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 (42)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Anomalous Hall effect
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Spin torque switching with the giant spin Hall effect of tantalum
• Spin Hall effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Spin Torque Ferromagnetic Resonance Induced by the Spin Hall Effect
• Direct electronic measurement of the spin Hall effect
• Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd${}_3$As${}_2$
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Spin Transfer Torque Generated by the Topological Insulator Bi_2Se_3
• Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures
• Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP
• Room Temperature Reversible Spin Hall Effect
• Layer thickness dependence of the current induced effective field vector in Ta|CoFeB|MgO
• Spin Pumping and Inverse Spin Hall Effect in Platinum: The Essential Role of Spin-Memory Loss at Metallic Interfaces
• Quantitative characterization of the spin orbit torque using harmonic Hall voltage measurements
• Role of transparency of platinum-ferromagnet interface in determining intrinsic magnitude of spin Hall effect
• Dependence of the Efficiency of Spin Hall Torque on the Transparency of Pt-Ferromagnetic Layer Interfaces
• Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal metal bilayers
• 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
• Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation
• Tuning the spin Hall effect of Pt from the moderately dirty to the superclean regime
• Giant intrinsic spin Hall effect in the TaAs family of Weyl semimetals
• Ab initio calculation of intrinsic spin Hall effect in semiconductors
• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Signatures of Electron Fractionalization in Ultraquantum Bismuth
• The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons
• Carrier screening, transport, and relaxation in 3D Dirac semimetals
• Spin-Orbit Torque and Nernst Effect in Bi-Sb/Co Heterostructures
• Universal density scaling of disorder-limited low-temperature conductivity in high-mobility two-dimensional systems
• Transport and spin conversion of multi-carriers in semimetal bismuth
• Spin-Hall Effect and Diamagnetism of Dirac Electrons
• Origin of the large anisotropic g-factor of holes in bismuth
• Spin projection and spin current density within relativistic electronic transport calculations
• Intrinsic and Extrinsic Spin Hall Effects of Dirac Electrons
• Interface enhanced helicity dependent photocurrent in metal/semimetal bilayers
• Seebeck effect of Dirac electrons

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• 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