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Abstract An emerging paradigm in modern electronics is that of CMOS+$${\mathsf{X}}$$ $X$requiring the integration of standard CMOS technology with novel materials and technologies denoted by$${\mathsf{X}}$$ $X$. In this context, a crucial challenge is to develop accurate circuit models for$${\mathsf{X}}$$ $X$that are compatible with standard models for CMOS-based circuits and systems. In this perspective, we present physics-based, experimentally benchmarked modular circuit models that can be used to evaluate a class of CMOS+$${\mathsf{X}}$$ $X$systems, where$${\mathsf{X}}$$ $X$denotes magnetic and spintronic materials and phenomena. This class of materials is particularly challenging because they go beyond conventional charge-based phenomena and involve the spin degree of freedom which involves non-trivial quantum effects. Starting from density matrices—the central quantity in quantum transport—using well-defined approximations, it is possible to obtain spin-circuits that generalize ordinary circuit theory to 4-component currents and voltages (1 for charge and 3 for spin). With step-by-step examples that progressively become more complex, we illustrate how the spin-circuit approach can be used to start from the physics of magnetism and spintronics to enable accurate system-level evaluations. We believe the core approach can be extended to include other quantum degrees of freedom like valley and pseudospins starting from corresponding density matrices. 

The spintronic stochastic spiking neuron (S3N) developed herein realizes biologically mimetic stochastic spiking characteristics observed within in vivo cortical neurons, while operating several orders of magnitude more rapidly and exhibiting a favorable energy profile. This work leverages a novel probabilistic spintronic switching element device that provides thermally-driven and current-controlled tunable stochasticity in a compact, low-energy, and high-speed package. Simulation program with integrated circuit emphasis (SPICE) simulation results indicate that the equivalent of 1 second of in vivo neuronal spiking characteristics can be generated on the order of nanoseconds, enabling the feasibility of extremely rapid emulation of in vivo neuronal behaviors for future statistical models of cortical information processing. Their results also indicate that the S3N can generate spikes on the order of ten picoseconds while dissipating only 0.6–9.6 μW, depending on the spiking rate. Additionally, they demonstrate that an S3N can implement perceptron functionality, such as AND-gate- and OR-gate-based logic processing, and provide future extensions of the work to more advanced stochastic neuromorphic architectures.