Communications in Mathematical Sciences

Volume 15 (2017)

Number 6

Energy-transport models for spin transport in ferromagnetic semiconductors

Pages: 1527 – 1563

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n6.a3

Authors

Ansgar Jüngel (Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien, Austria)

Polina Shpartko (Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien, Austria)

Nicola Zamponi (Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien, Austria)

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 is 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 dissipation of the entropy (or free energy) is quantified, 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.

Keywords

spin transport, energy-transport equations, entropy inequalities, existence of weak solutions, finite-volume method, semiconductors

2010 Mathematics Subject Classification

35J47, 35J60, 65M08, 82D37

Received 19 April 2016

Published 27 June 2017