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

TL;DR

This paper presents a theoretical analysis of spin transport in a ferromagnetic/semiconductor/ferromagnetic trilayer, deriving analytical expressions for transmission and TMR, and applying the model to Fe/SC/Fe structures with various semiconductors.

Contribution

The work provides a new analytical model for spin transport and TMR in PSV heterostructures considering SOC and magnetization orientations.

Findings

Maximum TMR occurs when magnetization is aligned with the crystallographic axis.

Dresselhaus SOC has negligible effect on TMR in studied structures.

Analytical expressions for transmission probability as a function of magnetization direction.

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 Schr\"odinger-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-B\"{u}ttiker} 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.