Direct and inverse spin-orbit torques

Abstract

In collinear magnets lacking inversion symmetry application of electric currents induces torques on the magnetization and conversely magnetization dynamics induces electric currents. The two effects, which both rely on spin-orbit interaction (SOI), are reciprocal to each other and denoted direct spin-orbit torque (SOT) and inverse spin-orbit torque (ISOT), respectively. We derive expressions for SOT and ISOT within the Kubo linear response formalism. We show that expressions suitable for density-functional theory calculations can be derived either starting from a Kohn-Sham Hamiltonian with time-dependent exchange field or by expressing general susceptibilities in terms of the Kohn-Sham susceptibilities. For the case of magnetic bilayer systems we derive the general form of the ISOT current induced under ferromagnetic resonance. Using \textit{ab initio} calculations within density-functional theory we investigate SOT and ISOT in Co/Pt(111) magnetic bilayers. We determine the spatial distribution of spin and charge currents as well as torques in order to expose the mechanisms underlying SOT and ISOT and to highlight their reciprocity on the microscopic level. We find that the spin Hall effect is position-dependent close to interfaces.

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Cited by in corpus (60)

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• Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films
• Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems
• Surface orbitronics: new twists from orbital Rashba physics
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• Relativistic theory of magnetic inertia in ultrafast spin dynamics
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• Effects of transition-metal spacers on the spin-orbit torques, spin Hall magnetoresistance, and magnetic anisotropy of Pt/Co bilayers
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• Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques
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• Self-induced inverse spin Hall effect in ferromagnets: demonstration through non-monotonous temperature-dependence in permalloy
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• Another view on Gilbert damping in two-dimensional ferromagnets
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• Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role for damping, gyromagnetism, and current-induced torques in noncollinear magnets
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• Current-induced quasiparticle magnetic multipole moments
• Local spin Hall conductivity
• Geometric Dynamics of Magnetization: Electronic Contribution
• Tunable spin-charge conversion through topological phase transitions in zigzag nanoribbons
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• Strong Spin-Orbit Torque effect on magnetic defects due to topological surface state electrons in Bi${}_2$Te${}_3$
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