  We have proposed a method to synchronize multiple spin-transfer torque
oscillators based on spin pumping, inverse spin Hall, and spin Hall effects.
The proposed oscillator system consists of a series of nano-magnets in junction
with a normal metal with high spin-orbit coupling, and an accumulative feedback
loop. We conduct simulations to demonstrate the effect of modulated charge
currents in the normal metal due to spin pumping from each nano-magnet. We show
that the interplay between the spin Hall effect and inverse spin Hall effect
results in synchronization of the nano-magnets.
