  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.
