Giant Spin Lifetime Anisotropy and Spin-Valley Locking in Silicene and Germanene from First-Principles Density-Matrix Dynamics

Through first-principles real-time density-matrix (FPDM) dynamics simulations, we investigated spin relaxation due to electron-phonon and electron-impurity scatterings with spin-orbit coupling (SOC) in two-dimensional Dirac materials silicene and germanene at finite temperatures. We discussed the applicability of conventional descriptions of spin relaxation mechanisms by Elliott-Yafet (EY) and D'yakonov-Perel' (DP) compared to the FPDM method, which is determined by a complex interplay of intrinsic SOC, external fields, and scattering strength. For example, the electric field dependence of the spin lifetime by FPDM is close to the DP mechanism for silicene at room temperature but similar to the EY mechanism for germanene. Because of its stronger SOC strength and buckled structure in contrast to graphene, germanene has a giant spin lifetime anisotropy and spin-valley locking effect under nonzero E_z and low temperatures. More importantly, germanene has a long spin lifetime (∼100 ns at 50 K) and an ultrahigh carrier mobility, making it advantageous for spin-valleytronic applications.