# Integer, fractional and side band injection locking of spintronic feedback nano-oscillator to microwave signal

**Authors:** Hanuman Singh, K. Konishi, S. Bhuktare, A. Bose, S. Miwa, A. Fukushima, K. Yakushiji, S. Yuasa, H. Kubota, Y. Suzuki, A. A. Tulapurkar  
**arXiv:** [1711.00691](https://arxiv.org/abs/1711.00691)  
**Date:** 2017-11-02  
**Summary page:** https://www.summarizepaper.com/en/paper/1711.00691v1/

## Key points

- Injection locking of a spintronic feedback nano oscillator to microwave magnetic fields
- Delay as a new degree of freedom enables side band peaks in power spectrum
- Possibility to lock the oscillator on these side band peaks
- Synchronization measurements using RF signal generator and co-planar waveguide (CPW)
- Phase locking phenomena at integer and fractional multiples of oscillator frequency
- Small line widths and high peak amplitudes indicate successful locking to external source
- Side band locking improves quality factor for low driving fields, suppresses main peak for higher driving fields
- Fabrication process involves MTJ stack on SiO2, elliptical nano pillars, and CPW fabrication
- Insights into spintronic feedback nano oscillators and their ability to be injection locked to microwave magnetic fields
- Implications for development of phase locked oscillators with large frequency differences

## Summary

In this article, the authors present their findings on the injection locking of a spintronic feedback nano oscillator to microwave magnetic fields. The feedback oscillator has a delay as a new degree of freedom, which enables side band peaks to appear alongside the main peak in its power spectrum. The authors demonstrate that it is possible to lock the oscillator on these side band peaks, opening up new possibilities for phase locked oscillators with large frequency differences. The authors conducted synchronization measurements by connecting an RF signal generator to the feedback path of the oscillator and passing RF current through a co-planar waveguide (CPW) to create an external RF magnetic field that influences the magnetization of the free layer in the oscillator. They calibrated this magnetic field by comparing it to the shift of the tunnel magnetoresistance (TMR) loop with DC current through CPW. The results showed clear phase locking phenomena at both integer and fractional multiples of the free running frequency of the oscillator. The power spectral density (PSD) obtained at different external frequencies demonstrated small line widths and high peak amplitudes within a certain range, indicating successful locking to external source. The authors also observed that for low driving fields, side band locking improved quality factor of main peak while for higher driving fields suppression of main peak occurred. The fabrication process involved creating an MTJ stack on thermally grown SiO2 and fabricating elliptical nano pillars using e-beam lithography and Ar ion milling from multilayer stack. A CPW was then fabricated on top of one pillar and electrically insulated from it by SiO2 layer with fixed layer magnetization along one axis while external magnetic field applied along another axis. Overall, this study provides valuable insights into spintronic feedback nano oscillators and their ability to be injection locked to microwave magnetic fields at both integer and fractional multiples of their auto oscillation frequency. The findings have implications for development of phase locked oscillators with large frequency differences, and role symmetry plays in determining fractional locking is also explored.