United States

Soft magnetic elastomers (ME) are a class of smart materials consisting of magnetic particles dispersed within soft elastomer networks. Their excellent magnetic and
mechanical properties enable fast, untethered and reversible responses to external magnetic induction1. Magnetic field sensors have rather broad applicability in many biomedical
applications such as biological activity monitoring or medical devices navigation. Fiber-optic magnetic field sensors are promising alternatives to their electrical counterparts due to their
small size, low cost, no field-induced heating, intrinsic material safety and immunity to electromagnetic (EM) interference.2 Nevertheless, their development is largely limited by the low
sensitivity and reliability due to poor integration of magnetic materials with the optical fiber, and the complexity of the sensor design.
In this work, we proposed a compact design for a fiber-optic magnetic sensor based on highly responsive ME composites, which enables real-time measurement of small changes in
magnetic fields using interferometric interrogation scheme. Dip-coating method was introduced to directly deposit uniform ME composite films on the end of a single mode fiber and create
a interferometric structure for sensing of mechanical deformations induced by external magnetic field (Fig1 and 2). ME composites of different compositions and magnetic sensors with
various coating structures were developed and further optimized. A fiber-optic interferometric sensing system was established for magnetic actuation and sensing performance evaluation.
The proposed sensor exhibited excellent sensing performance enabling measurement of magnetic fields in millitesla level. These highly sensitive, miniature sensors are cost-effective,
simple in design, immune to EM interference and are well-suited to a wide range of biomedical applications. Further studies will entail simultaneous measurement of magnetic field and
gradient.&lt;br&gt;
**References:**&lt;br&gt;

1. Bira, N., Dhagat, P. &amp; Davidson, J. R. Front. Robot. AI 7, 1–9 (2020).&lt;br&gt;
2. Peng, J. et al. Sensors 19, 2860 (2019).&lt;br&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fabbf2674d23dae2b34b4d1060725834.png)&lt;br&gt;

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MMM 2022

Soft Magnetic Elastomer Composites Enabling Magnetic Actuation and Field Sensing Based on Fiber Optic Interferometry

Soft magnetic elastomers (ME) are a class of smart materials consisting of magnetic particles dispersed within soft elastomer networks. Their excellent magnetic and
mechanical properties enable fast, untethered and reversible responses to external magnetic induction1. Magnetic field sensors have rather broad applicability in many biomedical
applications such as biological activity monitoring or medical devices navigation. Fiber-optic magnetic field sensors are promising alternatives to their electrical counterparts due to their
small size, low cost, no field-induced heating, intrinsic material safety and immunity to electromagnetic (EM) interference.2 Nevertheless, their development is largely limited by the low
sensitivity and reliability due to poor integration of magnetic materials with the optical fiber, and the complexity of the sensor design.
In this work, we proposed a compact design for a fiber-optic magnetic sensor based on highly responsive ME composites, which enables real-time measurement of small changes in
magnetic fields using interferometric interrogation scheme. Dip-coating method was introduced to directly deposit uniform ME composite films on the end of a single mode fiber and create
a interferometric structure for sensing of mechanical deformations induced by external magnetic field (Fig1 and 2). ME composites of different compositions and magnetic sensors with
various coating structures were developed and further optimized. A fiber-optic interferometric sensing system was established for magnetic actuation and sensing performance evaluation.
The proposed sensor exhibited excellent sensing performance enabling measurement of magnetic fields in millitesla level. These highly sensitive, miniature sensors are cost-effective,
simple in design, immune to EM interference and are well-suited to a wide range of biomedical applications. Further studies will entail simultaneous measurement of magnetic field and
gradient. 
**References:** 

1. Bira, N., Dhagat, P. & Davidson, J. R. Front. Robot. AI 7, 1–9 (2020). 
2. Peng, J. et al. Sensors 19, 2860 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fabbf2674d23dae2b34b4d1060725834.png) 

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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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Thermal stability of the half-metallic band gap at the Fermi energy and high spin polarization of Co2FeAl0.5Si0.5 (CFAS) Heusler alloys (1,2) have made these systems attractive for spintronic applications. However, a stringent requirement is a controllable growth of highly ordered CFAS Heusler alloys. Moreover, giant magnetoresistance (GMR) (3,4) and the anomalous Hall effect (5,6) crucially depend on the magnitude of electrical resistivity (ρxx) and its temperature dependence. Thus, a complete understanding of the different contributions to ρxx is needed. To investigate the effect of film thickness on the structural- and electrical- properties, CFAS thin films of thickness, t, in the range 12 - 75 nm, were deposited by ultrahigh vacuum dc magnetron sputtering on Si(100) substrates with SiO2 buffer layer (300 nm), at the optimum substrate temperature of 500°C. The GIXRD patterns, shown in figure 1, reveal that B2 structural order grows with increasing t and peaks at t = 50 nm. The film with t = 75 nm showed A2 disorder. Irrespective of the magnitude of t, ρxx(T) goes through a minimum at Tmin. An elaborate quantitative analysis (6-8) of the ρxx(T, H=0) data, taken over the temperature range 5 K to 300 K, demonstrates that the electron-diffuson (e – d) and weak localization (WL) effects (responsible for the negative temperature coefficient of resistivity (TCR) for T < Tmin) compete with the electron-magnon (e – m) and electron-phonon (e – p) scattering (positive TCR) contributions to produce a minimum at Tmin. Figure 2 shows the normalized resistivity ρxx(T, H=0) / ρxx(T = 300 K, H=0) (open circles) along with the optimum theoretical fits (continuous lines), go through a minimum at Tmin. Consistent with the maximum B2 order at t = 50 nm, residual resistivity, ρ5K, and the e – d, wl, e - m and e - p scattering contributions to ρxx(T, H=0), ρe-d, ρwl, ρe-m and ρe-p, all go through a minimum at t = 50 nm. Regardless of t, the thermal renormalization of the spin-wave stiffness makes a significant contribution to ρe-m. 

**References:** 
(1) G. H. Fecher and C. Felser, J. Phys. D: Appl. Phys. 40, 1582 (2007). 
(2) Balke et al, Appl. Phys. Lett. 90, 242503 (2007). 
(3) Tezuka et al., Appl. Phys. Lett. 89, 112514 (2006). 
(4) Tezuka et al., Appl. Phys. Lett. 94, 162504 (2009). 
(5) A. Valet and T. Fret, Phys. Rev. B 48, 7099 (1993). 
(6) Hazra et al., Phys. Rev. B 96, 184434 (2017). 
(7) Srinivas et al., J. Non. Cryst. Solids 248, 211 (1999). 
(8) Kaul et al., Phys. Rev. B 33, 4987 (1986). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e37971143d1386fe7d1f4891815a9b3c.png)

Effect of film thickness on the electrical transport in Co2FeAl0.5Si0.5 thin films

Spin-orbit torques (SOTs) in heavy metal (HM)/ferromagnet (FM) have gathered much attention due to its potential for non-volatile, high-speed, and low-power spintronic devices [1-3]. While the majority of research has focused on the development of digital memories, previous studies on antiferromagnet (AFM)/FM structures showed field-free as well as analog-like (memristive) switching behavior [4,5], opening a new paradigm, the neuromorphic spintronics [6]. For applications, one needs to address a challenge that the memristive characteristics diminish with a reduction of device dimensions; for the case of PtMn/[Co/Ni] system, it totally disappears at around 200 nm [7,8]. In this study, we introduce a nanocomposite FM CoPtCrB towards SOT-based nanoscale memristors. A stack with Si sub./ Ta(4)/ Pt(4)/ CoPtCrB(7)/ Ru(1) is processed into single nanodot devices with various dot diameters (Ddot: 30-1000 nm) through the electron beam lithography and Ar ion milling. Memristive characteristics are studied by switching experiments with perpendicular magnetic fields or pulse currents (Ich) under an in-plane external field (Hx). Fig. 1 shows the results of SOT switching at Âµ0Hx = 90 mT for Ddot = 400 nm. Memristive behavior is observed, in contrast to the previous work with uniform FM exhibiting much fewer intermediate states [7]. Fig. 2 shows the obtained relationship between the square root of the number of intermediate states NIS and Ddot. Ddot below which devices show binary switching is around 60 nm, which is much smaller than the previous study (~ 200 nm) [7]. The present study demonstrates the potential of nanocomposite FM for nanoscale spintronic memristors. The authors thank A. Kurenkov, T. Koga, K. K. Tham, and S. Saito for their support. This work is partly supported by JST-CREST JPMJCR19K3, JSPS Kakenhi 19H05622, and RIEC Cooperative Research Projects. K. V. D. Z. acknowledges WISE program for AIE for financial support.

Memristive Spin Orbit Torque Switching in Nanocomposite CoPtCrB

Convolutional neural networks (CNN) are state of the art algorithms for image processing. Despite a small number of synaptic weights, the CNNs remain computationally costly to train in software due to the necessity to exchange huge data flows between memory and processing units. Unconventional hardware is suited to address this limitation. In neuromorphic spintronics, it has been previously demonstrated that the spin diode effect can be used to apply a synaptic weight on a radiofrequency signal [1][2]. Here we go a step beyond, to show an experimental implementation of a convolutional layer employing chains of spin-diodes. We design a compact architecture of 3 chains with 3 spin-diodes connected in series, that performs a padded convolution with a filter of 3 pixels on 5 input pixels multiplexed in frequency in one RF signal (See Figure 1). The synaptic weights corresponding to the filter are encoded by a small frequency detuning between the inputs and the spin-diodes resonance and are controlled in parallel using currents in 3 strip lines. This architecture exploits the intrinsic weight redundancy of convolutions (all filters share the same weights) to enhance the compacity of the hardware and greatly simplify the process of updating a weight, only requiring updating a the current in one strip line. We will also present processed experimental results highlighting the scalability of the proposed architecture. An error on the performed convolution as low as 0.28% was achieved (See Figure 2). The proposed architecture enables us to both reduce the size of this hardware implementation while, at the same time, performing the convolution in one timestep contrary to previous time-multiplexed implementations. According to a previous study [3] we can achieve to decrease by one order of magnitude the energy consumption compared to current GPUs and two orders of magnitude in operating latency. This proof of concept of spintronic CNN, opens the path to spintronic neural networks that can exploit the power of convolutional layers in a fully parallel, compact, and energy efficient way.

Fully Parallel Convolution with Chains of Spin

Writing using spin-orbit torque (SOT) has been widely investigated in the field of magnetic random-access memory (MRAM) as it provides several advantages over Spin transfer torque (STT) based writing, including a much faster writing speed, better writing endurance, and protection to MgO from oxide breakdown due to a large current flowing across it during STT writing process, among others. Heavy metal(HM)/CoFeB/MgO is the core of this SOT-MRAM structure. The heterostructure consisting of Ta as the spin current source and CoFeB/MgO as the perpendicular magnetic anisotropy (PMA) material is the most researched structure owing to the high tunneling magneto-resistance ratio. However, Ta is difficult to be integrated into the CMOS process due to its poor thermal stability against annealing at temperatures greater than 350 Â°C. Currently, Î²-Tungsten (W) is the only heavy metal with CoFeB/MgO system, which can provide both thermal stability and spin-orbit torque switching simultaneously. Nevertheless, achieving a high resistive Î² phase of W is a challenging task, and the high resistivity of Î²-W makes the devices susceptible to Joule's heating. Here, we report another material Rhenium (Re) capable of providing thermally stable PMA up to temperature 425 Â°C with a perpendicular anisotropic field greater than 5000 Oe; Re possesses a spin hall angle (Î¸SH) of 0.065 Â± 0.003 and spin-orbit torque switching can be achieved with current density around 1.36Ã—1011 A/m2. Our findings pave a new avenue for the material design of perpendicular SOT-based MRAM.

Spin orbit torque driven perpendicular magnetization switching in Re/CoFeB/MgO with high thermal stability.

Applying spintronics devices to neuromorphic computing have recently gained much attention. For example, a speech recognition task using a spin-torque oscillator (STO)
and based on the algorithm of physical reservoir computing was experimentally demonstrated [1]. In this experiment, the nonlinear magnetization dynamics in STO is used as a
computational resource, where the modulation of the dynamics due to the injection of human voice, converted to electric voltage, is used to recognize the input data. Therefore, it is
essential to investigate the relationship between the physical properties reflected in the magnetization dynamics and the computational capability of physical reservoir computing.
It has been widely believed that the computational capability of physical reservoir computing is enhanced at the edges of chaos because complex dynamics near the chaos is useful to
distinguish several kinds of input data. However, the physical reservoir computing in previous works has been performed in the dynamical state far away from chaos. Therefore, the
computational capability of STO near the edge of chaos is still unclear.
In this work, we investigated the relationship between the dynamical properties of STO and the computational capability in reservoir computing. We consider two kinds of STO, where the
one is a conventional STO consisting of a pinned (P) and free (F) layer, while the other, P/F/F, includes two free layers; see Fig. 1. This is because, in principle, the former cannot show
chaos while the latter has a possibility to show chaotic dynamics, and therefore, the comparison between them is useful to study the role of the chaos on the computational capability. We
evaluate the short-term memory capacity [2] as a figure of merit and the Lyapunov exponent [3] to distinguish the dynamical state. It was found that the short-term memory capacity in
P/F/F STO is greatly enhanced near the edge of chaos (see Fig. 2) and becomes much larger than the maximum value of the capacity in the conventional P/F STO.
References [1] J. Torrejon et al., Nature 547, 428 (2017).
[2] K. Fujii and K. Nakajima, Phys. Rev. Applied 8, 024030 (2017).
[3] S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, Boulder, CO, 2001). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/09c01428e1ce12b4a80fc7ddb5e1c030.png) 
Fig.1 Conceptual picture of (a) P/F and (b) P/F/F. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/03a7125ddd653ac21b4860e9c3be7f4c.png) 

Fig.2 (a) Short-term memory capacity and (b) Lyapunov exponent in P/F/F combination.

Computational Capability of Physical Reservoir Computing in Spin Torque Oscillator with Two Free Layers

Over the last decade, quantum systems offering new computational and sensing capabilities have emerged [1]. One of these promising hybrid systems involves the
interaction between photons and magnons. This interaction is quantitatively known by the strength coupling g and furthermore by its ratio with the cavity frequency g/ω. It exists three
different domains of this ratio: the Strong Coupling (SC) for g/ω < 0.1; the Ultra-Strong Coupling (USC) for 0.1 < g/ω < 1; and the Deep-Strong Coupling (DSC) for g/ω > 1. One of the
objectives of this last decade is to achieve the USC, and to approach the DSC [2]. A few experimental works already exist on the USC regime [3] and it is still complicated to understand
the different Hamiltonian approximations used to fit experimental data [2]. Here, we present a tuneable hybrid system which makes possible experimental observation of a coupling regime
from strong to ultra-strong at room temperature (RT).
The hybrid system presented here is made of a double re-entrant cavity and a commercial single crystal of YIG (see Fig. 1). It is possible to tune the ratio g/ω with decreasing the gap
between the top of pillars and cavity which will decrease ω without changing g. We optimized two different cavities considering two YIG shapes (sphere and slab). These two cavities work in the USC regime, from the SC/USC limit to g/ω = 0.6. One of these measures
is presented in Fig. 2 where is shown the S21 parameter according to a sweep on RF frequencies and the static H-field. With the use of Finite Element Modelling, we were able to follow the
coupling strength from the SC to the USC domains and were in a good agreement with measurements. We observed that the standard Hamiltonians (Dicke and Hopfield) do not describe
our system. With modifying the Dicke model with adding a frequency shift ωΔ on the FMR, we were able to fit measures and simulations. It should be noted that this added term is
proportional to g2/ω.
We demonstrated the capability of a 3D magnonic cavity to work in the USC regime and its tuneability
with playing with the gap. To reach the DSC, it will be interesting to work on other cavity shapes to have a bigger ratio g/ω.
**References** [1] D. Lachance-Quirion, Y. Tabuchi, A. Gloppe, Appl. Phys. Exp., vol. 12, p. 070101 (2019)
[2] I.A. Golovchanskiy, N.N. Abramov, V.S. Stolyarov, Phys. Rev. Applied., vol. 16, p. 034029 (2021)
[3] A.F. Kockum, A. Miranowicz, S. De Liberato, Nat. Rev. Phys., vol. 1, p. 19-40 (2019)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2bebaf6c860d0278cb8854b56f601370.png) 
Fig. 1: Machined cavity 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8a647d4399590dfbaff83ff0e4148d48.png) 

Fig. 2: Spectral transmission S21

Spin Cavitronics System: from Strong to Ultra Strong Coupling

Amorphous magnetic systems provide a unique platform to study dynamics of exotic spin-textures which are fundamentally intriguing and potentially promising for
spintronics. A key question to address is how symmetric and anti-symmetric exchange coupling between atomic spins modulate the length scale of fluctuations near critical phase transition
points [1, 2]. Amorphous Fe-Ge thin films is a prototype system whereby controlling the Fe concentration one can tune the magnitude and randomness of the symmetric Heisenberg
exchange and anti-symmetric Dzyaloshinskii-Moriya interaction (DMI) respectively [3, 4]. In this work we performed soft x-ray photon correlation spectroscopy (XPCS) measurements to
probe the nanoscale magnetic fluctuations of stripe domains in amorphous FexGe1−x
thin films for x=0.51, 0.52 and 0.53 [5, 6]. At lower temperatures all the domains remain static but
with increase in temperature few domains of certain length scales start showing higher fluctuations indicative of intermittent behavior. As temperature reaches the phase transition, domains
of all length scales fluctuate collectively with increased magnitude showing the scale invariance nature at critical points. For similar reduced temperature, we observed dramatically
activated fluctuations for Fe = 0.51 concentration. Such enhanced fluctuations away from the critical temperature could be driven by the proximity from a critical point that is quantum in
origin [7]. The higher instability of the stripe domains with lowering in Fe concentration also corroborate the increased resistivity trend previously observed in those systems [3]. 
**References** 
1]. J. Wild, T. N. G. Meier, S. Pöllath, Science Advances., 3, e1701704 (2017)
2]. L. Shen, M. Seaberg, E. Blackburn, MRS Advances., 6, 221, (2021)
3]. D. S. Bouma, Z. Chen, B. Zhang, Phys. Rev. B., 101, 014402 (2020)
4]. R. Streubel, D. S. Bouma, F. Bruni, Advanced Materials., 33, 2004830 (2021)
5].S. K. Sinha, Z. Jiang, and L. B. Lurio, Advanced Materials., 26, 7764 (2014)
6]. M. Holt, M. Sutton, P. Zschack, Physical Review Letters., 98, 065501 (2007).
7]. Y. Feng, J. Wang, R. Jaramillo, Proceedings of the National Academy of Sciences., 109, 7224, (2012) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ade65df09f6f367e2c36a612872bc0e9.png) 

Figure 1. (a) Magnified images of the speckle pattern evolution at 210K for Fe = 0.52 from 1.9 sec to 1900 sec. Light blue and red color dotted circles showing a static and a dynamic
portion respectively of the speckle pattern. Mean intensity (gray colormap) and temporal heterogeneity (jet colormap) of (b, d, f & c, e, g) Fe0.51Ge0.49 and (h, j, l & i, k, m) Fe0.53Ge0.47 at
different temperatures. With increase in temperature more speckles fluctuate with higher amplitude. Red boxes in (b, h) maps the mean intensity with (c, i) fluctuation heterogeneity for
same Qr positions.

Domain Walls Dynamics in Randomized Dzyaloshinskii Moriya Interaction Mediated Amorphous Fe

Due to the strong spin fluctuation in two dimensions, the magnitude of the magnetization is highly dependent on both the exchange interaction and the magnetic anisotropy at any finite temperature and the existence of an energy gap is essential for the long-range order, which is known as the Wigner and Mermin theorem. As a result, the process of magnetic switching for the 2D magnets is completely different from the process we know for the 3D case. We show here several fundamentally different hysteresis properties between 2D and 3D magnets. The magnetization switching diagram known as the asteroid figure in the conventional Stoner-Wohlfarth model becomes highly temperature-dependent and asymmetric with respect to the transverse and longitudinal magnetic fields. Also, we show the difference in the magnetic switching dynamics between both cases. Our results provide new insights for 2D magnetic materials-based spintronics applications.

Magnetic Switching and Stoner Wohlfarth Model of 2D Single Domain Magnets

Under a longitudinal applied magnetic field, microwires increase/decrease length depending on the magnetostriction sign, where the magnetostrictive elongation is due to magnetization rotational processes as well known in classical magnetism. In amorphous alloys, magnetostriction is usually evaluated making use of inverse magnetoelastic effects (e.g., SAMR method) that sometimes is not fully reliable (e.g., for positive magnetostriction) [1]. 
This study in magnetostrictive and non-magnetostrictive amorphous microwires introduces two original aspects: i) Direct magnetostrictive elongation measurements as a function of applied field and tensile stress; and ii) Re-interpretation of the magnetization mechanism by comparing magnetostrictive elongation and magnetization curve. 
A home-made setup with suitable induction/pickup coils, a mechanical system to apply stress and a high-accuracy LVDT position sensor has been used to measure magnetization, M, and magnetostrictive elongation, δl/l,[2] in two amorphous microwire families: i) In-water-quenched (~145 μm diameter) highly magnetostrictive FeSiB, and vanishing positive/negative magnetostriction (CoFe)SiB microwires; and ii) Glass-coated FeSiBC microwire (20 μm diameter).
The figures show high-sensitivity (down to δl/l=10-8) representative data of δl/l vs. M/Mmax and H where the applied stress increases/reduces the elongation for negative/positive magnetostriction. Quantitative information on the rotational magnetization for low/high field regions is obtained: note in Fig. 1 the different elongation slopes for low (domain wall) and high (rotational) magnetization processes. It is also noticeable the magnetostrictive effect in Fig. 2 inset during domain wall motion in the tiny wire due to a helical magnetization component. This method to properly quantify the magnetostrictive elongation allows for a new magnetization/magnetostrictive analysis as required in mechanical sensor devices. 
**References:** [1] C. Gómez-Polo and M. Vazquez, J. Magn. Magn. Mater. 118, 86 (1993); K. Chichay et al., J. Appl. Phys. 116, 173904 (2014). 
[2] J. Moya et al., J. Magn. Magn. Mater. 476, 248 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/1dc47202896b5978b613db88b267b339.png) 
Fig.1 Magnetostrictive elongation (δl/l) vs. Magnetization (M/Mmax) for a range of applied stresses (σ) in water quenched microwires. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2899920f693e4ffe650e3eedd4a9c203.png) 
Fig. 2 Magnetostrictive elongation (dl/l) vs. applied Field (H) in FeSiB glass-coated microwire. The inset shows the low-field magnetization and elongation loops.

Magnetization process evaluation and tensile stress effect in direct magnetostriction measurement of amorphous microwires

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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