Enhancing the injection locking range of spin torque oscillators through mutual coupling

Abstract

We investigate how the ability of the vortex oscillation mode of a spin-torque nanooscillator to lock to an external microwave signal is modified when it is coupled to another oscillator. We show experimentally that mutual electrical coupling can lead to locking range enhancements of a factor 1. 64. Furthermore, we analyze the evolution of the locking range as a function of the coupling strength through experiments and numerical simulations. By uncovering the mechanisms at stake in the locking range enhancement, our results will be useful for designing spin-torque nano-oscillators arrays with high sensitivities to external microwave stimuli.Spin-torque nano-oscillators (STNOs) are promising candidates for the next generation of multifunctional spintronic nano-devices [1] such as efficient integrated microwave generators [2] and detectors [3,4]. One of their characteristic features compared to other auto-oscillators is their high non-linearity [5]. On one hand, this high nonlinearity translates into one of their most attractive properties: their ability to easily adapt their frequencies to external stimuli. On the other hand, by increasing their sensitivity to noise, it has the undesirable effect of broadening the spectral linewidth. In the last few years, many efforts have been made to improve the spectral purity of spintorque oscillators, a crucial step towards most applications. From these studies, a promising approach consists in the synchronization of the oscillators to an external microwave source [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] (injection locking), or to other oscillators [21][22][23][24][25][26][27] (mutual synchronization). In both cases, a crucial parameter to optimize for applications is the locking range, which should be as large as possible. A first way to increase the locking range is to work in regimes where the oscillator's nonlinearity is the largest. However, as mentioned earlier, this comes at the detriment of spectral purity. In the case of injection locking, another possibility is to increase the power of the external signal, but this is limited by the breakdown voltage of the tunnel barrier of the device and results in an increase of power consumption. Therefore, finding alternative paths to enhance the locking range is an important step towards designing next generation's magnetic microwave devices.In this manuscript we combine experimental results with numerical simulations to show that the injection locking range of a spin-torque oscillator can be enhanced by coupling it to another spintorque oscillator. Furthermore, it is shown that the locking range can be tuned by changing the mutual coupling strength between oscillators. (7) is the free layer and numbers represent thickness in nanometers. Samples were grown by sputterdeposition and patterned down to the bottom electrode into circular nanopillars with a diameter of 200 nm. The nano-pillars exhibit a TMR of 64% and a resistance-area product of RA~1 Ω.μm 2 . With this combination of materials and geometry, th...

Vowel recognition with four coupled spin-torque nano-oscillators

“…As shown in Fig. 3c and d, the mutual coupling between oscillators also enhances their locking ranges 27 , leading to increased recognition rates when the mutual interactions increase. The red star in Fig.…”

Designing Large Arrays of Interacting Spin-Torque Nano-Oscillators for Microwave Information Processing

“…Here, X i = (x i , y i ) is the vortex core position, G i is the gyrovector, D i is the damping, W i is the potential energy of the vortex, F STT i is the spin-transfer force. The same numerical framework including the mutual electrical coupling has been shown previously to reproduce quantitatively the synchronization state features observed experimentally for an array of two [28] and four [14] coupled nano-oscillators in presence of external microwave stimuli. Fig.…”

“…Electrical connections between oscillators for instance can lead to high mutual interactions when the frequency difference becomes small, of the order of 1 MHz for the oscillators modeled here [14,16,24]. This modifies their oscillation frequency and can lead to their mutual synchronization which can affect their ability to be synchronized to an external microwave input [28]. This collective coupling effect is not captured by the analytical description that we considered until now.…”

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission and energy harvesting

“…Normally STOs can be mutually synchronized only with a finite difference (Δ f diff ) of their stand-alone oscillation frequency. In contrast to the vortex-based STOs which can be synchronized for a very small Δ f diff of a few MHz 34 , 39 , the STOs in our work can be synchronized for Δ f diff as large as 180 MHz due to larger coupling. This feature offers additional flexibility during the on-chip design.…”

“…These values are ~3.5 times larger compared to that of a single STO. It should be noted that in previous works, very limited f L enhancements from 1.69 to 2.87 MHz 39 and 2–10 MHz 34 have been demonstrated in a system of two vortexes STOs controlled by multiple dc sources connected in series. The enhancement in the locking range of four synchronized oscillators can be understood by the fact that due to different locking ranges and free-running frequencies of STOs, an STO with a minimum free-running frequency ( f 0,min ) in the array can lock to the external source frequency ( f rf ) at a much lower frequency, f rf < f 0,min and the STO with the maximum free-running frequency ( f 0,max ) can lock to a much higher frequency, f rf > f 0,max .…”