Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals

Abstract

We study the intrinsic spin Hall conductivity (SHC) in various $5d$-transition metals (Ta, W, Re, Os, Ir, Pt, and Au) and 4d-transition metals (Nb, Mo, Tc, Ru, Rh, Pd, and Ag) based on the Naval Research Laboratory tight-binding model, which enables us to perform quantitatively reliable analysis. In each metal, the obtained intrinsic SHC is independent of resistivity in the low resistive regime ($\rho <50\mu \Omega \text{cm}$) whereas it decreases in proportion to ${\rho }^{-2}$ in the high resistive regime. In the low resistive regime, the SHC takes a large positive value in Pt and Pd, both of which have approximately nine $d$-electrons per ion ($n_d=9$). On the other hand, the SHC takes a large negative value in Ta, Nb, W, and Mo where $n_d<5$. In transition metals, a conduction electron acquires the trajectory-dependent phase factor that originates from the atomic wavefunction. This phase factor, which is reminiscent of the Aharonov-Bohm phase, is the origin of the SHC in paramagnetic metals and that of the anomalous Hall conductivity in ferromagnetic metals. Furthermore, each transition metal shows huge and positive $d$-orbital Hall conductivity (OHC), independently of the strength of the spin-orbit interaction (SOI). Since the OHC is much larger than the SHC, it will be possible to realize a {\it orbitronics device} made of transition metals.

17 pages, 12 figures, 3 tables, resubmitted to Physical Review B

References in corpus (7)

• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Spin-Hall effect in a disordered 2D electron-system
• Anomalous Transport Phenomena in Fermi Liquids with Strong Magnetic Fluctuations
• Giant Intrinsic Spin and Orbital Hall Effects in Sr2MO4 (M=Ru,Rh,Mo)
• Absence of vertex correction for the spin Hall effect in p-type semiconductors
• Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi d-orbital tight-binding model

Cited by in corpus (7)

• Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects
• Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to Non-collinearity:Significance of Orbital Aharonov-Bohm Effect
• Giant Extrinsic Spin Hall Effect due to Rare-Earth Impurities
• Intrinsic Spin Hall Effect in s-wave Superconducting State: Analysis of Rashba Model
• Intrinsic spin Hall effect in graphene: Numerical calculations in a multi-orbital mode
• Theory of AC Anomalous Hall Conductivity in d-electron systems
• Spin Hall effect in Sr2RuO4 and transition metals (Nb,Ta)