Towards mutual synchronization of serially connected Spin Torque Oscillators based on magnetic tunnel junctions

TL;DR

The study tackles the challenge of synchronizing multiple spin-torque oscillators (STOs) by experimentally and numerically examining two serially connected MTJs with mixed anisotropies. Using LLGS-based macrospin modeling and precise measurements, it maps the desynchronization thresholds as functions of anisotropy mismatch $\Delta K$, coupling $\chi$, and field-like torque $\beta$, and demonstrates VCMA-driven control to move a device in and out of the synchronized state. The experimental results show a finite synchronization window with a desynchronization boundary near $H \approx 145\ \mathrm{kA/m}$, which the simulations reproduce, and the authors quantify synchronization with CHNR and the order parameter $\rho$. The work proposes VCMA-based schemes to actively regulate synchronization in series STOs, offering a pathway toward scalable neuromorphic networks with improved oscillation power and linewidth via coupled oscillator chains.

Abstract

Multiple neuromorphic applications require the tuning of two or more devices to a common signal. Various types of neuromorphic computation can be realized using spintronic oscillators, where the DC current induces magnetization precession, which turns into an AC voltage generator. However, in spintronics, synchronization of two oscillators using a DC signal is still a challenging problem because it requires a certain degree of similarity between devices that are to be synchronized, which may be difficult to achieve due to device parameter distribution during the fabrication process. In this work, we present experimental results on the mechanisms of synchronization of spin-torque oscillators. Devices are based on magnetic tunnel junction with a perpendicularly magnetized free layer and take advantage of a uniform magnetization precision in the presence of the magnetic field and a DC bias. By using an external microwave source, we show the optimal condition for the synchronization of the magnetic tunnel junctions. Finally, we present results on the in-series connection of two junctions and discuss the possible path towards improving oscillation power and linewidth. In addition, using numerical simulations of the coupled oscillators model, we aim to reproduce the conditions of the experiments and determine the tolerance for achieving synchronization.

Figures (7)

• Figure 1: Lithography mask of a single device consisting of two serially (head-to-tail) connected MTJs. Pink color denotes a bottom electrode, red the via, violet represents the top electrode. MTJs are not visible at this scale and are fabricated on thin intersections of top and bottom electrode.
• Figure 2: Experimental electrical frequency synchronization and desynchronization of two serially connected MTJs. (a) In-series signal with insets illustrating separate left (L) and right (R) MTJ in the entire field region (0, 155) $kA/m$, and a mathematical average of left and right (L + R) compared with a zoom of the in-series (S), both zoomed in the range (125, 155) $kA/m$. In the zoomed region, we can observe a line with a small FWHM separating from a wide mode; a similar picture does not emerge simply by adding the left and right signals together. (b) Main oscillating frequency of the L, R and in series systems, with a zoom of the desynchronization region. (c) the synchronization and desynchronization ranges of L and R and in-series (S) signal respective to the trend line (T) fitted to the L signal. L signal should, in theory, be least affected by the in-series electrical connection, and therefore is used as a reference. The arrow marks the spot where the R signal diverges from L, and S diverges both from L and R. As shown, up until about 145 kA/m, the S signal follows R closely, then settles to oscillate with its own distinct frequency. In all panels we also include a mathematical average of (L) and (R) signals, (L+R)/2, for reference. In (c) that signal is subtracted from (S) for comparison.
• Figure 3: Simulated desynchronization of serially coupled MTJs in function of the anisotropy change $\Delta \mathrm{K}$ of the (R) MTJ in series. Panels (a) and (b) show two sample spectra for R junction taken at $\Delta \mathrm{K} = -5 \%$ (a) and $\Delta \mathrm{K} = 4\%$ (b). The arrow leads from the desynchronization boundary at $\approx 68 ~ \mathrm{kA/m}$ and $\Delta \mathrm{K} = 4\%$ in (c) to a precise place of desynchronization in the spectrum of (b), with the desynchronization moment placed in zoom in (b). (a-b) The blue marker follows the line of the main oscillating frequency of L, and the red marker tracks the one for R. The black dots show the main oscillating frequency line of R when the two MTJs are decoupled, i.e. $\chi = 0$. Otherwise, simulations performed assuming $\chi = 0.3$. We used $\beta = 0.5$. (d) Frequency difference in (GHz) between the L and R junctions. For $\Delta \mathrm{K} > 0$, i.e. $K_\mathrm{R} > K_\mathrm{L}$ there is a desynchronization boundary where the L and R junctions start to fall out of synchronization, i.e. leave the dark blue region (white line in (c) denotes that desynchronization boundary $H_\mathrm{thres}$). (c) illustrates that the dark-blue region from (d) is characterized by a large CHNR, supporting the evidence for strong synchronization. The asymmetry between the frequency de-synchronization fields for $\Delta K > 0$ and $\Delta K < 0$ arise from the particular arrangement of the (L) and (R) MTJs in series, and is a direct consequence of a smaller frequency changes due to current change. High order parameter values (e) confirm a good degree of synchronization within the desynchronization boundary.
• Figure 4: The effect of field-like torque scaling $\beta$ and the magnitude of the electric coupling $\chi$ on the desynchronization threshold $\mathrm{H}_\mathrm{thres}$ in function of the anisotropy change $\Delta \mathrm{K}$ of the (R) MTJ in series. Case (a) corresponds to $\beta = \alpha_\mathrm{G}$. Increasing $\beta$ positively correlates with the increased synchronization range across magnetic parameter dispersion, having a similar effect to increasing the coupling constant $\chi$. External field range is capped to 175 kA/m. Plotted points denote only states that were synchronized at some field, a lack of a marker means that the state either did not start in a synchronized state at lower field values or it has already desynchronized.
• Figure 5: A simulated VCMA-controlled synchronization of and in-series MTJ system. The VCMA controller switches from $\Delta \mathrm{K}_1$ to $\Delta \mathrm{K}_2$ first, then back to $\Delta \mathrm{K}_1$. (a) shows the magnetoresistance during transition at 30 ns from $\Delta \mathrm{K}_1$ to $\Delta \mathrm{K}_2$, (b) at 60 ns from $\Delta \mathrm{K}_2$ back to $\Delta \mathrm{K}_1$ and (c) gives last couple nanoseconds from a synchronized state in $\Delta \mathrm{K}_1$ after the final switch. Frequency spectra corresponding to states $\Delta \mathrm{K}_1$, $\Delta \mathrm{K}_2$ and $\Delta \mathrm{K}_1$ (after the transition from $\Delta \mathrm{K}_2$) are shown in (d-f) respectively. Simulated for $\chi = 0.15$, $\Delta \mathrm{K}_1 = 4\%$, $\Delta \mathrm{K}_2 = 20\%$, $H_\mathrm{ext} = 80 \mathrm{kA/m}$.