  We have simulated the non-linear 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 synchronized
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 isolated spin-transfer
oscillators.
