  Designing new quantum materials with long-lived electron spin states urgently
requires a general theoretical formalism and computational technique to
reliably predict intrinsic spin relaxation times. We present a new, accurate
and universal first-principles methodology based on Lindbladian dynamics of
density matrices to calculate spin-phonon relaxation time ($\tau_s$) of solids
with arbitrary spin mixing and crystal symmetry. This method describes
contributions of Elliott-Yafet (EY) and D'yakonov-Perel' (DP) mechanisms to
spin relaxation for systems with and without inversion symmetry on an equal
footing. We show that intrinsic spin and momentum relaxation times both
decrease with increasing temperature; however, for the DP mechanism, spin
relaxation time varies inversely with extrinsic scattering time. We predict
large anisotropy of spin lifetime in transition metal dichalcogenides. The
excellent agreement with experiments for a broad range of materials underscores
the predictive capability of our method for properties critical to quantum
information science.
