Circuit Models for Spintronic Devices Subject to Electric and Magnetic Fields

In this paper, we develop circuit models for spintronic devices that are under the application of electric and magnetic fields. Starting from time-dependent drift-diffusion equations in nonmagnets and ferromagnets, we spatially and temporally discretize the resulting current-voltage relations using linear multistep methods, which yield equivalent circuit models characterized by finite-difference versions of the so-called 4 × 4 conductance matrices. By using a time-dependent formulation, introducing a new model for ferromagnets, and including ubiquitous effects such as spin dissipation, spin precession, as well as thermal noise, our model serves as a framework to unify and expand the existing models in the literature. To demonstrate our model's utility in applications, we performed simulations on several spintronic devices and validated the results against simulated and measured data. We also discuss extensions to the model and general directions for the future research.