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].