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arXiv 2012.06053cond-mat.mes-hall
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无序系统自旋动力学的半经典理论

The semiclassical theory for spin dynamics in a disordered system

Tsung-Wei Chen, Hsiu-Chuan Hsu

摘要:

本文研究了二维自旋轨道耦合系统中自旋动力学的Drude模型。在没有外加电场的情况下,自旋与k相关的有效磁场对齐。考虑了无序(动量弛豫时间$τ$)对系统的影响。在存在电场的情况下,动量的变化引起有效磁场的变化。面内自旋可以围绕有效磁场的取向的连续变化进行进动。我们发现,直到电场的线性顺序,自旋取向经历Larmor类和非Larmor类进动。此外,我们还发现在很短时间内的非Larmor运动($t\llτ$)正好等于由Kubo公式得到的结果.这意味着Kubo公式只能在很短的演化过程中捕捉系统的响应。解析计算了Rashba系统中Larmor和非Larmor旋进的自旋霍尔电导率。我们发现,内在的自旋霍尔电流是不是一个普适常数,正确地下降到零时,Rashba自旋轨道耦合下降到零。我们还计算了k-立方Rashba系统的时间平均Larmor和非Larmor自旋霍尔电导率(SHC),并将它们与实验值进行比较。时间平均的拉莫尔SHC消失,非拉莫尔SHC由$2.1(q/8π)$给出,其非常接近Wunderlich等人的实验值$2.2(q/8π)$ [Phys.Rev.Lett. { \bf 94},047204(2005)]。

英文摘要:

We investigate the Drude model of spin dynamics in two-dimensional spin-orbit coupled systems. In the absence of an applied electric field, the spin aligns with the k-dependent effective magnetic field. The influence of disorder (the momentum relaxation time $τ$) on the system is considered. In the presence of an electric field, the change in momentum causes a change in the effective magnetic field. The in-plane spin can precess around the successive change in the orientation of the effective magnetic field. We find that up to the linear order of the electric field, the spin orientation undergoes Larmor-like and non-Larmor like precession. Furthermore, we find that the non-Larmor motion over a very short time ($t\llτ$) exactly equals the result obtained from the Kubo formula. This means that the Kubo formula only captures the system's response over a very short evolution. The spin-Hall conductivity for Larmor and non-Larmor precession in the Rashba system is analytically calculated. We find that the intrinsic spin-Hall current is not a universal constant and correctly drops to zero when the Rashba spin-orbit coupling drops to zero. We also calculate the time-averaged Larmor and non-Larmor spin-Hall conductivities (SHCs) for the k-cubic Rashba system and compare them to experimental values. The time-averaged Larmor SHC vanishes and the non-Larmor SHC is given by $2.1(q/8π)$ which is very close to the experimental value $2.2(q/8π)$ by Wunderlich et al. [Phys. Rev. Lett. {\bf 94}, 047204 (2005)].

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