Spin relaxation and decoherence is at the heart of spintronics and spin-based quantum information science. Currently, theoretical approaches that can accurately predict spin relaxation of general solids including necessary scattering pathways and capable for ns to ms simulation time are urgently needed. We present a first-principles real-time density-matrix approach based on Lindblad dynamics to simulate ultrafast spin dynamics for general solid-state systems. Through the complete first-principles descriptions of pump, probe and scattering processes including electron-phonon, electron-impurity and electron-electron scatterings with self-consistent spin-orbit couplings, our method can directly simulate the ultrafast pump-probe measurements for coupled spin and electron dynamics over ns at any temperature and doping levels. We apply this method to a prototypical system GaAs and obtain excellent agreement with experiments. We found that the relative contributions of different scattering mechanisms and phonon modes differ considerably between spin and carrier relaxation processes. In sharp contrast to previous work based on model Hamiltonians, we point out that the electron-electron scattering is negligible at room temperature but becomes very important at low temperatures for spin relaxation in n-type GaAs. Most importantly, we examine the applicable conditions of the commonly-used Dyakonov-Perel relation, which may break down for individual scattering processes. Our work provides a predictive computational platform for spin relaxation in solids, which has unprecedented potentials for designing new materials ideal for spintronics and quantum information technology.
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