Spin injection into a ballistic semiconductor microstructure

Abstract

A theory of spin injection across a ballistic semiconductor embedded between two ferromagnetic leads is developed for the Boltzmann regime. Spin injection coefficient $\ensuremath{\gamma}$ is suppressed by the Sharvin resistance of the semiconductor ${r}_{N}^{*}{=(h/e}^{2})({\ensuremath{\pi}}^{2}{/S}_{N}),$ where ${S}_{N}$ is the Fermi-surface cross section. It competes with the diffusion resistances of the ferromagnets ${r}_{F},$ and $\ensuremath{\gamma}$ is small, $\ensuremath{\gamma}\ensuremath{\sim}{r}_{F}{/r}_{N}^{*}\ensuremath{\ll}1,$ in the absence of contact barriers. Efficient spin injection can be ensured by contact barriers. Explicit formulas for the junction resistance and the spin-valve effect are presented.