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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.
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Classical Magnetism and an Integral Formula Involving Modified Bessel Functions
Abstract We study an integral expression that is encountered in some classical spin models of magnetism. The idea is to calculate the key integral that represents the building block for the expression of the partition function of these models. The general calculation allows one to have a better look at the internal structure of the quantity of interest which, in turn, may lead to potentially new useful insights. We find out that application of two different approaches to solve the problem in a general-case scenario leads to an interesting integral formula involving modified Bessel functions of the first kind which appears to be new. We performed Monte Carlo simulations to verify the correctness of the integral formula obtained. Additional numerical integration tests lead to the same result as well. The approach under consideration, when generalized, leads to a linear integral equation that might be of interest to numerical studies of classical spin models of magnetism that rely on the well-established transfer-matrix formalism.
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- PAR ID:
- 10073049
- Date Published:
- Journal Name:
- International Journal of Nonlinear Sciences and Numerical Simulation
- Volume:
- 19
- Issue:
- 3-4
- ISSN:
- 1565-1339
- Page Range / eLocation ID:
- 409 to 414
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1515/ijnsns-2017-0193
