In the past decades, artificial neural networks (ANNs) have been extensively studied with excellent results in many domains of science, being image1 and speech2 recognition notable examples that have been extended to important areas, such as precision medicine3. These networks are made up of several layers of artificial neurons interconnected via artificial synaptic connections which require a programmable weighting mechanism between outputs and inputs to enable the artificial network to learn. ANNs implemented in software have been successful, but power efficient and scalable hardware implementations of such systems are lagging behind. To date, various technologies have been proposed to implement neuromorphic computing, namely optical4, semiconductor5,6, bioelectronic7, carbon-based8, superconducting9 and memristive10 devices.

In recent years, spintronic devices have also been proposed for the hardware implementation of neuromorphic computing systems11,12,13. Spin torque nano-oscillators (STNOs) are among the most studied spintronic devices for use in ANNs14,15,16,17,18,19,20,21. An STNO consists of a spin valve22,23 or, more often, an MgO-based magnetic tunnel junction (MTJ)24,25, combining a resistive output which depends on the magnetization state of a ferromagnetic layer with rich magnetization dynamics that can be manipulated by spin-polarized currents26,27. These RF oscillators show a high degree of versatility since, depending on the input signal, they can work as nano-scale RF sources28,29 as well as RF detectors30,31,32,33.

Significant advances have been made recently14,15,16,17,18,19,20, with reports showing STNO neural capabilities in reservoir computing systems16,17,18, where the transient dynamic state of the oscillator (i.e. short-term memory) is used to compute time-varying input signals. Non-trivial tasks such as vowel recognition were achieved in a synchronization-based computing system19, where the recognition is performed based on the synchronization state between the input signal and a chain of four STNOs representing artificial neurons. More recently, STNOs have also been proposed to work as synapses in ANNs where, based on the spin diode effect, the synaptic weight depends on the frequency difference between the input RF signal and the resonator20,21. In this work, we propose the possibility of adding non-volatility to an STNO working as an artificial synapse, which in turn enables learning in an ANN using such devices. Specifically, we show that the detection (i.e. synaptic weight) of a vortex-based spin torque nano-oscillator (STVO) by spin diode effect depends on the vortex chirality and can be persistently changed after fabrication by means of a proper initialization via electrical signals applied selectively to each device alone.

Experimental details

This work is based on circular nanopillars with diameters of 0.9 μm and 1.0 μm, patterned from a 6.0 IrMn/2.0 CoFe30/0.7 Ru/2.6 CoFe40B20/0.8 MgO/2.0 CoFe40B20/0.2 Ta/7.0 NiFe MTJ stack (thickness in nanometers). The MgO barrier thickness results in a resistance-area product of 8.0 Ω µm2 (resistance of the parallel configuration of the MTJ considered) and the 2.0 CoFe40B20/0.2 Ta/7.0 NiFe free layer provides a remanent vortex state34. A field line antenna with a width of 3 µm is vertically integrated with the nanopillar, at a distance of approximately 600 nm on top of the free layer (Fig. 1a). The field line antenna allows the application of a local in-plane magnetic field (Fig. 1b) along the reference direction (yy axis in Fig. 1a) set by the synthetic antiferromagnetic structure (SAF), which is defined by a 1 Tesla magnetic field applied during the cool down of an annealing step performed at a temperature of 330 °C with a duration of 2 h. In this geometry, the field line is capable of producing a local magnetic field large enough to saturate the free layer, so Fig. 1c shows how the field line in conjunction with the local bias current applied to the MTJ can be used to set the vortex chirality. Here, a positive DC bias current corresponds to electrons traveling from the free to the reference layer and a positive chirality (C =  + 1) corresponds to a clockwise rotation of the free layer magnetization as seen from the bottom (see inset of Fig. 1c). The protocol used to deterministically set the vortex chirality can be described as a three-step initialization of the vortex. In the first step, a DC bias current (IDC) is applied directly through the MTJ, together with a field line current producing a local magnetic field large enough to saturate the free layer (point 1). In the second step, the magnetic field is reduced down to a value that results in the renucleation of the vortex (point 2). In this example, the magnetic field was reduced down to zero (but a range of other values is possible in accordance to the specific R-H loop of the device) and the bias current amplitude is set to 5.0 mA (which results in a current density of 6.4 × 109 A/m2). At this point, the chirality of the vortex is defined by the direction of the Oersted field associated with the DC bias current35. A positive bias IDC results in the nucleation of a vortex with a positive chirality, while a negative bias IDC results in the nucleation of a vortex with a negative chirality. In the third step, the magnetic field and bias IDC are set to zero. After this process is complete, the vortex chirality is defined and remains stable. This process of setting the vortex chirality is completely deterministic, so that switching the vortex to the opposite chirality is achieved simply by repeating the process with an initialization bias current applied in the opposite direction. Once the vortex is initialized with a specific chirality, a spin diode measurement is performed using a bias tee to apply an RF signal with a sweeping frequency directly to the MTJ and measuring as output the rectified voltage across the MTJ nanopillar, as shown in Fig. 1b.

Figure 1
figure 1

(a) Top view optical image of the devices after fabrication with an integrated local field line fabricated on top of the MTJ nanopillar. (b) Illustration of the experimental setup used for the initialization and spin diode measurements. (c) Two terminal R-H loop for an MTJ with a diameter of 1.0 µm, explaining the 3-step initialization process. The insets show how each chirality is associated with a different vortex configuration of the in-plane magnetic moments of the free layer, as seen from the bottom of the MTJ.


Figure 2a,b show a spin diode measurement obtained from an MTJ with a diameter of 1.0 µm, as a function of the input RF current density (JRF) at zero external magnetic field. There is an obvious dependence of the spin diode output on the chirality of the vortex. The difference between the two chiralities is made evident in Fig. 2c, obtained by measuring the spin diode voltage output as a function of the RF current frequency for a fixed RF amplitude, corresponding to a current density of 2.8 × 109 A/m2 across the MTJ. The output obtained for each chirality shows a degree of symmetry with respect to the central frequency of detection. In Fig. 2d, the frequency of the RF signal is fixed at 60 MHz (a point close to the central frequency) and the RF signal amplitude is swept, resulting in a rectified voltage that is symmetric with respect to each of the two chiralities across the whole range. It is also worth noting that, for both chiralities, the spin diode voltage output is proportional to the RF signal amplitude, indicating that the nonlinear characteristics of the detector36 have a small effect with this specific geometry and current density range. In this way, the STVO can function as an artificial synapse whose weight can be persistently changed in a binary and non-volatile scheme, so that the rectified voltage measured for positive (V+) and negative (V) chiralities is given by21

Figure 2
figure 2

Spin diode measurements presented as a function of the input RF current density for (a) positive and (b) negative chiralities. (c) Spin diode measurement obtained for an input RF current density of 2.8 × 109 A/m2. (d) Rectified voltage measured at a fixed frequency of 60 MHz and presented as a function of the input RF current density.

$${V}^{+}={W}^{+} \cdot {J}_{RF}$$


$${V}^{-}={W}^{-} \cdot {J}_{RF},$$

where W+ and W are the synaptic weights (i.e. slope of each linear fit in Fig. 2d) for each chirality. Similar to an STT-MRAM37 , where a large current density is used to set MTJs between two possible states that are read at low current densities, the initialization step allows to switch the chirality of the vortex, which in turn changes the spin diode output at fixed values of input RF signal amplitude and frequency. The synaptic weight is proportional to the output voltage measured for a given JRF. In turn, the output voltage depends on the amplitude of the vortex core oscillation during resonance, in a way that, by TMR effect, a larger orbit of the core leads to a larger output voltage. Thus, to maximize the synaptic weights, it is required to maximize the radius of the vortex orbit. That radius depends in a complex way on a large number of material properties31 but, as an example, an obvious way to do it is to optimize the spin torque efficiency and/or decrease the Gilbert damping of the free layer38.

To have a physical insight of the experimental results, micromagnetic simulations were performed using the GPU-based software MuMax339. The simulations comprised a circular nanodisk with a diameter of 1.0 µm and a thickness of 9.0 nm. The reference layer is set with an in-plane magnetization along the yy axis of the simulation plane. Based on experimental VSM data taken from NiFe films and standard values, the physical parameters were chosen as: saturation magnetization \({\mathrm{M}}_{\mathrm{S}}=680\times {10}^{3} \;\; \mathrm{ A}/\mathrm{m}\), uniaxial anisotropy constant along the yy axis \({\mathrm{K}}_{\mathrm{u}}=340 \;\; \mathrm{ J}/\text{m}^{3}\), Gilbert damping \(\alpha =0.01\) and exchange stiffness \(\mathrm{A}=1.3\times {10}^{-11}\;\;\mathrm{ J}/\mathrm{m}\). An RF current density was applied in the direction perpendicular to the nanodisk plane, being its radial Oersted magnetic field also considered, with a spin-polarization \(\mathrm{P}=0.4\) and a secondary spin-torque term \({\varepsilon }{^{\prime}}=0.4\). In this way, the simulated gyrotropic motion is considered to be driven, not only by the spin-transfer torque (STT)40 that naturally arises from the spin-polarized current, but also by a realistic Oersted field torque (OFT) coming from the RF current. The initial magnetization configuration for the micromagnetic simulations was set as a vortex with the two possible chiralities at a positive polarity. According to the simulations, the polarity switching does not change the spin diode results (see the supplementary information).

Figure 3a shows the amplitude of the simulated spin diode results, calculated as a function of the RF current density for both chiralities. The results are calculated at a fixed frequency of 81 MHz. The effective field (i.e. sum of all the internal and external magnetic fields) acting on the free layer41,42 leads to a displacement of the vortex core position from the geometric center of the pillar, which needs to be considered (i.e. in-plane magnetic field along the yy direction) to properly simulate the experimental conditions and was determined to be \({\mathrm{H}}_{\mathrm{eff}}=39.8\pm 0.3 (\mathrm{Oe})\) (see the supplementary information). The simulated nanodisk does not give a complete description of the real MTJ nanopillar, so that the frequency discrepancy between experimental and simulated data is expected. The rectified voltage (VREC) is estimated based on experimental data, so that

Figure 3
figure 3

(a) Simulated rectified voltage calculated as a function of the input RF current density for the two different vortex chiralities at a fixed frequency of 81 MHz. An in-plane magnetic field of 39.8 Oe is applied in the yy direction. The simulated spin diode measurements for (b) positive and (c) negative chiralities are presented for different excitation mechanisms: spin-transfer torque (STT), Oersted field torque (OFT) and where both mechanisms are considered (OFT + STT). The results were obtained for an RF current density of 3.0 × 109 A/m2. (d,e) Simulated ΔMY time traces obtained for both chiralities. Similar to (b) and (c), different excitation mechanisms are considered. The results were obtained for an RF current density of 3.0 × 109 A/m2 at a frequency of 81 MHz whose time traces are also presented.

$${V}_{REC}=\frac{{R}_{AP}-{R}_{P}}{2}\cdot S\cdot \frac{1}{T}{\int }_{0}^{T}{\Delta M}_{Y}\left(t\right)\cdot {J}_{RF}\left(t\right) dt,$$

where RP (RAP) is the resistance of the MTJ in the parallel (antiparallel) configuration, S the area of vortex (S = πd2/4, being d = 1.0 µm the diameter of the nanodisk) and ΔMY the variation in time of the normalized magnetization in the yy direction. To estimate VREC, values of RP and RAP are measured with a bias DC current of 0.1 mA from the MTJ device whose spin diode measurement is presented in Fig. 2 (see supplementary information). For each frequency value, the simulations are performed for a time period T = 300 ns. Similar to the experimental results, the voltage presents different signs, as a result of the two different lineshapes given by different chiralities (see OFT + STT curve from Fig. 3b,c). In order to study the role of the OFT in the gyrotropic motion, Fig. 3b,c also show the simulated spin diode detection when only one excitation mechanism is considered at a time: a pure STT-driven oscillation (red data) and a pure OFT-driven oscillation (blue data). For an STT-driven oscillation, the spin diode response is the same for both chiralities. On the other hand, the OFT-driven output shows two symmetric lineshapes which depend on the vortex chirality. As described in Eq. (3), VREC is calculated according to the time-averaged phase difference between ΔMY and JRF. The OFT-driven oscillation leads to two perfectly symmetric lineshapes, meaning that a chirality switching results in a 180° phase shift of the OFT-driven ΔMY oscillation.

To see how the combination of the STT and OFT creates distinct spin diode lineshapes for different chiralities, Fig. 3d,e show time traces of the simulated gyrotropic motion for different oscillation-driven mechanisms. Again, the frequency of JRF is 81 MHz, near the central frequency of detection and the results are presented for the two chiralities. The time-averaged phase difference ψ between ΔMY and JRF can be defined as

$$\psi =\frac{1}{T}{\int }_{0}^{T}[ {\varphi }_{{\Delta M}_{Y}}\left(t\right)-{\varphi }_{{J}_{RF}}\left(t\right) ]dt$$

being \({\mathrm{\varphi }}_{{\Delta \mathrm{M}}_{\mathrm{Y}}}\) the phase of the ΔMY oscillation and \({\mathrm{\varphi }}_{{\mathrm{J}}_{\mathrm{RF}}}\) the phase of the RF current density. For C =  + 1, the STT and OFT oscillations are in-phase, so that their combination results in a larger gyrotropic orbit with ψ = − 15° which, according to Eq. (3), leads to a positive voltage of 1.2 mV (Fig. 3b). For C = − 1, the STT oscillation is unchanged, but due to the 180° shift of the OFT-driven oscillation, now they are out-of-phase, which damps the oscillation to a smaller orbit with ψ = 163°, leading to a negative voltage of − 0.7 mV (Fig. 3c). These results clearly demonstrate the major role of the Oersted field in defining the spin diode output voltage.

It should be emphasized the importance of having a displacement of the vortex core at the remanent state. In fact, if the core is at the center, the spin diode output for C =  + 1 and C = − 1 should be the same (see the supplementary information). The Oersted field creates magnetic field lines whose center is also the central point of the pillar. When the core is at the center of the pillar, the vortex in-plane magnetization will be collinear with the Oersted field lines, so no oscillation of the vortex core is expected33. If there is no OFT-driven oscillation, the STT would be the only mechanism responsible for the gyrotropic motion, so that the MY oscillation would be the same for both chiralities. The role of the in-plane field acting on the free layer is clarified by simulated results shown in Fig. 4. For each value of the external magnetic field, the spin diode output is computed for the two chiralities at a fixed RF current density, as shown in Fig. 4b for the particular case of a setpoint field of 18.0 Oe. The interest relies on the frequency fMAX that maximizes the difference ΔV(fMAX) = V+(fMAX) – V(fMAX), where V+(fMAX) and V(fMAX) are the output voltages calculated at fMAX for C =  + 1 and C = − 1, respectively. Out of these results, ΔV(fMAX) is calculated for each value of the effective field acting on the free layer (Fig. 4a). As expected, at zero field, there is no distinction between the spin diode of different chiralities, so that ΔV = 0. The applied field allows to increase the vortex core displacement, which in turn increases the OFT contribution to the overall gyrotropic oscillation that breaks the symmetry of the resonance phenomenon (see supplementary information). Considering that the synaptic weight is proportional to the measured output voltage, these results suggest that the difference between W+ and W (i.e. non-volatile effect) can be optimized by promoting the maximum core displacement, which should only be limited to avoid a possible vortex core expulsion during the resonance process31,43, due to the proximity of the core with the pillar boundary.

Figure 4
figure 4

(a) Difference of the output voltage (ΔV) calculated for C =  + 1 and C = − 1. For each setpoint field, ΔV is calculated at the frequency fMAX that maximizes the difference. (b) Example of the ΔV calculation for a setpoint field of 18.0 Oe.

Once a non-volatile control of the synaptic weight is achieved for a single STVO, this control mechanism can be extended to a set of STVOs with different geometries and dynamic properties. Figure 5a,b demonstrates this possibility for a pair of circular STVOs with different diameters, where the spin diode outputs are presented for each pillar individually. Due to its lower dimensions, the MTJ with a diameter of 0.9 µm presents a larger resonance frequency than the MTJ with a diameter of 1.0 µm43,44, meaning that it is straightforward to program a fixed input frequency, so that the rectified voltage measured by each pillar is different. Figure 5c shows four possible spin diode outputs calculated as the sum of the output voltage measured individually for each pillar when subjected to a variable amplitude RF signal injected with a fixed input frequency of 60 MHz. Considering that each pillar has two possible synaptic weights (i.e. two possible chirality configurations), the system ends up with four possible programmable outputs (N non-identical STVOs lead to 2N programmable outputs) that may vary depending on the frequency and power of the input signal. In addition to fabricate MTJ pillars with different diameters, there are other possible ways to obtain non-identical detectors. An alternative could be to change the thickness of the free layer by deposition of a free layer wedge during the nanofabrication process (i.e. changing the vortex aspect ratio34). This step would lead not only to a smooth variation of the resonance frequency over the wedge, but also to a smaller variation of the resistance between non-identical STVOs, which would be essentially dependent on the sample-to-sample variability. The resistance variability between STVOs should be minimized to make sure that, for the same input RF power, all the STVOs receive approximately the same RF current density.

Figure 5
figure 5

Spin diode measurements obtained for an STVO with a diameter of (a) 1.0 µm and (b) 0.9 µm, for an RF input power of 0.398 mW. The four possible programmable sums of the output voltages are presented in (c) as a function of the input RF power for a frequency of 60 MHz.


In conclusion, it is shown that a vortex-based spin torque nano-oscillator (STVO) working as a rectifier can be used as a binary non-volatile artificial synapse, enabling learning to be performed in ANNs making use of these devices. The synaptic weight can be persistently changed by switching the chirality of the vortex induced in the free layer. Micromagnetic simulations show that the Oersted field created by the RF current density is the main responsible for the symmetry breaking. It is also proposed to scale up the programming outputs by using two STVOs with different resonance frequencies, in this way opening new perspectives to a full integration of spintronic devices in neuromorphic hardware.