Tunnel Magneto-resistance in GaMnAs: going beyond Julli\`{e}re formula

TL;DR

This paper investigates how strong spin-orbit interactions in GaMnAs-based tunnel junctions affect TMR, revealing dependencies beyond the traditional Julliere formula, with implications for spintronic device modeling.

Contribution

It introduces a detailed theoretical analysis of TMR in GaMnAs structures considering spin-orbit effects, going beyond the Julliere formula with a comprehensive 6-band k·p model.

Findings

TMR depends on spin polarization and barrier thickness.

Strong spin-orbit interactions cause TMR to vary with the angle between current and magnetization.

Julliere formula's validity is compromised under these conditions.

Abstract

The relation between tunnel magneto-resistance (TMR) and spin polarization is explored for GaMnAs/GaAlAs/GaMnAs structures where the carriers experience strong spin-orbit interactions. TMR is calculated using Landauer approach. The materials are described in the 6 band $\bf {k}\cdot \bf{p}$ model which includes spin orbit interaction. Ferromagnetism is described in the virtual crystal mean field approximations. Our results indicate that TMR is a function of of spin polarization and barrier thickness. As a result of the stong spin orbit interactions, TMR also depends on the the angle between current flow direction and the electrode magnetization. These results compromise the validity of Julliere formula.