Hardware implementations of the Ising model offer promising solutions to large-scale optimization tasks. In the literature, various nanodevices have been shown to emulate the spin dynamics for such Ising machines with remarkable effectiveness. Other nanodevices have been shown to implement spin-spin coupling with compact footprint and minimal energy dissipation. However, an ideal Ising machine would associate both types of nanodevices, and they must operate synergistically to support annealing: a progressive reduction of machine stochasticity that allows it to settle to an energy minimum. Here, we report an Ising machine that combines two nanotechnologies: memristor crossbar – storing multi-level couplings – and stochastic magnetic tunnel junction (SMTJ), acting as thermally driven spins. Because the same read voltage that interrogates the crossbar also biases the SMTJs, increasing this voltage automatically lowers the effective temperature of the machine, providing an intrinsic, analog-native annealing technique. Operating at zero magnetic field, our prototype consistently reaches the global optimum of a 24-vertex weighted MAX-CUT and a 10-vertex, three-color graph-coloring problem using an externally implemented feedback loop. Given that both nanotechnologies in our demonstrator are CMOS-integrated, this approach is compatible with advanced 3D integration, offering a scalable pathway toward compact, fast, and energy-efficient large-scale Ising solvers.

Developing energy-efficient artificial intelligence requires moving learning out of conventional von Neumann hardware and into physical neural networks that compute and train in place. Thermally activated superparamagnetic tunnel junctions (SMTJs) provide a promising platform for this goal. By reducing the lateral dimensions of the free layer of a magnetic tunnel junction (MTJ), the device enters the superparamagnetic regime, where nanosecond magnetization fluctuations driven purely by thermal noise, without any additional driving current, emulate binary stochastic neurons at room temperature [1]. Because SMTJs and non-volatile MTJs share the same material stack and fabrication process, neuron-like and synapse-like functions can be accessed within a single CMOS-compatible spintronic platform through geometry and operating conditions alone, opening a concrete route toward dense, fully spintronic neural networks.

Efficient training of such physical networks remains the central challenge. Backpropagation, the dominant algorithm in modern AI, is poorly suited to hardware because gradients must be shuttled back and forth between memory and processing units at every layer, an overhead that grows with network depth. In contrast, local learning rules update each synapse from signals already available at its two terminals. We employ Equilibrium Propagation, a spatially local rule for energy-based models that is provably equivalent to gradient descent [2]. The SMTJ-and-crossbar network is itself an energy-based physical system whose stochastic Langevin dynamics, together with Kirchhoff laws, directly realize the equilibrium phase of the algorithm, so that the device physics performs inference with no auxiliary solver.

We present the first experimental on-chip training of a stochastic spintronic neural network, in which SMTJs act as binary stochastic neurons and a resistive crossbar implements the synaptic weights. Using SMTJs of 50 nm nominal diameter and 75% tunnel magnetoresistance, the network learns the XOR and two-moons benchmarks, reaching testing accuracies of 97.5% and 99.0% after 50 epochs, with the intrinsic device stochasticity aiding rather than hindering convergence. To the best of our knowledge, this is the first experimental demonstration of Equilibrium Propagation applied directly to stochastic hardware. Device-accurate simulations extend the approach to deeper architectures, where networks of more than 1000 SMTJs classify MNIST and FashionMNIST with accuracies up to 97.8% and 89.8%, comparable to state-of-the-art software results of equivalent size.

Beyond binary weights, we extend the same platform toward analog synapses. A series array of 18 perpendicular MTJs realizes a single multilevel nano-synapse whose junctions reverse sequentially under a quasi-static voltage sweep, producing a staircase resistance characteristic with 19 distinct non-volatile levels. Both potentiation and depression are obtained entirely electrically at a fixed applied field. In parallel, we nanofabricate passive crossbar arrays of binary synaptic MTJs designed to be interconnected with stochastic MTJs emulating the neurons, each cross-point executing the multiply-accumulate operation through Ohm and Kirchhoff laws while sharing the single magnetic stack used for the neurons.

Taken together, these results combine on-chip local learning, multilevel analog synapses, and passive binary crossbars within one spintronic technology, outlining a concrete path toward scalable, low-power neuromorphic and Ising-based systems that learn locally by turning thermal noise into the engine of computation [3].

The electricity consumed by artificial-intelligence (AI) workloads is becoming a major sustainability concern, and a large share of it is wasted not on computation itself but on the constant shuttling of data between the physically separated processing and memory units of conventional von Neumann computers, the so-called memory wall [1]. In-memory computing (IMC), which performs the computation directly inside an analog memory array where the data already reside, removes this energy bottleneck and is one of the most promising routes to sustainable AI hardware [2,3]. Its energy efficiency, however, hinges critically on the memory device. The ideal cell would be non-volatile, so that the stored neural-network weights consume zero static power and survive power-down with no need for refresh, while also being CMOS-compatible for cheap integration and offering many evenly spaced conductance levels for dense, high-precision analog encoding. Here we show that spintronics, the branch of electronics that exploits the electron's intrinsic magnetic moment (its spin) rather than only its charge, supplies exactly such a device. Our cell is a multi-state magnetic tunnel junction (M2TJ): two ferromagnetic layers shaped as crossing ellipses are separated by a thin insulating barrier, and the relative orientation of their magnetizations sets the quantum-mechanical tunneling resistance [4]. Because magnetic shape anisotropy pins each ellipse's magnetization along its long axis, the junction settles into several discrete, well-defined, and naturally equidistant resistance states that persist without power. This combination of non-volatility, CMOS compatibility, and intrinsically equidistant levels makes M2TJs ideal n-ary (multi-level) building blocks for neuromorphic IMC, in which each cell stores a multibit synaptic weight, complementing other emerging multilevel routes such as ferroelectric-FET crossbars [5].

We present a simulation framework for multibit neural-network inference on n-ary crossbar arrays, developed for spintronic M2TJs but generalizable to any multistate memristive device [6]. The framework retrieves the matrix-vector multiplication (MVM) result from the measured analog output with minimal assumptions, letting the crossbar act as a standalone AI co-processor placed where the data are generated: analog data from a camera or sensor enter the array directly as row voltages, cell currents sum along the columns by Ohm's law, and threshold-sensing circuitry reads the outputs and feeds the next inference layer. Using simulated 4x4 arrays of 4-state M2TJs, we demonstrate successful inference on the XOR task and on MNIST handwritten-digit classification, reaching 94.48% accuracy against a 97.56% software baseline; principal-component-analysis (PCA) dimensionality reduction narrows this gap to 2.79%.

A systematic error analysis identifies weight quantization as the dominant error source. We further study systematic nonidealities shared by all cells and cell-specific random noise. Critically, cell-specific noise is less detrimental than systematic nonidealities of equal amplitude, thanks to beneficial averaging across the array: the root-mean-square error scales as the square root of the number of columns while the signal-to-noise ratio grows only logarithmically, favoring wide crossbar geometries. Finally, we show that an optimal number of resistance states N_opt minimizes the total MVM error by trading quantization error against state resolution, with N_opt decreasing in noisier device environments, a direct design rule linking magnetic-device quality to achievable system accuracy.

By turning the unique magnetic, non-volatile, and multilevel character of crossed-ellipse junctions into accurate analog computation, this work positions n-ary spintronic crossbars as a concrete, energy-efficient hardware substrate for the sustainable AI that future materials-for-sustainability applications, from autonomous edge sensors to renewable-energy management, will demand.

Novel spintronic devices can play a role in the quest for GreenIT if they are stable and can transport and manipulate spin with low power. Devices have been proposed, where switching by energy-efficient approaches is used to manipulate topological spin structures that are stable in multilayers [1] but also in 2D systems [2]. We combine ultimate stability of topological states due to chiral interactions [3,4] with ultra-efficient manipulation using novel spin torques [3-7].

We use stochastic MTJs and skyrmion dynamics for non-conventional stochastic computing applications [8,9]. Beyond spatially multiplexed quasi-static Reservoir Computing [9], we have recently realized time multiplexed Reservoir Computing [10]. Given the huge tunability of thermal spin dynamics of skyrmions, the reservoir response can be tuned to the input timescales allowing for a drastic simplification of the device architecture and dynamic detection of time series with variable input timescales [10, 11].

While stochastic dynamics is thus useful for unconventional computing, machine learning can also be useful for skyrmion research. We have developed a convolutional neural network [12] based on the U-Net framework [13]. Our network is capable of detecting skyrmions and using a three-class approach it outperforms other approaches.

References

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             R. Gruber et al., Nature Commun. vol. 13, pp. 3144, 2022.

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In-memory computing constitutes a promising route toward more energy-efficient artificial-intelligence hardware as it reduces data transfer between memory and processing units and allows physical devices to directly perform vector-matrix operations. A central challenge, however, is to program the individual non-volatile memory components storing the weights in these dense networks without sacrificing compactness, energy efficiency, or scalability.

Existing approaches face important trade-offs. Passive crossbar arrays require complex biasing schemes across rows and columns, which increase circuit overhead and programming energy. Adding a transistor-based selector restores individual control but increases the cell area by factors up to two orders of magnitude in current demonstrations, while also adding local access routing, and complicating dense 3D integration. In addition, programming and inference typically still rely on distinct peripheral circuits for write driving, sensing and computation. More generally, architectures that rely on individual synapse access preserve programmability, but their wiring overhead makes scaling to dense large networks difficult. This motivates approaches in which many channels can instead be routed through shared physical interconnects.

Among neuromorphic hardware platforms, architectures that exploit frequency multiplexing are especially attractive because many input channels can be routed and processed on shared physical interconnects. This opportunity has been explored for inference in photonic systems based on wavelength-selective microring resonators, microring weight banks and phase-change photonic memories, as well as in spintronic systems including radio-frequency (RF) networks based on magnetic tunnel junctions [1]. Yet in all these platforms, frequency multiplexing applies solely to network inputs for inference, while programming relies on individual electrical access to each synapse, limiting scalability.

Here we introduce a different architecture, in which chains of magnetic tunnel junctions connected in series are addressed through a single shared RF strip line for synaptic programming, state readout and RF input delivery. Unlike individually addressed arrays, this scheme does not require per-synapse selector devices nor dedicated access lines. It exploits the frequency selectivity of magnetic tunnel junctions and the microwave-induced reversal of their magnetic state, here their vortex-core polarity. Because each junction is designed with a distinct resonance frequency, a broadcast RF signal can selectively switch or read any synapse within the chain.

Since all 11 junctions in the experimentally realized chain can be independently programmed through this single shared access, the chain can be placed in any of its 2048 binary configurations. Traversing this configuration space strongly reshapes the spectral transfer function of the chain, which we exploit for RF signal classification.  During inference, RF inputs are frequency multiplexed, so that the input dimensionality is not constrained by the number of magnetic tunnel junctions in the chain. Using two such chains, we physically implement a 22-synapse network that can be remotely reconfigured between handwritten-digit classification and drone RF-signature identification. After reconfiguration for each task, the experimental network reaches 94.91 ± 0.26% and 97.33 ± 0.62% accuracy, respectively, showing that the same hardware can switch between distinct functions while maintaining high task-specific performance. These results identify broadcast RF programming as a scalable route toward compact and rapidly reconfigurable neuromorphic hardware based on spintronic devices [2].

The ability to manipulate magnetic properties through ionic motion in ferromagnet/oxide opens exciting opportunities for the development of advanced spintronic functionalities, including reconfigurable multistate memories and cumulative gate effects. Inspired by memristor technologies, magneto-ionics has emerged as one of the most advanced approaches for controlling magnetic properties through ionic motion. Integrating ionic and spintronic technologies provides new degrees of freedom for designing neuromorphic hardware that combines novel magnetic functionalities with the well-established analogue behavior of ionic devices.

In this talk, I will present different strategies for implementing synaptic functionalities by exploiting the magneto-ionic control of magnetic anisotropy in CoFeB-based ionic/spintronic devices. I will demonstrate that magneto-ionic nanodevices not only operate as synaptic elements, by encoding multiple non-volatile electrically readable states through voltage-control of magnetic anisotropy, but also provide a versatile platform for realising more advanced bioinspired functionalities. In particular, we show that synaptic depression/potentiation in magneto-ionic synaptic elements can be tuned by an applied magnetic field, enabling dynamic control of the linearity of synaptic weight updates. This behavior is reminiscent of neuromodulation in biological systems. Neural network simulations further reveal that the magnetically induced improvement in weight-update linearity enhances learning accuracy over a broad range of learning rates.

Beyond non-volatile magneto-ionic effects, other material systems enable the exploration of volatile ionic effects in spintronic devices. In this case, we exploit the gate-induced transient reduction of magnetic anisotropy to engineer a time-dependent switching probability in a spintronic memory element driven by spin-orbit-torque-induced domain wall motion. While the magnetic state remains binary and non-volatile, the gate-induced magneto-ionic state is volatile. The device therefore separates two distinct functions: long-term information storage in the magnetic state and short-term update eligibility in the volatile magneto-ionic state, a feature that could be particularly attractive for reward-based learning schemes.

These findings highlight the versatility and promise of magneto-ionic devices as multifunctional synaptic elements for next-generation neuromorphic hardware.

The mutual synchronization of spintronic oscillators is a powerful phenomenon that enhances spectral performance for wireless communication and signal processing while opening new opportunities for unconventional computing and energy harvesting [1]. Early demonstrations with spin-torque nano-oscillators (STNOs) confirmed synchronization feasibility but were limited to small arrays due to challenges in coupling control and scalability [1,2]. Here, we report major advances using nano-constriction spin Hall nano-oscillators (NC-SHNOs), which provide a scalable, programmable, and CMOS-compatible platform for building large oscillator networks [1]. SHNOs, based on heavy-metal/ferromagnet bilayers driven by spin–orbit torques, offer precise frequency, phase, and coupling tunability through current, field, and geometry. Our previous work demonstrated synchronization in small chains and two-dimensional arrays, but limited coupling control and thermal effects constrained scalability [3,4].
Recently, SHNOs with perpendicular magnetic anisotropy (PMA), particularly W/CoFeB/MgO trilayers, have enabled propagating spin waves (PSWs) that naturally transmit phase information over micrometer distances [5]. We demonstrate variable-phase mutual synchronization mediated by PSWs [6], with electrical and μ-BLS measurements showing both in-phase and anti-phase modes, tunable by field angle and current. Micromagnetic simulations link this phase control to PSW dispersion characteristics, underscoring the advantages of PMA-SHNOs.
Building on this, we have scaled SHNO arrays to over 100,000 synchronized oscillators [7] using high-SOT W–Ta/CoFeB/MgO multilayers patterned into sub-20-nm constrictions [8]. These networks achieve output powers above 9 nW, quality factors exceeding one million, and exhibit long-range coherence suitable for wave-based computing, including reservoir computing and Ising machines. The platform also supports local, energy-efficient control via voltage-controlled magnetic anisotropy (VCMA) and memristive gating. Together, these advances establish SHNO networks as a leading candidate for next-generation spintronic systems, combining scalability, programmable phase control, and high coherence to enable powerful computing and microwave applications.

Physical neural networks typically train linear synaptic weights while treating device nonlinearities as fixed. We show the opposite - by training the synaptic nonlinearity itself using a Kolmogorov-Arnold framework, we yield markedly higher task performance per physical resource than conventional linear weight-based networks, and demonstrate that network topologies which directly learn nonlinear physical dynamics can enable strong learning at compact network sizes - up to 40-500x smaller than linear weight approaches. We demonstrate this in silicon-on-insulator on-chip devices operating at room temperature, 0.1-1 microampere currents, 750 fJ per nonlinear operation and 2 MHz speeds.

We show that physical KANs can be trained without reliance on backpropagation or surrogate device models, using forward-only noise-based decorrelated perturbative learning – which can match or exceed the performance of backpropagation.

Physical KANs demonstrate higher performance than equally-sized linear-weight based networks across a range of classification & regression tasks. These results establish programmable heterogenous physical nonlinearity as a promising computational primitive for compact and efficient learning systems.

Taglietti, Fabiana, et al. & Jack C. Gartside "Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks." arXiv preprint arXiv:2601.15340 (2026).

Liu, Ziming, et al. "Kan: Kolmogorov-arnold networks." arXiv preprint arXiv:2404.19756 (2024).