Spin injection into a ballistic semiconductor microstructure

A theory of spin injection across a ballistic semiconductor embedded between two ferromagnetic leads is developed for the Boltzmann regime. Spin injection coefficient γ is suppressed by the Sharvin resistance of the semiconductor rN*=(h/e²)(π²/SN), where SN is the Fermi-surface cross section. It competes with the diffusion resistances of the ferromagnets rF, and γ is small, γ~rF/rN*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.