Spin Hall effect driven by the spin magnetic moment current in Dirac materials

Abstract

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 spin angular momentum. In contrast, the off-diagonal components of the spin Hall conductivity are non-zero and scale with the carrier velocity (and the effective $g$-factor) when spin current consists of the flow of spin magnetic moment. We derive 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 (${\sigma }_{\mathrm{SH}}$) takes a maximum near the Dirac point and decreases with increasing carrier density ($n$). The sign of ${\sigma }_{\mathrm{SH}}$ is the same regardless of the majority carrier type. The spin Hall mobility, proportional to ${\sigma }_{\mathrm{SH}}/n$, increases with increasing carrier mobility with a scaling coefficient of $\sim$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.

References in corpus (10)

• Dissipationless Quantum Spin Current at Room Temperature
• Direct electronic measurement of the spin Hall effect
• Current induced electron spin polarization in strained semiconductors
• On A Proper Definition of Spin Current
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Signatures of Electron Fractionalization in Ultraquantum Bismuth
• Carrier screening, transport, and relaxation in 3D Dirac semimetals
• Spin-Hall Effect and Diamagnetism of Dirac Electrons
• Intrinsic and Extrinsic Spin Hall Effects of Dirac Electrons

Cited by in corpus (8)

• Intrinsic orbital and spin Hall effect in bismuth semimetal
• Anisotropic spin Hall and spin Nernst effects in bismuth semimetal
• Inverse Faraday effect in massive Dirac electrons
• Circular Photon Drag Effect in Dirac electrons by Quantum Geometry
• Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film
• Anisotropy of the spin Hall effect in a Dirac ferromagnet
• Current induced magneto-optical Kerr effect as a probe of Dirac carriers in Bi${}_{1-x}$Sb${}_x$ alloy
• Charge-to-spin conversion in epitaxial and polycrystalline Bi and Bi/Ag layers