Synchronization of spin-torque oscillators via spin pumping

A theoretical treatise is presented on coupled dynamics between spin torque oscillators consisting of perpendicularly magnetized free layers and in-plane magnetized pinned layers. As a coupling mechanism, an injection of pure spin current from one oscillator to the other is considered because the free layer is capable of emitting the pure spin current by spin pumping effect. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates that an in-phase synchronization is excited in the oscillators for a wide range of applied current. The results indicate that injection of the spin current by spin pumping is the efficient approach for an enhancement of emission power in spintronics devices using an array of spin torque oscillators.