Integer, Fractional, and Sideband Injection Locking of a Spintronic Feedback Nano-Oscillator to a Microwave Signal

Abstract

In this article we demonstrate the injection locking of recently demonstrated spintronic feedback nano oscillator to microwave magnetic fields at integers (n=1, 2, 3) as well fractional multiples (f=1/2, 3/2 and 5/2) of its auto oscillation frequency. Feedback oscillators have delay as a new "degree of freedom" which is absent for spin-transfer torque based oscillators, which gives rise to side peaks along with a main peak. We show that it is also possible to lock the oscillator on its side band peaks, which opens a new avenue to phase locked oscillators with large frequency differences. We observe that for low driving fields, sideband locking improves the quality factor of the main peak, whereas for higher driving fields the main peak is suppressed. Further, measurements at two field angles provide some insight into the role of symmetry of oscillation orbit in determining the fractional locking.Nano-oscillators based on the phenomenon of spin-transfer torque (STT) [1][2][3][4][5][6][7] have been the subject of considerable research due to their potential applications in microwave communication devices as well as due to the rich physics involved in their operation. Recently our group demonstrated a spintronic feedback nano-oscillator (SFNO) [8,9] based on the tunneling magnetoresistance (TMR) effect and works without STT. The working principle of SFNO is as follows: SFNO comprises a magnetic tunnel junction (MTJ) nano-pillar connected to a waveguide on top of it. Such a system, when powered by dc current can amplify rf signals: Rf current passing through the waveguide excites the magnetization of the free layer via oscillating Oersted magnetic field, and the dc current passing through MTJ converts the oscillations of magnetization into ac voltage via tunneling magneto-resistance (TMR) effect. Above a certain dc current level, the input signal is amplified. Thus the free layer of MTJ apart from being a resonator can also work as an amplifier. If we connect a feedback path from MTJ to the waveguide, the system works as an oscillator.It was demonstrated that SFNO [9] can exhibit very large quality factors exceeding 10,000. However, to obtain large output power, it is necessary to connect many oscillators together. If many oscillators can be synchronized, i.e. they oscillate with the same frequency and phase [10], we can get larger power output. We therefore studied the injection locking of a single SFNO to a microwave source, which acts as the second oscillator. Further such studies are also important to understand the complex non-linear dynamics of an auto-oscillator and its possible applications to neuromorphic computing [11][12][13]. Injection locking of spin-transfer nano-oscillator (STNO) [14][15][16][17][18][19][20][21][22][23] has been the subject of many experimental and theoretical investigations with the same 2 motivation. SFNO is not limited to the feedback from Oersted magnetic field, but can be even realized from spin current generated by using inverse . Even interfacial Rashba coupling can be used as ...

Modulation and phase-locking in nanocontact vortex oscillators

“…5(b). Phase-locking of modulation sidebands and fractional synchronization are phenomena that have already been reported in previous studies on STNOs [56], though it is in a feedback loop, and not related to core reversal.…”

Microwave magnetic field modulation of spin torque oscillator based on perpendicular magnetic tunnel junctions

“…In contrast to the measurement performed at P MOD = 0, where a linear dependence of the sideband and modulation frequency is measured, an increased modulation power results in the main peak frequency deviation from its original position, determined by the bias current and magnetic field. We ascribe this effect to the injection-locking of the STO to higher harmonics of the modulating signal 23,24 .…”

Effects of delayed feedback on the power spectrum of spin-torque nano-oscillators

“…This can * joo-von.kim@c2n.upsaclay.fr lead to self-oscillations [41] and self-injection locking [42]. Such feedback loops lead to the appearance of complex power spectra with several modulation sidebands [43]. A similar phenomenon can also be achieved using the spin Hall effect as a feedback mechanism [44].…”