Perfect and robust phase-locking of a spin transfer vortex nano-oscillator to an external microwave source

Abstract

We study the synchronization of the auto-oscillation signal generated by the spin transfer driven dynamics of two coupled vortices in a spin-valve nanopillar to an external source. Phase-locking to the microwave field h rf occurs in a range larger than 10% of the oscillator frequency for drive amplitudes of only a few Oersteds. Using synchronization at the double frequency, the generation linewidth is found to decrease by more than five orders of magnitude in the phase-locked regime (down to 1 Hz, limited by the resolution bandwidth of the spectrum analyzer) in comparison to the free running regime (140 kHz). This perfect phase-locking holds for frequency detuning as large as 2 MHz, which proves its robustness. We also analyze how the free running spectral linewidth impacts the main characteristics of the synchronization regime.Spin transfer nano-oscillators (STNOs) are nanoscale microwave generators [1,2] which have become very attractive due to their wide range of potential applications (frequency generation [3,4] and detection [5,6], signal processing [7,8], dynamic recording [9,10]). The transfer of angular momentum from a spin-polarized current to a ferromagnetic layer can excite the gyrotropic mode of a magnetic vortex [11,12] having typical frequency between 20 MHz and 2 GHz [13]. Vortex-based STNOs are very promising due to their narrow generation linewidth (about 1 MHz) and potentially high output power [14]. Recently, we have proposed a way to minimize even more the auto-oscillation linewidth by operating a STNO based on two coupled vortices in a spin-valve nanopillar, which can yield highly coherent signals (Q > 15000) with linewidths under 50 kHz at room temperature and near zero magnetic field [15].Synchronization to an external periodic signal and mutual phase-locking of several STNOs have been proposed as means to increase the emitted power and reduce the phase noise of STNOs [16]. It has also been suggested that synchronized arrays of STNOs could be operated as associative memories [17]. So far, mutual phase-locking has been achieved using spin wave coupling between nanocontacts [18-20] and 2D arrays of vortices and antivortices [21]. It is also predicted to occur using the common microwave current emitted [22,23] or the dipolar interaction between adjacent STNOs [24,25]. To demonstrate the efficiency of these two types of coupling, synchronization to an external microwave current passing through the device [26][27][28][29] or to a microwave field produced by an external antenna [30,31] have been studied.Two key characteristics to analyze the quality of the synchronization are the locking range and the generation linewidth in the phase-locked regime, which are respectively related to the coupling efficiency and the response to noise of the oscillator. In a single vortex-based tunneling magnetoresistance (TMR) device, it was shown that using an external microwave current, the locking range could reach up to one third of the oscillator frequency, and the linewidth be reduced by 3 orders of magnitu...

Understanding of Phase Noise Squeezing Under Fractional Synchronization of a Nonlinear Spin Transfer Vortex Oscillator

“…Indeed, thanks to their large intrinsic coherence compared to other types of STNOs [7,15,16], we succeed to elucidate the strong correlation between the oscillator parameters and the locking process through a thorough experimental study combining time domain measurements and analytical developments. This allows understanding of the locking range characteristics [8,17,18] as well as the high phase coherence in the locked regime [19][20][21]. Our results demonstrate the specific spin transfer locking process of our vortex based STNO, and its potential outcomes for synchronizing multiple oscillators in series, which is an important breakthrough toward rf devices or associative memory applications [1].…”

“…In the phase-locked regime, we have to include all the different contributions of the spin transfer forces that are directly acting on the phase θ(t) of the STNO through an alternative current ( ). It is to be noticed that, in a simple double vortex based spin valve system [15,21], the circular symmetry gives rise to spin transfer forces that allows reaching a selfsustained regime but that are independent of the oscillator phase [29]. Thus phase locking to an external rf current was not achievable in such a system.…”

Critical current and linewidth reduction in spin-torque nano-oscillators by delayed self-injection

“…Additionally, the amplitude of an externally driven signal is controlled by the user. 13 Here the self-injected signal depends not only on details of the electronics and MTJ magneto-resistance (through and ), but also the radius of gyration. This may be tuned by the amplification of the delayed signal through and the base DC current driving the dynamics.…”

“…6,8 The nonlinearity inherent to STNOs is both the boon and bane of these devices: non-linearities couple the frequency and amplitude of the oscillator, allowing for the large frequency tunability, but also providing the main source of linewidth broadening. [9][10][11] Experimentally, linewidth reduction has been recently achieved through strategies aimed at controlling the oscillator's phase 12 such as injection locking to an external signal, 13 self-synchronization of several oscillators [14][15][16] and phase-locked loop techniques. 17 In this study, we calculate the effect of delayed self-injection on the critical current, frequency response, and linewidth of STNOs.…”

“…13,21 For an AC drive, when the driving frequency is sufficiently close to the fundamental frequency of the oscillator, the system can lock to the driving frequency. The system also becomes robust to noise near the driving frequency.…”