Spin-wave-mediated mutual synchronization of spin-torque nano-oscillators: A micromagnetic study of multistable phase locking

We present a detailed micromagnetic study of the synchronization dynamics of two spin-torque nano-oscillators which are dynamically coupled by the emission of spin waves through an extended magnetic layer. We show that the intercontact distance and the wavelength of the emitted spin waves have a large impact on the possible synchronization states. Depending on the intercontact distance, there exist three different synchronization regions which can be characterized as in-phase and antiphase synchronization as well as a bistability region with both in-phase and antiphase synchronization. We demonstrate under which conditions bistability can be achieved and how the system can be switched from one to the other synchronization state. Finally, we develop a reduced semianalytical model which reproduces the simulation results and allows us to understand the physical origin of the bistability. It turns out that the bistability is caused by time-delay effects.