![]() ![]() Dotted lines are phase locking bandwidths Δ = | d ϕ / d t | calculated in micromagnetic simulations (e),(f). ![]() The 2 f component’s amplitude is doubled to account for the second harmonic frequency. (b) Solid lines show Adler’s equation predictions with V 1 f = − V 2 f = 66 mV. (a) Odd and even series of the SHNO ISF based on a typical clamshell orbit. ISF and Adler’s equation for a device with the parameters given in Appendix pp1. Our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency. With this abstract model, we analyze the performance of the spin Hall oscillator network at the circuit level using conventional electronic components and considering phase noise and scalability. ![]() We integrate our analytical model into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillators in circuit simulators. By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, we explicitly show the mapping between the coupled oscillators’ properties and the Ising model. Here we propose using an electrically coupled array of gigahertz spin Hall nano-oscillators to realize such a network. Fast, compact oscillator networks that provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. ![]()
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