Diffusion theory of spin injection through resistive contacts

TL;DR

This paper develops a concise theoretical framework for analyzing spin injection through resistive contacts in ferromagnetic/semiconductor junctions, simplifying calculations of junction resistance and spin-related effects.

Contribution

A new self-consistent equation system for spin injection coefficients is derived, enabling straightforward analysis of spin injection and junction resistance in complex structures.

Findings

Explicit expression for junction resistance including spin effects

Positive nonequilibrium resistance proven under certain conditions

Impact of Coulomb screening and spin non-conservation clarified

Abstract

Insertion of a resistive contact between a ferromagnetic metal and a semiconductor microstructure is of critical importance for achieving efficient spin injection into a semiconductor. However, the equations of the diffusion theory are rather cumbersome for the junctions including such contacts. A technique based on deriving a system of self-consistent equations for the coefficients of spin injection, "gamma", through different contacts are developed. These equations are concise when written in the proper notations. Moreover, the resistance of a two-contact junction can be expressed in terms of "gamma"'s of both contacts. This equation makes calculating the spin valve effect straightforward, allows to find an explicit expression for the junction resistance and to prove that its nonequilibrium part is positive. Relation of these parameters to different phenomena like spin-e.m.f. and the junction transients is established. Comparative effect of the Coulomb screening on different parameters is clarified. It is also shown that the spin non-conservation in a contact can have a dramatic effect on the non-equilibrium resistance of the junction.