  Spin relaxation, dephasing and diffusion are at the heart of spin-based
information technology. Accurate theoretical approaches to simulate spin
lifetimes ($\tau_s$), determining how fast the spin polarization and phase
information will be lost, are important to the understandings of underlying
mechanism of these spin processes, and invaluable to search for promising
candidates of spintronic materials. Recently, we develop a first-principles
real-time density-matrix (FPDM) approach to simulate spin dynamics for general
solid-state systems. Through the complete first-principles' descriptions of
light-matter interaction and scattering processes including electron-phonon,
electronimpurity and electron-electron scatterings with self-consistent
spin-orbit coupling, as well as ab initio Land'e g-factor, our method can
predict $\tau_s$ at various conditions as a function of carrier density and
temperature, under electric and magnetic fields. By employing this method, we
successfully reproduce experimental results of disparate materials and identify
the key factors affecting spin relaxation, dephasing, and diffusion in
different materials. Specifically, we predict that germanene has long $\tau_s$
(~100 ns at 50 K), a giant spin lifetime anisotropy and spin-valley locking
effect under electric fields, making it advantageous for spin-valleytronic
applications. Based on our theoretical derivations and ab initio simulations,
we propose a new useful electronic quantity, named spin-flip angle
$\theta^{\uparrow\downarrow}$, for the understanding of spin relaxation through
intervalley spin-flip scattering processes. Our method can be further applied
to other emerging materials and extended to simulate exciton spin dynamics and
steady-state photocurrents due to photogalvanic effect.
