Circuit-level model of phase-locked spin-torque oscillators

Spin-torque oscillators (STOs) are new oscillating devices based on spintronics technology with many advantageous features, i.e., nanoscale size, high tunability, and compatibility with standard silicon processing. Recent research has shown that two electrically connected STOs may operate as a single device when specific conditions are met. To overcome the limitation of the small output power of STOs, the phase-locking behavior of multiple STOs is hereby extensively investigated. In this paper, we present a circuit-level model of two coupled STOs considering the interaction between them such that it can represent the phase-locking behavior of multiple STOs. In our model, the characteristics of each STO are defined first as functions of applied DC current and external magnetic field. Then, the phase-locking condition is examined to determine the properties of the two coupled STOs on the basis of a theoretical model. The analytic model of two coupled STOs is written in Verilog-A hardware description language. The behavior of the proposed model is verified by circuit-level simulation using HSPICE with CMOS circuits including a current-mirror circuit and differential amplifiers. Simulation results with various CMOS circuits have confirmed the effectiveness of our model.