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.