Global attractors and the difficulty of synchronizing serial spin-torque oscillators

Abstract

Previously, synchronization of spin-torque oscillator ͑STO͒ has usually been analyzed by phase oscillator model. Here we show that STO is more precisely described as a perturbed heteroclinic cycle where the frequency is sensitive to the distance between the cycle and a saddle. In the presence of external signal or coupling, the frequency changes mainly due to the modification on this distance rather than on the phase directly. Multiple attractors coexist and synchronization depends sensitively on the initial conditions when a STO is driven by an external ac. We reveal that these properties underlay the mechanisms why synchronization region in two serially connected STOs is quite small and why time delay can enhance synchronization. When more STOs are added, the parameter region for a globally attracting synchronization state may disappear. Our analysis suggests that initial conditions have to be controlled or different designs have to be fabricated in order to obtain robust synchronization of a large number of STOs for the purpose of applications.

Quasiperiodic, periodic, and slowing-down states of coupled heteroclinic cycles

“…Our results can give a precise understanding of the upward or downward shift or the synchronized frequency observed for coupled oscillators in neuronal system [5] and also shed some light on a similar phenomenon in magnetic system [46,47], and the rich dynamical behavior we find suggests further experiments in these and related systems. The dynamical behavior of two coupled heteroclinic cycles is also progress toward better understanding systems of a large number of cycles.…”

Optimizing magnetodipolar interactions for synchronizing vortex based spin-torque nano-oscillators

“…However, an important issue with such devices regarding their practical realization is their low-output oscillation power and low spectral stability. A possible solution to these issues could be the synchronization of a few STNOs [6,19,21,22,26,28]. Synchronization among multiple auto-oscillators can also be useful in the framework of developing associative memories architectures [29][30][31][32].…”

“…Synchronization among multiple auto-oscillators can also be useful in the framework of developing associative memories architectures [29][30][31][32]. Previous studies reported on synchronization of STNOs interacting with others via spin waves [25,26,33], exchange coupling [6], electric currents [3,28,34], noisy current injection [19], or via magnetodipolar interaction [21,22,[35][36][37][38][39][40][41].…”

Synchronization of spin torque nano-oscillators

“…Their work shows that the region of parameter space where synchronization exists is rather small, thus explaining the difficulty (already observed by experimentalists) to achieve synchronization. Li et al 20 showed that this difficulty was due, mainly, to the coexistence of multiple stable attractors, suggesting that the synchronization regime is highly sensitive to initial conditions. Persson et al…”