Compact Macrospin-Based Model of Three-Terminal Spin-Hall Nano Oscillators

Emerging spin-torque nano oscillators (STNOs) and spin-Hall nano oscillators (SHNOs) are potential candidates for microwave applications. Recent advances in three-terminal magnetic tunnel junction (MTJ)-based SHNOs opened the possibility to develop more reliable and well-controlled oscillators, thanks to individual spin Hall-driven precession excitation and read-out paths. To develop hybrid systems by integrating three-terminal SHNOs and CMOS circuits, an electrical model able to capture the analog characteristics of three-terminal SHNOs is needed. This model needs to be compatible with current electric design automation (EDA) tools. This work presents a comprehensive macrospin-based model of three-terminal SHNOs able to describe the dc operating point, frequency modulation, phase noise, and output power. Moreover, the effect of voltage-controlled magnetic anisotropy (VCMA) is included. The model shows good agreement with experimental measurements and could be used in developing hybrid three-terminal SHNO/CMOS systems.