Semiconductor spintronics in a participating phonon medium: Macroscopic equations

In the last two decades considerable interest has arisen on the spin related phenomena in semiconductor devices. In semiconductor materials two essential mechanisms act on the spin dynamics: the spin-orbit coupling and the spin-flip interactions. Here the novelty is that we adopt the asymptotic approach developed in previous papers of mine [A. Rossani, Physica A 305, 323 (2002); A. Rossani, G. Spiga, and A. Domaingo, J. Phys. A 36, 11955 (2003); A. Rossani and G. Spiga, J. Math. Phys. 47, 013301 (2006); A. Rossani and A. M. Scarfone, Physica B 334, 292 (2003); A. Rossani, J. Phys. A 43, 165002 (2010)]. The aim of this paper is to derive macroscopic equations starting from a kinetic approach. Moreover an equation for the evolution of the spin density is added, which account for a general dispersion relation. The treatment of spin-flip processes, derived from first principles, is new and leads to an explicit expression of the relaxation time as a function of the temperature.