Energy-transport models for spin transport in ferromagnetic semiconductors

TL;DR

This paper derives explicit energy-transport equations for spin-polarized carriers in ferromagnetic semiconductors, extending existing models and analyzing their properties through theoretical and numerical methods.

Contribution

It introduces simplified explicit models from a general spin energy-transport system, enabling detailed analysis of spin-charge interactions and solution existence.

Findings

Monotonicity of entropy and gradient estimates established.

Existence of weak solutions proved for a time-discrete model.

Numerical simulations demonstrate temperature and polarization effects.

Abstract

Explicit energy-transport equations for the spinorial carrier transport in ferromagnetic semiconductors are calculated from a general spin energy-transport system that was derived by Ben Abdallah and El Hajj from a spinorial Boltzmann equation. The novelty of our approach are the simplifying assumptions leading to explicit models which extend both spin drift-diffusion and semiclassical energy-transport equations. The explicit models allow us to examine the interplay between the spin and charge degrees of freedom. In particular, the monotonicity of the entropy (or free energy) and gradient estimates are shown for these models and the existence of weak solutions to a time-discrete version of one of the models is proved, using novel truncation arguments. Numerical experiments in one-dimensional multilayer structures using a finite-volume discretization illustrate the effect of the temperature and the polarization parameter.