[论文解读] Hydrodynamic theory of vorticity-induced spin transport

Gen Tatara|arXiv (Cornell University)|Aug 23, 2021

Magnetic properties of thin films参考文献 45被引用 15

一句话总结

本文提出了一种无序金属中自旋输运的流体动力学理论，表明由非均匀电场引起的电子涡度通过自旋-涡度耦合产生自旋电流。关键结果是自旋-涡度耦合引发的非保守自旋驱动力，该结果解释了本征逆自旋霍尔效应，并预测了一种新型的涡度诱导扭矩，其强度超过传统的二阶自旋轨道扭矩。

ABSTRACT

Electron spin transport in a disordered metal is theoretically studied from the hydrodynamic viewpoint focusing on the role of electron vorticity. The spin-resolved momentum flux density of electrons is calculated taking account of the spin-orbit interaction and uniform magnetization, and the expression for the spin motive force is obtained as the linear response to a driving electric field. It is shown that the spin-resolved momentum flux density and motive force are characterized by troidal moments expressed as vector products of the applied external electric field and the spin polarization and/or magnetization. The spin-vorticity and magnetization-vorticity couplings studied recently are shown to arise from the toridal moments contribution to the momentum flux density. Spin motive force turns out to have a nonconservative contribution besides the conventional conservative one due to the spin-vorticity coupling. Spin accumulation induced by an electric field is calculated to demonstrate the direct relation between vorticity and induced spin, and the spin Hall effect is interpreted as due to the spin-vorticity coupling. The spin-vorticity coupling is shown to give rise to a vorticity-induced torque and a spin relaxation. The vorticity-induced torque is a linear effect of the spin-orbit interaction and is expected to be larger than the second-order torques such as nonadiabatic ($\beta$) current-induced torque due to magnetization structure. The intrinsic inverse spin Hall effect is argued to correspond to the antisymmetric components of the momentum flux density in the hydrodynamic context.

研究动机与目标

• 开发一种超越传统玻尔兹曼方法的无序金属中自旋输运的流体动力学框架。
• 阐明电子涡度在产生自旋电流和自旋积累中的作用。
• 从动量通量密度各向异性的角度阐明本征逆自旋霍尔效应的起源。
• 证明涡度诱导的自旋扭矩在强度上超过传统电流诱导扭矩，并且与自旋轨道耦合呈线性关系。
• 建立环量矩与电子流中自旋分辨动量通量密度之间的联系。

提出的方法

• 将自旋分辨动量通量密度表述为对非均匀电场的线性响应。
• 利用包含局部电导率关系 j = σeE 的流体动力学方程，将响应表达为外加电场 E 的函数。
• 通过图解法和线性响应技术，从自旋轨道相互作用推导出自旋-涡度耦合。
• 识别出动量通量密度的反对称部分是本征逆自旋霍尔效应的根源。
• 通过电场、自旋极化和磁化强度的矢量积引入环量矩，以表征动量通量。
• 分析来自 ∇(s·ω) 和 (s·∇)ω 的非保守力，表明后者源于粘性/摩擦效应。

实验结果

研究问题

• RQ1 电子涡度如何在无序金属中诱导自旋输运？
• RQ2 环量矩在自旋分辨动量通量密度中起什么作用？
• RQ3 涡度诱导的自旋驱动力与传统保守力有何不同？
• RQ4 涡度诱导扭矩是否可能超过二阶电流诱导扭矩的强度？
• RQ5 本征逆自旋霍尔效应的流体动力学起源是什么？

主要发现

• 自旋分辨动量通量密度由涉及电场、自旋极化和磁化强度的环量矩表征。
• 非保守自旋驱动力源于 (s·∇)ω 项，该效应在传统模型中不存在。
• 涡度诱导扭矩与自旋轨道耦合呈线性关系，且预测其强度将超过传统 β-扭矩。
• 在电场作用下的自旋积累通过自旋-涡度耦合机制与涡度直接关联。
• 本征逆自旋霍尔效应源于动量通量密度的反对称分量。
• 自旋-涡度耦合同时诱导了涡度诱导扭矩和自旋弛豫，其中前者主要局域在表面和界面上。