Electron–phonon interactions in the Fermi–Dirac spintronics

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi–Dirac distribution function at the leading order. The balance equations for the electron number, total energy density, and total momentum for the whole system constitute now, together with the Poisson equation, a system of four equations for the electron chemical potential, the temperature of the system, the drift velocity, and the electric potential. er, an equation for the evolution of the spin density is added, which accounts 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 τ s f as a function of temperature.