Communications in Mathematical Sciences
Volume 15 (2017)
Energy-transport models for spin transport in ferromagnetic semiconductors
Pages: 1527 – 1563
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.
spin transport, energy-transport equations, entropy inequalities, existence of weak solutions, finite-volume method, semiconductors
2010 Mathematics Subject Classification
35J47, 35J60, 65M08, 82D37
The authors acknowledge partial support from the Austrian Science Fund (FWF), grants P22108, P24304, and W1245.
Received 19 April 2016
Published 27 June 2017