Gluing bifurcations in coupled spin torque nano-oscillators

Abstract

Over the past few years, it has been shown, through theory and experiments, that the AC current produced by spin torque nano-oscillators (STNO), coupled in an array, can lead to feedback between the STNOs causing them to synchronize and that, collectively, the microwave power output of the array is significantly larger than that of an individual valve. Other works have pointed, however, to the difficulty in achieving synchronization. In particular, Persson et al. [J. Appl. Phys. 101, 09A503 (2007)] shows that the region of parameter space where the synchronization state exists for even a small array with two STNOs is rather small. In this work, we explore in more detail the nature of the bifurcations that lead into and out of the synchronization state for the two-array case. The bifurcation analysis shows bistability between in-phase and out-of-phase limit cycle oscillations. In fact, there are two distinct pairs of such cycles. But as the input current increases, the limit cycles may increase their amplitudes until they merge with one another in a gluing bifurcation. More importantly, we show that changing the direction of the applied magnetic field can, in principle, increase the region of synchronized oscillations.