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Abstract An emerging paradigm in modern electronics is that of CMOS+$${\mathsf{X}}$$ requiring the integration of standard CMOS technology with novel materials and technologies denoted by$${\mathsf{X}}$$ . In this context, a crucial challenge is to develop accurate circuit models for$${\mathsf{X}}$$ 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+$${\mathsf{X}}$$ systems, where$${\mathsf{X}}$$ 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.more » « lessFree, publicly-accessible full text available December 1, 2025
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Singh, Nihal Sanjay; Niazi, Shaila; Chowdhury, Shuvro; Selcuk, Kemal; Kaneko, Haruna; Kobayashi, Keito; Kanai, Shun; Ohno, Hideo; Fukami, Shunsuke; Camsari, Kerem Y (, Technical digest)
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