Utilizing spin-pumping, inverse spin-Hall and spin-Hall phenomena for synchronization of nano magnetic oscillators

The spin-transfer torque (STT) phenomenon has recently been utilized for magnetic nano spin-transfer torque oscillators (STO) in patterned or nano-contact spin valves and magnetic tunnel junctions (MTJ). For applications, synchronization of multiple oscillators to achieve a higher microwave power and lower bandwidth is required. In order to realize such synchronization, a mutual feedback system among the nano STOs is required. Spin wave mediated interaction of two nano-contact STOs was the first demonstration of STOs synchronization. Despite many efforts, maximum four STOs have been experimentally synchronized so far. A new type of oscillator based on the spin-Hall effect (SHE) has been introduced, in which the oscillation mode is a self-localized spin wave bullet, and its injection locking has been demonstrated as well. The spin Hall oscillators (SHO) can be also realized in nano-magnetic elements.We have proposed a novel method for synchronization of multiple STOs on the basis of spin pumping, inverse spin Hall, and spin Hall phenomena . The proposed oscillator system consists of a series of patterned nano-magnets in junction with a stripe of a normal metal with high spin-orbit coupling. We include an accumulative feedback loop for the modulated part of the current. We perform numerical simulations to show the effect of modulated charge currents in the normal metal due to spin pumping from each nano magnet . Figure 1(c) shows the synchronization achieved for ten nano-magnet oscillators . The main important parameter for achieving the synchronization is the delay of the feedback line . We discuss that for the accumulative delay, the line delay should be close to 0, or q/f (q = 1, 2, ...) in order to achieve synchronization here 1/f~160ps . In addition to the ability to synchronize many nano STOs, the distance between nano-magnets is not bounded to the maximum values reported theoretically for spin-wave mediated synchronization, since the mutual feedback in our sys- em is through charge currents.