  Through First-Principles real-time Density-Matrix (FPDM) dynamics
simulations, we investigate spin relaxation due to electron-phonon and
electron-impurity scatterings with spin-orbit coupling in two-dimensional Dirac
materials - silicene and germanene, at finite temperatures and under external
fields. We discussed the applicability of conventional descriptions of spin
relaxation mechanisms by Elliott-Yafet (EY) and D'yakonov-Perel' (DP) compared
to our FPDM method, which is determined by a complex interplay of intrinsic
spin-orbit coupling, external fields, and electron-phonon coupling strength,
beyond crystal symmetry. For example, the electric field dependence of spin
relaxation time is close to DP mechanism for silicene at room temperature, but
rather similar to EY mechanism for germanene. Due to its stronger spin-orbit
coupling strength and buckled structure in sharp contrast to graphene,
germanene has a giant spin lifetime anisotropy and spin valley locking effect
under nonzero Ez and relatively low temperature. More importantly, germanene
has extremely long spin lifetime (~100 ns at 50 K) and ultrahigh carrier
mobility, which makes it advantageous for spin-valleytronic applications.
