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Ising Machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths of its binary spins. Using the intrinsic dynamics and different annealing schemes, the IM relaxes over time to its lowest energy state, which is the solution to the CO problem. IMs have been implemented in quantum, optical, and electronic hardware. One promising approach uses interacting nonlinear oscillators whose phases have been binarized through injection locking at twice their natural frequency. Here we demonstrate such Oscillator IMs using nano-constriction spin Hall nano-oscillator (SHNO) arrays. We show how the SHNO arrays can be readily phase binarized and how the resulting microwave power corresponds to well-defined global phase states. To distinguish between degenerate states we use phase-resolved Brillouin Light Scattering (BLS) microscopy to directly observe the individual phase of each nano-constriction.
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Large-amplitude magnetization dynamics is substantially more complex compared to the low-amplitude linear regime, due to the inevitable emergence of nonlinearities. One of the fundamental nonlinear phenomena is the nonlinear damping enhancement, which imposes strict limitations on the operation and efficiency of magnetic nanodevices. In particular, nonlinear damping prevents excitation of coherent magnetization auto-oscillations driven by the injection of spin current into spatially extended magnetic regions. Here, we propose and experimentally demonstrate that nonlinear damping can be controlled by the ellipticity of magnetization precession. By balancing different contributions to anisotropy, we minimize the ellipticity and achieve coherent magnetization oscillations driven by spatially extended spin current injection into a microscopic magnetic disk. Our results provide a novel route for the implementation of efficient active spintronic and magnonic devices driven by spin current.
Spin-orbit coupling stands as a powerful tool to interconvert charge and spin currents and to manipulate the magnetization of magnetic materials through the spin torque phenomena. However, despite the diversity of existing bulk materials and the recent advent of interfacial and low-dimensional effects, control of the interconvertion at room-temperature remains elusive. Here, we unequivocally demonstrate strongly enhanced room-temperature spin-to-charge (StC) conversion in graphene driven by the proximity of a semiconducting transition metal dichalcogenide(WS2). By performing spin precession experiments in properly designed Hall bars, we separate the contributions of the spin Hall and the spin galvanic effects. Remarkably, their corresponding conversion effiencies can be tailored by electrostatic gating in magnitude and sign, peaking nearby the charge neutrality point with a magnitude that is comparable to the largest efficiencies reported to date. Such an unprecedented electric-field tunability provides a new building block for spin generation free from magnetic materials and for ultra-compact magnetic memory technologies.
Spin Hall nano-oscillators (SHNOs) utilize pure spin currents to drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and sometimes mutually synchronize, in pairs or in short linear chains. Here we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 x 2 to 8 x 8 nano-constrictions, observed both electrically and using micro-Brillouin Light Scattering microscopy. The signal quality factor, $Q=f/Delta f$, increases linearly with number of mutually synchronized nano-constrictions ($N$), reaching 170,000 in the largest arrays. While the microwave peak power first increases as $N^2$, it eventually levels off, indicating a non-zero relative phase shift between nano-constrictions. Our demonstration will enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and neuromorphic computing.
We study the current tunable microwave signal properties of nano-constriction based spin Hall nano-oscillators (SHNOs) in oblique magnetic fields as a function of the nano-constriction width, $w=$~50--140 nm. The threshold current is found to scale linearly with $w$, defining a constant threshold current density of $J_{th}=$ 1.7 $times$ 10$^{8}$ A/cm$^2$. While the current dependence of the microwave frequency shows the same generic non-monotonic behavior for all $wgeqslant$ 80 nm, the quality of the generated microwave signal improves strongly with $w$, showing a linear $w$ dependence for both the total power and the linewidth. As a consequence, the peak power for a 140 nm nano-constriction is about an order of magnitude higher than that of a 80 nm nano-constriction. The smallest nano-constriction, $w=$ 50 nm, exhibits a different behavior with a higher power and a worse linewidth indicating a crossover into a qualitatively different narrow-constriction regime.
Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks, which are encountered in fundamental areas and real-world practical problems including logistics, social networks, and cryptography. Physical machines have recently been proposed and implemented as an alternative to conventional exact and heuristic solvers for the Ising problem, one such optimization task that requires finding the ground state spin configuration of an arbitrary Ising graph. However, these physical approaches usually suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS) capable of converging to the ground state of various 4-spin graphs with high probability. The INPRIS exploits experimental physical noise as a resource to speed up the ground state search. By injecting additional extrinsic noise during the algorithm iterations, the INPRIS explores larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem, and could thus be implemented with optoelectronic architectures that enable GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), our work paves a way for orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.
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