A general circuit model for spintronic devices under electric and magnetic fields

In this work, we present a circuit model of diffusive spintronic devices capable of capturing the effects of both electric and magnetic fields. Starting from a modified version of the well-established drift-diffusion equations, we derive general equivalent circuit models of semiconducting/metallic nonmagnets and metallic ferromagnets. In contrast to other models that are based on steady-state transport equations which might also neglect certain effects such as thermal fluctuations, spin dissipation in the ferromagnets, and spin precession under magnetic fields, our model incorporates most of the important physics and is based on a time-dependent formulation. An application of our model is shown through simulations of a nonlocal spin-valve under the presence of a magnetic field, where we reproduce experimental results of electrical measurements that demonstrate the phenomena of spin precession and dephasing ('Hanle effect').