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Spin-transfer torque in magnetic tunnel junctions

机译：磁性隧道结中的自旋转移力矩

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摘要

We present a theoretical study of the spin-transfer torque vector and the tunneling magnetoresistance (TMR) for symmetric magnetic tunnel junctions (MTJ) using the single-band tight-binding model and the nonequilib-rium Keldysh formalism. We provide a comprehensive analysis of the effect of band filling and exchange splitting of the FM leads on the bias behavior of the spin-transfer component, T_‖, in the plane containing the magnetizations of the two magnetic layers, and the fieldlike component, T_⊥, perpendicular to this plane. We demonstrate that both components of the spin torque and the TMR can exhibit a wide range of interesting and unusual bias behavior. We show that T_‖(V) satisfies an expression involving the difference in spin currents between the ferromagnetic (FM) and antiferromagnetic (AF) configurations, which is general and independent of the details of the electronic structure. The spin current for the FM (AF) alignment is shown to have a linear (quadratic) bias dependence, whose origin lies in the symmetric (asymmetric) nature of the barrier. On the other hand, the bias dependence of T_⊥ is quadratic with d~2T_⊥ /dV~2<0, and it can change sign at finite bias. Finally, we show that the exchange splitting and band filling have a large effect on the bias dependence of the TMR.
机译：我们使用单带紧束缚模型和非平衡Keldysh形式主义，对对称磁性隧道结（MTJ）的自旋传递扭矩矢量和隧穿磁阻（TMR）进行了理论研究。我们对包含两个磁性层的磁化和平面分量T_的平面中FM引线的带填充和交换分裂对自旋传递分量T_''的偏置行为的影响进行了全面分析。 ⊥，垂直于此平面。我们证明，旋转转矩和TMR的两个分量都可以表现出广泛的有趣和不寻常的偏置行为。我们证明T_（V）满足一个表达式，该表达式涉及铁磁（FM）和反铁磁（AF）配置之间的自旋电流差异，这是一般性的，并且与电子结构的细节无关。 FM（AF）对准的自旋电流显示为具有线性（二次）偏置依赖性，其起因在于势垒的对称（非对称）性质。另一方面，T_⊥的偏置依存关系是二次的，d〜2T_⊥/ dV〜2 <0，并且可以在有限偏置下改变符号。最后，我们表明交换分裂和频带填充对TMR的偏置依赖性有很大影响。

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