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 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.

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