Intrinsic spin Hall effect in topological insulators: A first-principles study

Abstract

The intrinsic spin Hall conductivity of typical topological insulators Sb${}_2$Se${}_3$, Sb${}_2$Te${}_3$, Bi${}_2$Se${}_3$, and Bi${}_2$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 ($\hslash$/2e)(S/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.

14 pages (10 main + 4 supplemental), 8 figures