Compact Model of Superparamagnetic Tunnel Junction Controlled by Spin-Orbit Torque

Superparamagnetic tunnel junction (SMTJ), characterized by thermally driven random magnetization switching, offer novel pathways for high-sensitivity magnetic sensing and true random number generation. In this study, we developed a compact model based on magnetization dynamics and electrical characteristics for SMTJs modulated by spin-orbit torque (SOT). The temporal evolution of the magnetic moments in the free layer (FL) is described by a revised Landau-Lifshitz-Gilbert (LLG) equation, which accounts for thermal noise effect. A voltage-dependent tunneling magnetoresistance (TMR) model is introduced, thereby establishing a robust framework for circuit simulation. The model is developed by using the Verilog-A language, and the accuracy of the model was verified through simulations. The simulation results indicate that the magnetization state retention time of SMTJ is positively correlated with the thermal stability factor, and the external voltage can modulate the probability distribution of magnetization direction. This research provides theoretical support and design references for the application of superparamagnetic devices in low-power random circuits and high-precision sensors.