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 (12)

• Direct electronic measurement of the spin Hall effect
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Current-Induced Polarization and the Spin Hall Effect at Room Temperature
• 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
• Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction
• Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi d-orbital tight-binding model

Cited by in corpus (164)

• Roadmap of spin-orbit torques
• Skyrmions in Magnetic Multilayers
• Observation of the orbital Hall effect in a light metal Ti
• Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects
• Temperature dependence of spin diffusion length and spin Hall angle in Au and Pt
• Orbitronics: Orbital Currents in Solids
• Angular and temperature dependence of current induced spin-orbit effective fields in Ta/CoFeB/MgO nanowires
• Efficient conversion of orbital Hall current to spin current for spin-orbit torque switching
• Observation of long-range orbital transport and giant orbital torque
• Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures
• Magneto-Optical Detection of the Orbital Hall Effect in Chromium
• Strong damping-like spin-orbit torque and tunable Dzyaloshinskii-Moriya interaction generated by low-resistivity Pd${}_{1-x}$Pt${}_x$ alloys
• Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems
• Electrical control of magnetism by electric field and current-induced torques
• Orbital Hall effect as an alternative to valley Hall effect in gapped graphene
• Maximizing Spin-Orbit Torque Generated by the Spin Hall Effect of Pt
• Intrinsic spin currents in ferromagnets
• Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten
• Detection of long-range orbital-Hall torques
• Intrinsic Spin Hall Conductivity of MoTe2 and WTe2 Semimetals
• Intrinsic orbital and spin Hall effects in monolayer transition metal dichalcogenides
• An experimental demonstration of room-temperature spin transport in n-type Germanium epilayers
• Fully Spin-transparent magnetic interfaces enabled by insertion of a paramagnetic NiO layer
• Switching of Perpendicular Magnetization by Spin-Orbit Torque
• Current-induced magnetization switching in CoTb amorphous single layer
• Enhancing spin-orbit torque by strong interfacial scattering from ultra-thin insertion layers
• Ultrafast spin-currents and charge conversion at 3d-5d interfaces probed by time-domain terahertz spectroscopy
• Tunable Giant Spin Hall Conductivities in a Strong Spin-Orbit Semimetal: Bi${}_{1-x}$Sb${}_x$
• Y3Fe5O12 Spin Pumping for Quantitative Understanding of Pure Spin Transport and Spin Hall Effect in a Broad Range of Materials
• Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach
• Benchmarking of spin-orbit torque switching efficiency in Pt alloys
• Spin-Hall Torques Generated by Rare-Earth (Lanthanide) Thin Films
• Orbital Torque in Rare-Earth Transition-Metal Ferrimagnets
• Determination of the spin Hall angle, spin mixing conductance and spin diffusion length in Ir/CoFeB for spin-orbitronic devices
• Structural Chirality and Electronic Chirality in Quantum Materials
• Tunable Spin-Orbit Torques in Cu-Ta Binary Alloy Heterostructures
• Toward 100% Spin-Orbit Torque Efficiency with High Spin-Orbital Hall Conductivity Pt-Cr Alloys
• A new decomposition of the Kubo-Bastin formula
• Ultrafast THz probing of nonlocal orbital current in transverse multilayer metallic heterostructures
• Spin-orbit torques in L1${}_0$-FePt/Pt thin films driven by electrical and thermal currents
• Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to Non-collinearity:Significance of Orbital Aharonov-Bohm Effect
• Dominance of extrinsic scattering mechanisms in the orbital Hall effect: graphene, transition metal dichalcogenides and topological antiferromagnets
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Orbital Hall effect and orbital edge states caused by s electrons
• The spin Hall effect as a probe of nonlinear spin fluctuations
• Orbital relaxation length from first-principles scattering calculations
• Calculating spin transport properties from first principles: spin currents
• Colossal orbital-Edelstein effect in non-centrosymmetric superconductors
• Unidirectional orbital magnetoresistance in light metal/ferromagnet bilayers
• Giant efficiency of long-range orbital torque in Co/Nb bilayers
• Dyakonov-Perel-like Orbital and Spin Relaxations in Centrosymmetric Systems
• Spin Seebeck devices using local on-chip heating
• Intrinsic Spin and Orbital Hall Effects in Heavy Fermion Systems
• Orbital Pumping Incorporating Both Orbital Angular Momentum and Position
• Ultra-low-energy computing paradigm using giant spin Hall devices
• Role of Disorder in the Intrinsic Orbital Hall Effect
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Temperature dependence of the spin Hall angle and switching current in the nc-W(O)/CoFeB/MgO system with perpendicular magnetic anisotropy
• Terahertz Emission From an Exchange-Coupled Synthetic Antiferromagnet
• Interfacial and bulk spin Hall contributions to field-like spin-orbit torque generated by Iridium
• Efficient spin current source using a half-Heusler alloy topological semimetal with Back-End-of-Line compatibility
• Strong Spin-Orbit Torque Induced by the Intrinsic Spin Hall Effect in Cr1-xPtx
• Spin-flip diffusion length in 5d transition metal elements: a first-principles benchmark
• Disentanglement of intrinsic and extrinsic side-jump scattering induced spin Hall effect in N-implanted Pt
• Anisotropic intrinsic anomalous Hall effect in ordered 3dPt alloys
• Orbital Rashba effect as a platform for robust orbital photocurrents
• Spin and orbital transport in rare earth dichalcogenides: The case of EuS${}_2$
• Bulk and Interface Effects Based on Rashba-Like States in Ti and Ru Nanoscale-Thick Films: Implications for Orbital-Charge Conversion in Spintronic Devices
• Efficient generation of spin currents by the Orbital Hall effect in pure Cu and Al and their measurement by a Ferris-wheel ferromagnetic resonance technique at the wafer level
• Large Chiral Orbital Texture and Orbital Edelstein Effect in Co/Al Heterostructure
• Giant Extrinsic Spin Hall Effect due to Rare-Earth Impurities
• Intrinsic Spin Hall Effect in s-wave Superconducting State: Analysis of Rashba Model
• Anomalous Hall Effect due to Non-collinearily in Pyrochlore Compounds: Role of Orbital Aharonov-Bohm Effect
• Mitigation of Gilbert Damping in the CoFe/CuOx Orbital Torque System
• Breakdown of the drift-diffusion model for transverse spin transport in a disordered Pt film
• Orbitronics in Two-dimensional Materials
• Negative orbital Hall effect in Germanium
• Orbital Pumping in Ferrimagnetic Insulators
• Orbital Hall effect in mesoscopic devices
• Spin-Hall Effect and Diamagnetism of Anisotropic Dirac Electrons in Solids
• Spin and orbital Hall currents detected via current induced magneto-optical Kerr effect in V and Pt
• Efficient generation of out-of-plane polarized spin current in polycrystalline heavy metal devices with broken electric symmetries
• Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents
• Symmetry constraints on the orbital transport in solids
• Helicity-tunable spin Hall and spin Nernst effects in unconventional chiral fermion semimetals XY (X=Co, Rh; Y=Si, Ge)
• Ultrafast Orbital Hall Effect in Metallic Nanoribbons
• Interface transparency to orbital current
• Role of orbital hybridization in anisotropic magnetoresistance
• Promoting $p$-based Hall effects by $p$-$d$-$f$ hybridization in Gd-based dichalcogenides
• Giant spin torque efficiency in naturally oxidized polycrystalline TaAs thin films
• Topological orbital Hall effect caused by skyrmions and antiferromagnetic skyrmions
• Geometric Origin of Intrinsic Spin Hall Effect in an Inhomogeneous Electric Field
• Intrinsic orbital and spin Hall effect in bismuth semimetal
• Optical induced Spin Current in Monolayer NbSe${}_2$
• Orbital Hall effect in transition metals from first-principles scattering calculations
• Intrinsic spin Hall effect in graphene: Numerical calculations in a multi-orbital mode
• Linear Response in Topological Materials
• Chirality-induced orbital Edelstein effect in an analytically solvable model
• Spin-memory loss induced by bulk spin-orbit coupling at ferromagnet/heavy-metal interfaces
• Vanishing of the quantum spin Hall phase in a semi-Dirac Kane Mele model
• Anisotropic spin Hall and spin Nernst effects in bismuth semimetal
• Spin and anomalous Hall effects emerging from topological degeneracy in Dirac fermion system CuMnAs
• Strain-induced nonrelativistic altermagnetic spin splitting effect
• Different spin relaxation property observed in linearly and circularly polarized laser induced terahertz emission from Bi/Co bilayer
• The Role of Self-Torques in Transition Metal Dichalcogenide/Ferromagnet Bilayers
• Ultra-low-current-density single-layer magnetic Weyl semimetal spin Hall nano-oscillators
• Spin current generation from an epitaxial tungsten dioxide WO${}_2$
• Staggered spin Hall conductivity
• Theory of AC Anomalous Hall Conductivity in d-electron systems
• Theory of spin and orbital charge conversion at the surface states of Bi_{1-x}Sb_x topological insulator
• Spin orbit effects in CoFeB/MgO hetereostructures with heavy metal underlayers
• Spin Hall Effects in Antiferromagnets
• Symmetry-protected difference between spin Hall and anomalous Hall effects of a periodically driven multiorbital metal
• Orbital Edelstein effect of electronic itinerant orbital motion at edges
• Giant orbital Hall effect due to the bulk states of 3D topological insulators
• Ferroelectric polarization controlled orbital Hall conductivity in a higher-order topological insulator: \textit{d1T}-phase monolayer MoS${}_2$
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Inverse Faraday effect in 3d, 4d, and 5d transition metals
• Light-induced Orbital and Spin Magnetism in $3d$, $4d$, and $5d$ Transition Metals
• Valley-dependent giant orbital moments and transport feature in rhombohedral graphene multilayers
• Optically induced spin Hall current in Janus transition-metal dichalcogenides
• Filtering Spin and Orbital Moment in Centrosymmetric Systems
• Spin Hall effect in Sr2RuO4 and transition metals (Nb,Ta)
• Chirality-induced selectivity of angular momentum by orbital Edelstein effect in carbon nanotubes
• Large Spin-to-Charge Conversion in Ultrathin Gold-Silicon Multilayers
• Emergent spin Hall conductivity in Tantalum-Rhenium alloys
• Theoretical study of orbital torque: Dependence on ferromagnet species and nonmagnetic layer thickness
• Intrinsic nature of the giant spin Hall conductivity of Pt
• Three-dimensional topological orbital Hall effect caused by magnetic hopfions
• Optically tunable spin Hall effect in periodically driven monolayer transition metal dichalcogenides
• Quantum Geometric Origin of Orbital Magnetization
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• Fluctuation contribution to Spin Hall Effect in Superconductors
• Coexistent multifractal mesoscopic fluctuations in Integer Quantum Hall Transition and in Orbital Hall Transition
• Eightfold Degenerate Dirac Nodal Line in Collinear Antiferromagnet Mn${}_5$Si${}_3$
• Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film
• First-principles calculations of spin-orbit torques in Mn${}_2$Au/heavy-metal bilayers
• Giant orbital magnetoresistance in the antiferromagnet CoO driven by dynamic orbital angular momentum interaction
• Dynamical Orbital Angular Momentum Induced by Circularly Polarized Phonons
• Probing quantum geometric nonlinear magnetization via second-harmonic magneto-optical Kerr effect
• Proper Theory of Magnon Orbital Angular Momentum at Equilibrium
• Comparing the Extrinsic Orbital Hall Effect in Centrosymmetric and Noncentrosymmetric Systems: Insights from Bilayer Transition Metal Dichalcogenides
• Giant Impurity Effects on Charge Loop Current Order States in Kagome Metals
• Negligible current-induced torque from the bulk and interface of Al
• Inductive detection of inverse spin-orbit torques in magnetic heterostructures
• Relativistic Spin-Lattice Interaction Compatible with Discrete Translation Symmetry in Solids
• Orbital torques and orbital pumping in two-dimensional rare-earth dichalcogenides
• Efficient spin-pumping and spin transport across epitaxial Mn${}_3$Sn(0001) noncollinear antiferromagnet/permalloy interfaces
• Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics
• Orbital Dynamics in Centrosymmetric Systems
• Phonon-mediated spin transport in quantum paraelectric metals
• Chiral orbital/spin textures and Edelstein effects in monolayer Janus TMDs
• Beyond spin-1/2: Multipolar spin-orbit coupling in noncentrosymmetric crystals with time-reversal symmetry
• Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles
• Fermi Surface Geometry
• Probing the Chirality of Trigonal Selenium and Tellurium by Spin and Orbital Hall Effects
• Current induced magneto-optical Kerr effect as a probe of Dirac carriers in Bi${}_{1-x}$Sb${}_x$ alloy
• Injection of orbital angular momentum into transition metals from first-principles
• Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas
• Theory of magnetic spin and orbital Hall and Nernst effects in bulk ferromagnets
• Quantum Christoffel Nonlinear Magnetization
• Anisotropy of the spin Hall effect in a Dirac ferromagnet
• Electrical Conductivity in Quantum Materials
• Onsager Reciprocal Relations for Charge and Spin Transport in Periodically Driven Systems