Phase-Locking of Spin-Torque Nano-Oscillator Pairs by Magnetic Dipolar Coupling in Electrical Serial Connection
Synchronization of spin-torque nano-oscillators (STNOs) by magnetic dipolar interactions in a parallel electrical connection (PC) introduces the technological possibility for an enhancement of output signal. In this study, we consider two identical or nonidentical STNOs in serial electrical connection (SC). By using a pendulum-like approximation model, we analytically predict the dipolar coupling strength, critical current and frequency of phase-locking precession. The numerical calculations of those analytical expressions are confirmed by macrospin simulations, revealing that the dipolar coupling strength responsible for the phase-locking in SC case is three times larger than that in the PC case for the two STNOs with the same separation, which results in the enlarged and symmetric phase-locking window of frequency versus current. These results suggest that the SC of multiple STNOs could be more promising for the enhancement of output power.