A fully relativistic description of spin-orbit torques by means of linear response theory

Abstract

Symmetry and magnitude of spin-orbit torques (SOT), i.e., current-induced torques on the magnetization of systems lacking inversion symmetry, are investigated in a fully relativistic linear response framework based on the Kubo formalism. By applying all space-time symmetry operations contained in the magnetic point group of a solid to the relevant response coefficient, the torkance expressed as torque-current correlation function, restrictions to the shape of the direct and inverse response tensors are obtained. These are shown to apply to the corresponding thermal analogues as well, namely the direct and inverse thermal SOT in response to a temperature gradient or heat current. Using an implementation of the Kubo-Bastin formula for the torkance into a first-principles multiple-scattering Green's function framework and accounting for disorder effects via the so-called coherent potential approximation (CPA), all contributions to the SOT in pure systems, dilute as well as concentrated alloys can be treated on equal footing. This way, material specific values for all torkance tensor elements in the fcc (111) trilayer alloy system Pt | Fe${}_x$Co${}_{1-x}$ | Cu are obtained over a wide concentration range and discussed in comparison to results for electrical and spin conductivity, as well as to previous work - in particular concerning symmetry w.r.t. magnetization reversal and the nature of the various contributions.

12 pages, 6 tables, 3 figures

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Cited by in corpus (29)

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• Altermagnetism and magnetic groups with pseudoscalar electron spin
• Laser-induced torques in metallic ferromagnets
• First-principles calculation of spin-orbit torque in a Co/Pt bilayer
• A new decomposition of the Kubo-Bastin formula
• Quantitative comparison of electrically induced spin and orbital polarizations in heavy-metal/3d-metal bilayers
• The relation of the Dzyaloshinskii-Moriya interaction to spin currents and to the spin-orbit field
• Microscopic Origin of Spin-Orbit Torque in Ferromagnetic Heterostructures: A First Principles Approach
• Semiclassical theory of spin-orbit torques in disordered multiband electron systems
• Skew-scattering-induced giant antidamping spin-orbit torques: Collinear and out-of-plane Edelstein effects at two-dimensional material/ferromagnet interfaces
• Magneto-optic and transverse transport properties of non-collinear antiferromagnets
• Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques
• Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
• Semi-realistic tight-binding model for spin-orbit torques
• Non-equilibrium spin density and spin-orbit torque in three dimensional topological insulators - antiferromagnet heterostructure
• Composition-dependent magnetic response properties of Mn${}_{1-x}$Fe${}_x$Ge alloys
• Ab initio theory of the spin-dependent conductivity tensor and the spin Hall effect in random alloys
• Spin-wave stiffness and micromagnetic exchange interactions expressed by means of the KKR Green function approach
• Emergent Phenomena with Broken Parity-Time Symmetry: Odd-order vs. Even-order Effects
• Geometric Dynamics of Magnetization: Electronic Contribution
• Chirality-induced linear response properties in non-coplanar Mn${}_3$Ge
• Spin accumulation from non-equilibrium first principles methods
• Topological damping Rashba spin orbit torque in ballistic magnetic domain walls
• Scaling of the Rashba spin-orbit torque in magnetic domain walls
• Topological Aspects of Antiferromagnets
• Intrinsic spin currents in bulk noncentrosymmetric ferromagnets
• Magnetic precession induced spin accumulation in collinear antiferromagnets