Theoretical spin transport analysis for a spin pseudovalve-type ${\mathrm{L}}_j$/semiconductor/${\mathrm{L}}_j$ trilayer (with ${\mathrm{L}}_j$ = ferromagnetic)

Abstract

In this work, a theoretical study of spin transport in a pseudovalve spin (PSV) heterostructure is conducted. For the semiconductor (SC), the conduction band at the $\Gamma$ point of reciprocal space and spin-orbit coupling (SOC) are considered. For the ferromagnetic (FM) electrodes on the left ($l$) and right ($r$), the internal exchange energy (${\Delta }_j$, where $j=\left(l,r\right)$) and the magnetization normal vector (${\mathbf{n}}_j$) on the barrier plane are taken into account. An analytical expression for the transmission probability as a function of ${\mathbf{n}}_j$ direction was obtained from the {\em Schrödinger-Pauli} equations with the boundary conditions. Furthermore, the tunnel magnetoresistance (TMR) at T $\approx$ 0 K was calculated, depending on the direction of the crystallographic axis favoring the magnetization (${\theta }_m$) of the FM and the thickness of the SC, using the {\em Landauer-Büttiker} formula for a single channel. It is observed that the TMR reaches its maximum value when the ${\mathbf{n}}_l$ direction is parallel to ${\theta }_m$. Applying this physico-mathematical model to the Fe/SC/Fe PSV, with SC as GaAs, GaSb, and InAs, it was found that the {\em Dresselhaus} SOC does not significantly contribute to the TMR.

This article has been withdrawn due to an error in the calculation related to the implementation of boundary conditions. Please refer to the more complete version, arXiv:2603.19435