The intrinsic spin Hall conductivity of typical topological insulators ${\mathrm{Sb}}_2{\mathrm{Se}}_3,$ ${\mathrm{Sb}}_2{\mathrm{Te}}_3,$ ${\mathrm{Bi}}_2{\mathrm{Se}}_3,$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ in the bulk form, is calculated from first principles by using density functional theory and the linear response theory in a maximally localized Wannier basis. The results show that there is a finite spin Hall conductivity of 100–200 $(\hslash /2\mathrm{e})(\mathrm{S}/\mathrm{cm})$ in the vicinity of the Fermi energy. Although the resulting values are an order of magnitude smaller than that of heavy metals, they show a comparable spin Hall angle due to their relatively lower longitudinal conductivity. The spin Hall angle for different compounds are then compared to that of recent experiments on topological-insulator/ferromagnet heterostructures. The comparison suggests that the role of the bulk in generating a spin current and consequently a spin torque in magnetization switching applications is comparable to that of the surface including the spin-momentum locked surface states and the Rashba-Edelstein effect at the interface.

• Received 4 August 2020
• Accepted 3 November 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.114202