spectrum, iii) double-frequency SW excitation.

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Fig.1 Dependence of the energy on momentum for a DW in FM, AFM (gray), and FiM near compensation point (blue) nano-strips.

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Fig.2 Spectra of the dynamic state inside the DW (a) and magnons emitted outside (b).

Nonstationary domain wall dynamics in almost compensated ferrimagnets: a novel scenario

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 &gt;30,000 for NiFe/Pt and &gt;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.

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Robust mutual synchronization of spin Hall nano-oscillator chains

Robust mutual synchronization of spin Hall nano-oscillator chains

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.

**References:**

[1] J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999). [2] M. I. D’yakonov’ et al., J. Exp. Theor. Phys.Lett.13, 467 (1971). [3] V. E. Demidov, et al. ,Nat. Mater. 3459, 1028 (2012). [4] T. Chen et al., Proc. IEEE 104, 1919 (2016). [5] M. Haidar et al., Appl. Phys. Lett. 118, 012406 (2021). [6] M. W. Keller, et al., Phys. Rev. B 99,214411 (2019). [7] A. Slavin et al., IEEE Transactions on Magnetics 45, 1875 (2009).

**Images:**

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Fig. 1 (a, b) Variation in |μ0 ΔH /I| and the spin Hall angle (θSHA) as a function of Fe composition extracted from the ST-FMR measurements. (c) Threshold current vs. Fe concentration. Inset shows how the threshold is extracted from a linear fit of p−1 vs. I at low currents (dashed line).

 Compositional effect on spin-wave auto-oscillation behavior of Ni100-xFex/Pt spin Hall nano-oscillators

Mutually synchronized spin-torque nano-oscillators (STNOs) are one of the promising platforms for bioinspired computing and microwave signal generation [1]. Using STNOs one can achieve 90% recognition rate in spoken vowels [2]. However, in order to do more complex tasks, larger-scale synchronized oscillators are needed, something that is not easily done with the STNOs demonstrated so far. In my talk, I will describe a different type of spin current-driven device called spin Hall nano-oscillators (SHNOs), which can generate microwave frequencies over a very wide frequency range [3]. The SHNOs are based on 50 – 120 nm wide nano-constrictions in Pt(5)/Hf(0.5)/NiFe(3) trilayers (all numbers in nm). When multiple nano-constrictions are fabricated close to each other (300 – 1200 nm separation) they can mutually synchronize and chains of up to nine nano-constrictions have been demonstrated to exhibit complete synchronization [4]. For the first time, we can now also synchronize two-dimensional SHNO arrays with as many as 8 x 8 = 64 SHNOs [5]. The mutual synchronization is observed both electrically and using scanning micro-BLS microscopy. Both the output power and linewidth of the microwave signal improves substantially with increasing number of mutually synchronized SHNOs, such that quality factors of about 170,000 can be reached. Following the approach of Romera et al, we also demonstrate neuromorphic computing using a 4 x 4 SHNO array with two injected microwave signals as inputs. Given their high operating frequency (~10 GHz), easy fabrication, and highly robust synchronization properties, nano-constriction SHNO arrays are likely the most promising candidates for neuromorphic computing based on oscillator networks.References: [1] Torrejon J., et al. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428 (2017) [2] Torrejon J., et al. Vowel recognition with four coupled spin-torque nano-oscillators. Nature 563, 230 (2018) [3] Chen T., et al. Spin-torque and spin-Hall nano-oscillators. Proc. IEEE 104, 1919 (2016) [4] Awad A. A. et al. Long-range mutual synchronization of spin Hall nano-oscillators. Nature Physics 13, 292 (2017) [5] Zahedinejad M., et al. Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing. Nature Nanotechnology 15, 47 (2020)

2D Mutually Synchronized Spin Hall Nano-Oscillator Networks for Neuromorphic Computing INVITED

SF: Computing with Spintronic Oscillators

technical paper

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INTERMAG 2021

Q3: Neuromorphic Computing with Spin-Torque Oscillators

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SHORT BIO

Presentations

Synchronization of Spin Hall nano

Freezing and thawing magnetic droplet solitons

Tunable spin orbit torques in Ferrimagnet/Ferromagnetic heterostructures

Composition dependent threshold current polarity in ferrimagnetic spin Hall nano oscillators based on GdFeCo

Alloying effect on auto-oscillation properties of W100-xTax/CoFeB/MgO spin Hall nano-oscillators

Spin transport in a long Josephson junction based on an antiferromagnetic domain wall.

Memristor-controlled mutual synchronization of spin Hall nano-oscillator arrays for neuromorphic computing and spintronic Ising machines

Nonstationary domain wall dynamics in almost compensated ferrimagnets: a novel scenario

Robust mutual synchronization of spin Hall nano-oscillator chains

Compositional effect on spin-wave auto-oscillation behavior of Ni100-xFex/Pt spin Hall nano-oscillators

2D Mutually Synchronized Spin Hall Nano-Oscillator Networks for Neuromorphic Computing INVITED

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