Hardware realization of the multiply and accumulate operation on radio-frequency signals with magnetic tunnel junctions

Radio-frequency (RF) signals are widely used to convey information and there is an ever increasing demand for their accurate and quick analysis. Recently, artificial neural networks have proven successful for many RF processing applications such as signal classification [1], medical diagnosis [2–4], RF fingerprinting [5], gesture sensing [6], radar applications [7] or aerial vehicle detection and identification [8]. Furthermore, they perform better than conventional algorithms, which rely on feature extractors and complex analysis tools, in terms of resilience to real-world conditions (noisy electromagnetic environment, imperfect RF components or antennas, etc) [1]. However, processing RF signals with neural networks requires analog signal digitization and training on CMOS (complementary-metal-oxide-semiconductor)-based hardware such as graphical processing units, tensor processing units or dedicated application specific integrated circuits. This process leads to millisecond delays and consumes hundreds of watts, limiting the deployment of RF oriented artificial intelligence on embedded systems [9, 10].

The need for compact and energy efficient RF hardware has stimulated research on emerging technologies which exhibit native RF dynamics. In particular, spintronic nano-oscillators can receive, transform and emit RF signals [11–13]. They have been proposed as RF emitters and receivers for on-chip communication [14–16] and can implement key operations for RF signal processing, such as spectral analysis [17, 18]. Furthermore, they are promising building blocks for neuromorphic computing [19, 20]. They have been implemented as neurons in feed-forward neural networks [21], reservoir computing [22–24] and synchronization-based computing [25–27]. Recently, Leroux et al [28] have proposed using magnetic tunnel junctions as RF synapses to perform the multiply and accumulate (MAC) operation, i.e., a weighted sum in hardware, directly on analog RF signals. The MAC operation is a key operation of neural networks, but it is particularly sensitive to the Von Neumann bottleneck because of the necessity to access memory for reading and writing the weights. Using emerging technologies to perform the MAC operation with collocation of memory and computing is thus projected to offer a hundred fold improvement in energy efficiency [29–34]. Magnetic tunnel junctions can be scaled down to tens of nanometers wide [35] and monolithically integrated into CMOS circuits [36]. Thus, their use as RF synapses provides a path for compact, fast and energy efficient classification of RF signals. Leroux et al used analytical work and numerical simulations to demonstrate that this MAC implementation could perform the classification of handwritten digits images encoded into the RF signals powers [28].

In this work, we experimentally demonstrate that magnetic tunnel junctions can be used as RF synapses with tunable positive and negative weights. We further demonstrate experimentally the MAC operation on two RF inputs with two synapses, and use this MAC to perform a 2D classification of RF signals.

We first demonstrate that a single magnetic tunnel junction can act as a synapse and multiply an RF power by a tunable weight, as schematized in figure 1(a). The device is a nanopillar magnetic tunnel junction stack of 250 nm diameter, made of SiO₂//5 Ta/50 CuN/5 Ta/50 CuN/5 Ta/5 Ru/6 IrMn/2.0 Co₇₀Fe₃₀/0.7 Ru/2.6 Co₄₀Fe₄₀B₂₀/MgO/2.0 Co₄₀Fe₄₀B₂₀/0.5 Ta/7 NiFe/10 Ta/30 CuN/7 Ru, where thickness are indicated in nm. It consists of a pinned reference ferromagnetic layer (2.6 nm Co₄₀Fe₄₀B₂₀), a tunnel barrier (MgO with RA of 8 Ω μm²) and a free magnetic layer (2.0 nm Co₄₀Fe₄₀B₂₀/0.5 nm Ta/7 nm NiFe, where the CoFeB layer is there to ensure good crystallisation and is fully coupled to the NiFe layer such that they can be considered a single layer). The magnetization of the free layer is in a vortex state. When we inject an RF current through a magnetic tunnel junction, the core of the magnetic vortex in the free layer can be driven into gyrotropic motion, provided the input frequency is near the resonance frequency of the vortex. The tunnel magnetoresistance effect translates these magnetic oscillations into resistance oscillations. The mixing of the input RF current with the resistance oscillations at the same frequency give rise to a dc voltage across the junction, called a spin-diode voltage [12, 37]. Figure 1(b) presents this rectified voltage versus the input frequency f_RF. We observe a characteristic resonance curve around the resonance frequency (marked by a dashed vertical line). The amplitude of the voltage increases proportionally to the input power P_RF. By injecting a direct current in the strip-line placed above the device, we generate a local Oersted field collinear to the easy axis of the junction, as schematized in figure 1(a). This in-plane field pushes the core of the magnetic vortex away from the center of the magnetic dot. The potential well in which the vortex core oscillates is thus deformed, which leads to a change in its intrinsic resonance frequency. Figure 1(c) illustrates this phenomenon: we observe the resonant response of the device shifts to the higher frequency as the injected current increases. To demonstrate the synaptic operation, we fix the input frequency f_RF at 346 MHz (marked by a dashed vertical line in figure 1(c)), which is within the resonance window of the magnetic tunnel junction. Figure 1(d) presents the output voltage V_DC versus the input power P_RF, for various dc currents in the strip-line. We observe that the measured voltage (dots) shows a linear dependence (dashed lines) on the power P_RF, with the proportionality factor dependent on the dc tuning current, i.e. on the resonance frequency. As a consequence, the magnetic tunnel junction performs the operation:

$$\begin{equation*}{V}_{\mathrm{D}\mathrm{C}}={P}_{\mathrm{R}\mathrm{F}}{\times}W\end{equation*}$$

where $W=W\left({f}_{\mathrm{R}\mathrm{F}}-{f}_{\text{res}}\right)$ is the synaptic weight, which is a function of the difference between the resonance frequency and the input frequency. Tuning the resonance frequency allows us to tune the synaptic weight. In order to successfully implement the synaptic operation, it is critical to be in the low power linear regime where the resonance frequency does not vary significantly with the input power, which is the case here. In future implementations, the tuning of the weight could be achieved in a non-volatile fashion by placing a memristive device on top of the free magnetic layer and electrically controlling its resonance frequency [38]. Note that a single device is sufficient to implement both negative and positive values of the weight, which is an advantage over other synaptic nanodevices [30].

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In order to demonstrate the MAC operation, we connect by wire bonding two magnetic tunnel junctions in series head to tail (MTJ 1 and MTJ 2), forming a synaptic chain, as schematized in figure 2(b). Figure 2 shows the characterization of the synaptic chain submitted to a single RF signal. In figure 2(a) we plot the voltage across the chain versus the input frequency f_RF and observe two resonance peaks, indicated by yellow and green zones, corresponding to MTJ 1 and MTJ 2, respectively. Figures 2(c) and (d) show the effect of applying dc tuning currents I₁ and I₂ in the strip lines above MTJ 1 and MTJ 2, respectively. We observe that the resonance frequencies of both MTJs can be tuned within intervals larger than 100 MHz. Figures 2(e) and (f) show the voltage across the chain at fixed input frequencies f¹ _RF = 174 MHz and f² _RF = 540 MHz respectively (dashed lines in figures 2(c) and (d) respectively) versus the input power, for different dc tuning currents. Fixing the frequency at f¹ _RF = 174 MHz (resp. f² _RF = 540 MHz) makes it possible to address MTJ 1 (resp. MTJ 2). We observe that both MTJs perform the expected synaptic multiplication: the measured voltage (dots) can be described by a linear model (dashed lines). The synaptic weights W₁ and W₂ (slopes of the fits) are color coded and depend on the tuning currents I₁ and I₂.

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We now test the capability of this chain of two synapses to perform the MAC operation on two RF inputs. The inputs are two RF powers P₁ and P₂, carried by signals at frequencies f¹ _RF and f² _RF respectively. We sum the two RF inputs using a power combiner and inject the resulting signal into the synaptic chain, as schematized in figure 3(a). We measure the output voltage generated by the chain for different combinations of P₁, P₂, W₁ and W₂ (i.e. for different combinations of P₁, P₂, I₁ and I₂). P₁ and P₂ were each varied from 2 to 12 μW by steps of 2 μW while I₁ and I₂ were each varied from 0 to 10 mA by steps of 2 mA. In figure 3(b) we compare the measured voltage across the chain for each combination (blue dots) to the ideally expected MAC voltage computed from single RF signal measurements (black line):

$$\begin{equation*}{V}_{\text{MAC}}={P}_{1}{\times}{W}_{1}+{P}_{2}{\times}{W}_{2}\end{equation*}$$

with ${W}_{1}={W}_{1}\left({{f}_{\mathrm{R}\mathrm{F}}}^{1}-{{f}_{\text{res}}}^{1}\right)$ and ${W}_{2}={W}_{2}\left({{f}_{\mathrm{R}\mathrm{F}}}^{2}-{{f}_{\text{res}}}^{2}\right)$. For each combination of I₁ and I₂, the values of W₁ and W₂ are extracted from the linear fits of the single RF signal input characterization (shown in figures 2(e) and (f)). We observe that the experimental voltage matches closely the ideal MAC voltage, with a slope of 0.99 and a root mean square error over all data points of 0.41 μV. In the next section, we evaluate the quality of this MAC operation by using it for RF signals classification then compare it to a simulated noisy MAC.

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We illustrate the utility of this MAC operation by a simple classification example, shown in figure 4(a). The inputs are the powers P₁ and P₂ of RF signals at frequencies f_RF ¹ and f_RF ². We apply a MAC operation to the inputs using the synaptic chain. If the measured output voltage is positive we classify the (P₁, P₂) input as 'class 1' (blue squares), while if the voltage is negative we classify the (P₁, P₂) input as 'class 0' (red dots). Each combination of weights defines a boundary in the 2D plane of axis P₁ and P₂, and therefore constitutes a possible classification task. Here we first evaluate the classification accuracy for a classification task defined by a fixed predefined combination of weights. Figure 4(b) shows the classification results for one classification task, corresponding to the following weight configuration: W₁ = −0.50 V W⁻¹ and W₂ = 0.23 V W⁻¹ (achieved by applying I₁ = I₂ = 0 mA). The dashed line is the boundary between the two classes expected from this weight configuration. The assigned classes are labeled by the blue squares and red dots. For this classification task, the experimental accuracy obtained—i.e. the proportion of correctly classified (P₁, P₂) inputs—is 100%.

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Figure 4(c) shows the classification results for all fixed weight configurations, where each black dot corresponds to a classification task defined by a weight configuration. The y-axis is the proportion of correctly classified (P₁, P₂) inputs while the x-axis is the root mean square error of the measured voltage compared to the ideal MAC voltage, computed over all (P₁, P₂) inputs. We observe that there is a correlation between classification accuracy and error on the MAC operation: a more precise MAC operation provides more accurate classification. However, we observe a large spread in classification accuracy for each average MAC error. Indeed, the classification accuracy is mainly dictated by the error introduced by inputs close to the boundary (shown as the black dashed line in figure 4(b)). This error is itself largely dependent on the values of P₁ and P₂ (larger powers tend to lead to larger errors). This dependency of errors on inputs explains the observed spread.

The mean accuracy averaged over all classification tasks (weight configurations) of our MAC operation is 93.9%. In order to better evaluate the suitability of this accuracy, we perform the same classification with a simulated noisy MAC. We use the same inputs and weight configurations as for the experimental MAC. For each (P₁, P₂, W₁, W₂) configuration, we simulate the noisy MAC output by a voltage drawn from a normal distribution around the ideal MAC voltage. The standard deviation of the distribution is the mean square error obtained from the experiment for this weight configuration. The red crosses correspond to the classification results for the simulated noisy MAC. The overall accuracy for all the weights configurations is 93.6%. The fact that the experimental MAC and the simulated noisy MAC provide similar accuracies shows that the experimental MAC does not suffer from systematic errors and is indeed suitable for classification of RF signals.

We have experimentally demonstrated that a magnetic tunnel junction can act as an RF synapse able to perform the multiplication of RF powers on analog RF signals, with tunable synaptic weights taking both positive and negative values. We have also demonstrated that several synapses in series can perform the MAC operation, which is at the core of artificial neural networks. We illustrate the application of our system by performing a simple classification task on RF signals. This RF MAC implementation leverages the fact that each synapse is frequency selective, i.e. it only responds to RF signals in its resonance window. We expect this frequency multiplexing scheme to lead to the simplification of architecture for large neural networks, as a single signal combining all inputs can be sent to all synapses of a layer. These results were demonstrated here with vortex-state magnetic tunnel junctions, but could be applied to any spintronic resonator. Variability in the diameter of the devices will lead to variability in the resonance frequency of the synapses, which we expect to compensate for during the learning process as long as the variation range is lower than the tunability range. In order to classify RF signals from various sources for applications, it is critical to have resonators responding to a wide range of frequencies. Vortex-state magnetic tunnel junctions can exhibit frequencies from tens of MHz to several GHz [11], and uniform mode magnetic tunnel junctions or spin Hall oscillators could act as synapses with frequencies up to tens of GHz [26, 39]. The same stack of materials can lead to resonators of different frequencies, depending on the size and geometry of each device. Therefore, one could build an array of synapses of different resonance frequencies, able to respond to, and classify, RF signals over the 50 MHz–50 GHz frequency range in parallel. Magneto-electrical effects can also be used to tune synaptic weights in a non-volatile fashion. This opens the path for compact, fast and energy efficient devices, allowing RF-signal classification in embedded systems.

This work is supported by the European Research Council ERC under Grant No. bioSPINspired 682955, the French ANR project SPIN-IA (Grant No. ANR-18-ASTR-0015), and the French Ministry of Defense (DGA). We thank A Ross for helpful comments.

The data that support the findings of this study are available from the corresponding author upon reasonable request.