Synchronization of spin-transfer oscillators driven by stimulated microwave currents

This article presents numerical simulations to study the synchronization of electrically connected STOs (spin transfer oscillators). The motion of the magnetizations m_j of the layers F2 of a collection of different STOs were calculated. Each m_j is considered as a macrospin without any dipolar interaction with the other m_i. Its time evolution is given by a Landau-Lifschitz-Gilbert equation including a standard spin transfer term. The current through each junction is the sum of the injected dc current and the ac component due to the microwave current induced by the oscillations of all the other STOs. Simulations of the dynamics are performed using a fourth-order Runge-Kutta algorithm. It is shown that it is possible to synchronize a network of spin-transfer oscillators electrically connected to a load. The synchronization depends on the dispersion of the individual frequencies, on the coupling parameters and the delays induced by microwave cables in experimental setups. Under certain conditions, the synchronization can be complete.