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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.
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, whic
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 rece
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 mu
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 l
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. Physica