Spin Hall effect driven by the spin magnetic moment current in Dirac materials
Spin Hall effect driven by the spin magnetic moment current in Dirac materials
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DOI：
10.1103/physrevb.105.214419
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发表时间：
2022-06-01
影响因子：
3.7
通讯作者：
Hayashi, Masamitsu
中科院分区：
文献类型：
--
作者：
Chi, Zhendong;Qu, Guanxiong;Hayashi, Masamitsu
利用半经典分析和久保公式研究了Dirac哈密顿系统的自旋霍尔效应。在这个系统中，自旋霍尔电导率取决于自旋电流的定义。当自旋电流被定义为自旋角动量的流动时，自旋霍尔电导率的所有分量都消失了。与此相反，非对角分量的自旋霍尔电导率是非零和规模与载流子速度（和有效g因子）时，自旋电流由自旋磁矩的流动。我们推导了电导率、载流子迁移率和自旋霍尔电导率的解析公式，并与实验进行了比较。在实验中，我们使用Bi作为模型系统，其特征在于狄拉克哈密顿量。Te和Sn被掺杂到Bi中以分别改变电子和空穴浓度。我们发现自旋霍尔电导率（σ（SH））在狄拉克点附近取最大值，并随着载流子密度（n）的增加而减小。无论多数载流子类型如何，西格玛的符号（SH）都是相同的。自旋霍尔迁移率与σ（SH）/n成比例，随着载流子迁移率的增加而增加，比例系数类似于1.4。这些功能可以占定量使用导出的分析公式。结果表明，巨自旋磁矩，有效g因子接近100，是负责自旋霍尔效应在Bi。
The spin Hall effect of a Dirac Hamiltonian system is studied using semiclassical analyses and the Kubo formula. In this system, the spin Hall conductivity is dependent on the definition of spin current. All components of the spin Hall conductivity vanish when spin current is defined as the flow of the spin angular momentum. In contrast, the off-diagonal components of the spin Hall conductivity are nonzero and scale with the carrier velocity (and the effective g factor) when spin current consists of the flow of spin magnetic moment. We derive the analytical formula of the conductivity, carrier mobility, and the spin Hall conductivity to compare with experiments. In experiments, we use Bi as a model system that can be characterized by the Dirac Hamiltonian. Te and Sn are doped into Bi to vary the electron and hole concentration, respectively. We find the spin Hall conductivity (sigma(SH)) takes a maximum near the Dirac point and decreases with increasing carrier density (n). The sign of sigma(SH) is the same regardless of the majority carrier type. The spin Hall mobility, proportional to sigma(SH)/n, increases with increasing carrier mobility with a scaling coefficient of similar to 1.4. These features can be accounted for quantitatively using the derived analytical formula. The results demonstrate that the giant spin magnetic moment, with an effective g factor that approaches 100, is responsible for the spin Hall effect in Bi.