Synchronization of spin-transfer oscillators driven by stimulated microwave currents

We have simulated the nonlinear dynamics of networks of spin-transfer oscillators. The oscillators are magnetically uncoupled but electrically connected in series. We use a modified Landau-Lifschitz-Gilbert equation to describe the motion of each oscillator in the presence of the oscillations of all the others. We show that the oscillators of the network can be locked not only in frequency but also in phase. The coupling is due to the microwave components of the current induced in each oscillator by the oscillations in all the other oscillators. Our results show how the emitted microwave power of spin-transfer oscillators can be considerably enhanced by current-induced synchronization in an electrically connected network. We also discuss the possible application of our synchronization mechanism to the interpretation of the surprisingly narrow microwave spectrum in some experiments on a single isolated spin-transfer oscillator.