Solving highly complex optimization problems often requires significant resources using traditional computer hardware. Ising machines (IM) have been proposed as an energy-efficient computing approach to tackle these problems. One possible hardware implementation of the Ising machine is based on a system of coupled spin torque nano-oscillators (STNOs), with the solution to the optimization problem given by an optimal phase configuration (ψ1, ψ2, …) where ψi is the phase difference of each STNO i with an external 2f signal.
During this thesis project, we studied such a coupled STNO system in depth, focusing on the physical understanding of injection locking properties. The analysis was conducted using a bottom-up approach, from individual elements of the IM implementation to a complete set of coupled STNOs.
First, we consider that in an IM application based on STNOs, the STNOs are subject to signals 1f and 2f. By nf, we mean that the frequency of the coupling signal is approximately “n” times the free-running frequency of the STNO. We therefore begin by analyzing the coupling of a STNO to a 1f signal and a 2f signal independently of each other. Regarding the 1f case, synchronization under an RF signal aligned with the easy axis of the STNO, unexpected according to the injection-locking analytical model, is found when the symmetry of the magnetization trajectory along the easy axis is broken. This is important because it is an effect that could occur when coupling STNOs for IM. As far as the 2f case is concerned, a 2f magnetic field oriented along the easy axis of the STNO is found to have better synchronization characteristics than a 2f current.
Secondly, we investigated two coupled STNOs that are 2f injection locked, which represent a basic IM with two spins. The phase configuration (ψ1, ψ2), is studied. It is found that the optimal phase configuration or solution depends strongly on the frequency detuning and the coupling phase which characterizes the mutual coupling. Besides, the DC voltage can alter the solution when the mutual coupling is implemented through voltage, but this property is not observed for magnetic field coupling.
We carried out numerical simulations on arrays of three, four and eight coupled STNOs, and analyzed whether the optimal phase configuration corresponds to the solution of a MaxCut optimization problem. As an important outcome, it was found that the optimal configuration depends on frequency detuning, and is highly sensitive to changes in coupling strength.


Plus d'information :https://www.spintec.fr/phd-defense-phase-dynamics-of-injection-locked-spin-torque-nano-oscillators-from-synchronization-to-ising-machines/​
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Pour suivre la soutenance ​​​en visioconférence : https://grenoble-inp.zoom.us/j/93447088637​

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