Ising spin model using Spin-Hall Effect (SHE) induced magnetization reversal in Magnetic-Tunnel-Junction

Ising spin model is considered as an efficient computing method to solve combinatorial optimization problems based on its natural tendency of convergence towards low energy state. The underlying basic functions facilitating the Ising model can be categorized into two parts, "Annealing and Majority vote". In this paper, we propose an Ising cell based on Spin Hall Effect (SHE) induced magnetization switching in a Magnetic Tunnel Junction (MTJ). The stochasticity of our proposed Ising cell based on SHE induced MTJ switching, can implement the natural annealing process by preventing the system from being stuck in solutions with local minima. Further, by controlling the current through the Heavy-Metal (HM) underlying the MTJ, we can mimic the majority vote function which determines the next state of the individual spins. By solving coupled \textit{Landau-Lifshitz-Gilbert} (LLG) equations, we demonstrate that our Ising cell can be replicated to map certain combinatorial problems. We present results for two representative problems - Maximum-cut and Graph coloring - to illustrate the feasibility of the proposed device-circuit configuration in solving combinatorial problems. Our proposed solution using a Heavy Metal (HM) based MTJ device can be exploited to implement compact, fast, and energy efficient Ising spin model.