Substrate effects on spin relaxation in two-dimensional Dirac materials with strong spin-orbit coupling

Abstract

Understanding substrate effects on spin dynamics and relaxation is of key importance for spin-based information technologies. However, the key factors that determine such effects, in particular for materials with strong spin-orbit coupling (SOC), have not been well understood. Here we performed first-principles real-time density-matrix dynamics simulations with SOC and the electron-phonon and electron-impurity scattering for spin lifetimes (τs) of supported/free-standing germanene, a prototypical strong SOC 2D Dirac material. We show that the effects of different substrates on τs can surprisingly differ by two orders of magnitude. We find that substrate effects on τs are closely related to substrate-induced modifications of the SOC-field anisotropy, which changes the spin-flip scattering matrix elements. We propose a new electronic quantity, named spin-flip angle θ↑↓, to characterize spin relaxation through intervalley spin-flip scattering. We find that {tau }_{s}^{-1} is approximately proportional to the averaged value of {sin }^{2}left({theta }^{uparrow downarrow }/2right), which serves as a guiding parameter of controlling spin relaxation.