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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. 

Abstract A P-N junction engineered within a Dirac cone system acts as a gate tunable angular filter based on Klein tunneling. For a 3D topological insulator with a substantial bandgap, such a filter can produce a charge-to-spin conversion due to the dual effects of spin-momentum locking and momentum filtering. We analyze how spins filtered at an in-plane topological insulator PN junction (TIPNJ) interact with a nanomagnet, and argue that the intrinsic charge-to-spin conversion does not translate to an external gain if the nanomagnet also acts as the source contact. Regardless of the nanomagnet’s position, the spin torque generated on the TIPNJ is limited by its surface current density, which in turn is limited by the bulk bandgap. Using quantum kinetic models, we calculated the spatially varying spin potential and quantified the localization of the current versus the applied bias. Additionally, with the magnetodynamic simulation of a soft magnet, we show that the PN junction can offer a critical gate tunability in the switching probability of the nanomagnet, with potential applications in probabilistic neuromorphic computing. 

Neuromorphic computing, commonly understood as a computing approach built upon neurons, synapses, and their dynamics, as opposed to Boolean gates, is gaining large mindshare due to its direct application in solving current and future computing technological problems, such as smart sensing, smart devices, self-hosted and self-contained devices, artificial intelligence (AI) applications, etc. In a largely software-defined implementation of neuromorphic computing, it is possible to throw enormous computational power or optimize models and networks depending on the specific nature of the computational tasks. However, a hardware-based approach needs the identification of well-suited neuronal and synaptic models to obtain high functional and energy efficiency, which is a prime concern in size, weight, and power (SWaP) constrained environments. In this work, we perform a study on the characteristics of hardware neuron models (namely, inference errors, generalizability and robustness, practical implementability, and memory capacity) that have been proposed and demonstrated using a plethora of emerging nano-materials technology-based physical devices, to quantify the performance of such neurons on certain classes of problems that are of great importance in real-time signal processing like tasks in the context of reservoir computing. We find that the answer on which neuron to use for what applications depends on the particulars of the application requirements and constraints themselves, i.e., we need not only a hammer but all sorts of tools in our tool chest for high efficiency and quality neuromorphic computing. 

Abstract In the ‘Beyond Moore’s Law’ era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore’s Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries.