Self-consistent ballistic and diffusive spin transport across interfacial resistances in a hybrid ferromagnet-semiconductor trilayer

Abstract

Spin dependent interfacial resistance $({R}_{I})$ is crucial for achieving high spin injection efficiency from a ferromagnetic (FM) metal into a semiconductor (SC). We present a self-consistent model of spin transport across interfacial resistances at the FM--SC junctions of a FM--SC--FM trilayer structure. The SC layer consists of a highly doped ${n}^{++}$ $\mathrm{Al}\mathrm{Ga}\mathrm{As}\mathrm{Ga}\mathrm{As}$ 2DEG while the interfacial resistance at the FM--SC junction is modeled as delta potential $(\ensuremath{\delta})$ barriers. The self-consistent scheme consists of a ballistic model of spin-dependent transmission across the $\ensuremath{\delta}$ barriers to evaluate ${R}_{I}$, and a drift-diffusion model to obtain the spin--split $\ensuremath{\Delta}\ensuremath{\mu}$ in the electrochemical potentials. The ${R}_{I}$ values of the two junctions were found to be asymmetric despite the symmetry of the trilayer structure. This asymmetry arises from the finite biasing voltage which causes a difference in electrochemical potentials and spin accumulation at the two interfaces. The effect of ${R}_{I}$ on the spin-injection efficiency and magnetoresistance is studied over a range of $\ensuremath{\delta}$-barrier heights. Significant spin-injection efficiency $(50%)$ requires high $\ensuremath{\delta}$-barrier heights approaching $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Even higher barrier heights are required to obtain equivalent magnetoresistive effect.