Phase locking of spin-torque oscillators by spin-wave interactions

The spin-wave mediated interaction leading to the phase locking of two spin-torque oscillators is studied. The effective coupling parameter is derived and unexpectedly found to exhibit an oscillatory behavior as a function of intercontact distance. The period of the oscillation is shown to equal the wavelength of the spin wave radiated from the contact. As a result, the oscillators will alternate between in-phase and out-of-phase oscillations, corresponding to maximal and minimal output powers. The predictions are confirmed by micromagnetic simulation.