Semi-realistic tight-binding model for spin-orbit torques

Abstract

We compute the spin-orbit torque in a transition metal heterostructure using Slater-Koster parameterization in the two-center tight-binding approximation and accounting for d-orbitals only. In this method, the spin-orbit coupling is modeled within Russel-Saunders scheme, which enables us to treat interfacial and bulk spin-orbit transport on equal footing. The two components of the spin-orbit torque, dissipative (damping-like) and reactive (field-like), are computed within Kubo linear response theory. By systematically studying their thickness and angular dependence, we were able to accurately characterize these components beyond the traditional "inverse spin galvanic" and "spin Hall" effects. Whereas the conventional field-like torque is purely interfacial, we unambiguously demonstrate that the conventional the damping-like torque possesses both an interfacial and a bulk contribution. In addition, both field-like and damping-like torques display substantial angular dependence with strikingly different thickness behavior. While the planar contribution of the field-like torque decreases smoothly with the nonmagnetic metal thickness, the planar contribution of the damping-like torque increases dramatically with the nonmagnetic metal thickness. Finally, we investigate the self-torque exerted on the ferromagnet when the spin-orbit coupling of the nonmagnetic metal is turned off. Our results suggest that the spin accumulation that builds up inside the ferromagnet can be large enough to induce magnetic excitations.

arXiv comment13 pages, 11 figures

References in corpus (65)

• Spin torque switching with the giant spin Hall effect of tantalum
• Universal Intrinsic Spin-Hall Effect
• New Perspectives for Rashba Spin-Orbit Coupling
• Dissipationless Quantum Spin Current at Room Temperature
• Spin Torque Ferromagnetic Resonance Induced by the Spin Hall Effect
• Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems
• Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Layer thickness dependence of the current induced effective field vector in Ta|CoFeB|MgO
• Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals
• Quantitative characterization of the spin orbit torque using harmonic Hall voltage measurements
• Spin-orbit torques induced by interface-generated spin currents
• Current induced torques and interfacial spin-orbit coupling: Semiclassical Modeling
• Dependence of the Efficiency of Spin Hall Torque on the Transparency of Pt-Ferromagnetic Layer Interfaces
• Spin torque study of the spin Hall conductivity and spin diffusion length in platinum thin films with varying resistivity
• Intrinsic spin Hall effect in platinum metal
• Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects
• Spin-orbit torque engineering via oxygen manipulation
• Gigantic intrinsic orbital Hall effects in weakly spin-orbit coupled metals
• Spin Transport at Interfaces with Spin-Orbit Coupling: Phenomenology
• Orbital-Angular-Momentum Based Origin of Rashba-Type Surface Band Splitting
• Interface-generated spin currents
• Giant room temperature interface spin Hall and inverse spin Hall effects
• Giant intrinsic spin Hall effect in the TaAs family of Weyl semimetals
• First-principles study of magnetization relaxation enhancement and spin-transfer in thin magnetic films
• Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles
• Spin Transport at Interfaces with Spin-Orbit Coupling: Formalism
• Fieldlike and antidamping spin-orbit torques in as-grown and annealed Ta/CoFeB/MgO layers
• Anomalous Spin-Orbit Torques in Magnetic Single-Layer Films
• Ab initio calculation of intrinsic spin Hall effect in semiconductors
• Spin-orbit torques in locally and globally non-centrosymmetric crystals: Antiferromagnets and ferromagnets
• Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations
• Charge and spin Hall conductivity in metallic graphene
• Current-induced torques and interfacial spin-orbit coupling
• Influence of a Transport Current on Magnetic Anisotropy in Gyrotropic Ferromagnets
• Orbital Edelstein effect as a condensed-matter analog of solenoid
• Planar Hall torque
• Enhanced spin-orbit torque via modulation of spin current absorption
• Swapping of spin currents: interchanging spin and flow directions
• Interface enhanced spin-orbit torques and current-induced magnetization switching of Pd/Co/AlO${}_x$ layers
• Current-induced torques in textured Rashba ferromagnets
• Anisotropic spin Hall effect from first principles
• Intraband and interband spin-orbit torques in non-centrosymmetric ferromagnets
• Microscopic theory of spin-orbit torques and skyrmion dynamics
• Spin-orbit torque in 3D topological insulator-ferromagnet heterostructure: crossover between bulk and surface transport
• Tunable Giant Spin Hall Conductivities in a Strong Spin-Orbit Semimetal: Bi${}_{1-x}$Sb${}_x$
• Angular dependence of spin-orbit spin transfer torques
• Spin Swapping Transport and Torques in Ultrathin Magnetic Bilayers
• Spin-orbit torque opposing the Oersted torque in ultrathin Co/Pt bilayers
• Spin-Torque Generation in Topological-Insulator-Based Heterostructures
• Spin Hall and spin swapping torques in diffusive ferromagnets
• Spin-Orbit Torques in Two-Dimensional Rashba Ferromagnets
• Spin Hall effects in diffusive normal metals
• First-principles calculation of spin-orbit torque in a Co/Pt bilayer
• First Principles Study of Angular Dependence of Spin-Orbit Torque in Pt/Co and Pd/Co Bilayers
• Spin-orbit torques in L1${}_0$-FePt/Pt thin films driven by electrical and thermal currents
• A fully relativistic description of spin-orbit torques by means of linear response theory
• Angular dependence and symmetry of Rashba spin torque in ferromagnetic heterostructures
• Spin-Orbit Torques and Anisotropic Magnetization Damping in Skyrmion Crystals
• Lattice model for the surface states of a topological insulator with applications to magnetic and exciton instabilities
• Microscopic origin of the relativistic splitting of surface states
• Thermally induced magnonic spin current, thermomagnonic torques and domain wall dynamics in the presence of Dzyaloshinskii-Moriya interaction
• Spin-orbit torques and spin accumulation in FePt/Pt and Co/Cu thin films from first principles: the role of impurities
• Non-equilibrium spin density and spin-orbit torque in three dimensional topological insulators - antiferromagnet heterostructure
• Spin-orbit torques and tunable Dzyaloshinskii-Moriya interaction in Co/Cu/Co trilayers

Cited by in corpus (7)

• Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems
• A new decomposition of the Kubo-Bastin formula
• Orbital magnetoelectric effect in zigzag nanoribbons of p-band systems
• Light and microwave driven spin pumping across FeGaB-BiSb interface
• Spin-current-related magnetoresistance in epitaxial Pt/Co bilayers in the presence of spin Hall effect and Rashba-Edelstein effect
• Semi-realistic tight-binding model for Dzyaloshinskii-Moriya interaction
• Observation of charge-to-spin conversion with giant efficiency at Ni${}_{0.8}$Fe${}_{0.2}$/Bi${}_2$WO${}_6$ interface