自旋伪ovalve 型 $\mathrm{L}_j$/semiconductor/$mathrm{L}_j$ 三层($\mathrm{L}_j$ = 铁磁)的理论自旋输运分析

Julián A. Zúñiga, Arles V. Gil Rebaza, Diego F. Coral Coral
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摘要

在这项工作中,我们对伪自旋(PSV)异质结构中的自旋传输进行了理论研究。对于半导体(SC),考虑了倒易空间 $\Gamma$ 点的导带和自旋轨道耦合(SOC)。对于左侧($l$)和右侧($r$)的铁磁(FM)电极,考虑了内部交换能($\Delta_j$,其中$j =\left(l,r\right)$)和势垒平面上的磁化法向量($\mathbf{n}_j$)。根据带有边界条件的{em Schr\"odinger-Pauli} 方程,得到了传输概率作为 $\mathbf{n}_j$ 方向函数的解析表达式。此外,利用单通道的{em Landauer-B\"{u}ttiker}公式计算了T $/approx$ 0 K时的隧道磁阻(TMR),这取决于有利于调频磁化($\theta_m$)的晶体学轴的方向和SC的厚度。观察发现,当 $\mathbf{n}_l$ 方向与 $\theta_m$ 平行时,TMR 达到最大值。将这一物理数学模型应用于 Fe/SC/Fe PSV(SC 为 GaAs、GaSb 和 InAs)时,发现{em Dresselhaus} SOC 并未显著影响 TMR。SOC 对 TMR 的影响不大。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Theoretical spin transport analysis for a spin pseudovalve-type $\mathrm{L}_j$/semiconductor/$\mathrm{L}_j$ trilayer (with $\mathrm{L}_j$ = ferromagnetic)
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.
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