Theory of mutual phase-locking of a pair of generating magnetic nano-contacts driven by spin-polarized current is developed using the general theory of coupled nonlinear oscillators.
The expressions for the phase-locking band and for the frequency of phase-locked oscillations are derived and compared to experiments. It is shown, that in typical experiments, where separation $a$ between the nano-contacts lies in the interval 0.2 $mu$m $< a <$ 1.5 $mu$m, the coupling between the nano-contacts leading to the phase-locking effect is mainly caused by the propagating spin waves radiated into the common “free” layer, rather than by the direct magneto-dipole interaction.
Dep. of Physics, Oakland Univ., Rochester, MI 48309, USA