Non-Volatile Vortex MTJs with Opto-Electrical and Spin-Diode Nonlinearities as Multifunctional Neuromorphic Platforms

Abstract

The human brain achieves exceptional energy efficiency by co-locating memory and processing, yet reproducing this principle in hardware remains challenging because many neuromorphic devices require standby power, offer limited programmability, or separate state storage from nonlinear computation. Here we demonstrate a multifunctional spintronic platform based on storage-layer-enabled vortex magnetic tunnel junctions (MTJs) that unifies non-volatile weight storage, optoelectrically driven nonlinear computation, and multilevel readout within a single nanopillar. A thermally programmable FM/AFM storage layer retains analog synaptic weights with zero standby power and enables non-volatile tuning of the vortex gyrotropic resonance over ${\sim}15$~MHz. Under optoelectrical operation, combined laser heating and dc bias drive the junction into the bias-enhanced tunnel magneto-Seebeck (bTMS) regime, where the thermoelectric response exhibits a pronounced cubic nonlinearity providing a compact, hardware-native transfer function for weighted analog computation. The electrical and thermoelectric channels switch at matched coercive fields but with distinct amplitudes, yielding an effective four-level readout space. Crossbar-array simulations parameterized by measured device response maps evaluate two neuromorphic modes -- a bTMS mode (optical input, dc-bias weights) and a spin-diode mode (RF-frequency input, RF-power weights) -- achieving image-classification accuracies of $95.4\%$ and $94.9\%$, comparable to a digital single-layer network with sigmoid activations. Smaller 600~nm devices consistently outperform larger ones, identifying nonlinear-response engineering as a key device-level lever. Because bTMS and spin-diode rectification coexist in the same junction, a combined regime could enable nonlinear multi-input interactions, including quadratic cross-terms, within a single nanoscale element.

Figures (5)

• Figure 1: Device concept and nonlinear response characteristics enabling neuromorphic functionality. (a) Schematic representation of the studied structure. (b) Optical microscope image of the structure. (c) Scanning electron microscopy (SEM) image of the MTJ nanopillar. (d) Distribution of the magnetostatic field generated by the storage layer and acting on the free layer, obtained from micromagnetic simulations. (e) Schematic representation of a neural-network layer and the physical quantities that take the roles of input, output, and weights: in the case of the bTMS effect, the input is injected optically while synaptic weights are controlled with bias currents; in the case of the spin-diode effect, the input is encoded in the frequency of an RF signal while its power plays the role of a synaptic weight. The nonlinear device response in both cases enables nonlinear processing, playing a role analogous to a nonlinear activation function. (f) Measured spin-diode response under RF excitation, showing a strongly nonlinear voltage characteristic that directly supplies a rich analog transfer function for neuromorphic signal processing. (g) Measured bias-enhanced tunnel magneto-Seebeck (bTMS) thermovoltage versus dc bias current for two laser powers, highlighting a pronounced cubic-like nonlinearity suitable for neuron-like activation in neuromorphic hardware.
• Figure 2: Laser-induced thermomagnetic Seebeck effect in vortex spin-torque nano-oscillators. (a--c) Seebeck voltage $V^{\mathrm{AC}}$ as a function of in-plane magnetic field $B_{\parallel}$ for nanopillars with diameters $d = 600$, 800 and 1000 nm, measured for laser powers at the sample $P = 15\text{--}67~\mathrm{mW}$. (d--f) Power dependence of the Seebeck voltages in the parallel and antiparallel configurations, $V_{\mathrm{P}}^{\mathrm{AC}}$ and $V_{\mathrm{AP}}^{\mathrm{AC}}$, evaluated at $B_{\parallel}=\pm 30~\mathrm{mT}$, together with their difference $\delta V_{\mathrm{P,AP}} = V_{\mathrm{AP}}^{\mathrm{AC}} - V_{\mathrm{P}}^{\mathrm{AC}}$ and the TMS ratio. Solid lines are linear fits; the corresponding slopes $\alpha$ are given in $\mu\mathrm{V}\,\mathrm{mW}^{-1}$ and $\%\;\mathrm{mW}^{-1}$.
• Figure 3: Thermovoltage $\Delta V_{\mathrm{AC}}$ as a function of in-plane magnetic field $B$. (a,b) Vortex STNOs with $d=600\,\mathrm{nm}$ and (c,d) $d=800\,\mathrm{nm}$. The data were acquired with a magnetic-field step of $0.25\,\mathrm{mT}$.
• Figure 4: Measured thermovoltage in the P and AP states as well as bTMS ratio as a function of bias current for individual laser powers. Vortex STNO devices with nanopillar diameters $d = 600$ nm (top row) and $d = 800$ nm (bottom row). Solid lines in (a), (b), (d), and (e) represent cubic polynomial fits to the data of the form $V(I) = \sum_{n=0}^{3} a_n I^n = a_3 I^3 + a_2 I^2 + a_1 I + a_0$, while the curves in (c) and (f) serve as guides to the eye.
• Figure 5: Neuromorphic computing performance for different device dimensions and operations. (a) We leverage the nonlinear response due to the bTMS effect. The laser power is used to encode the input data, while the bias currents implement synaptic weights. (b) A crossbar-array architecture allows us to perform the linear multiply-accumulate operations as well as the nonlinear activation function in one go. Input powers are set equal across a column, and output voltages are accumulated along a row to yield the output of the neural network layer. (c) We use interpolation functions \ref{['eq:interpolation']} that interpolate linearly between measurement data points to realistically model the device response. We consider different device sizes and operation modes. (d) The evolution of the test accuracy during the training. Smaller devices attain a higher accuracy regardless of the mode of operation. We performed vanilla gradient descent with a learning rate of $10^{-2}$. (e) Best achieved test accuracy (dot) and fluctuations within the $+100$ and $-100$ epochs of the best attained accuracy (box plot). (f) Neuromorphic setup using the spin-diode effect: frequency and power of an incoming RF signal are used to encode the input data (frequency) and the weights (power), while, just as before, the accumulated voltages across a row serve as output. (g) The response of a single device to an RF signal at $B=0$. We only show the response for signal powers $P/P_\mathrm{max}\in[0.4,0.65]$ since outside of this regime, the response is relatively featureless. The frequency axis has been rescaled such that the measurement interval $[f_\mathrm{min},f_\mathrm{max}]$ aligns with $[0,1]$. (h) Training and test accuracy of the simulated neuromorphic chip based on the spin-diode effect.