Spin-phonon relaxation in diverse materials from a universal ab initio density matrix approach*

We present a new, universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate the spin-phonon relaxation time of solids with arbitrary spin mixing and crystal symmetry. In particular, this method describes contributions of the Elliott-Yafet and D'yakonov-Perel' (DP) mechanisms to spin relaxation, corresponding to systems with and without inversion symmetry, on an equal footing. Our \emph{ab initio} predictions are in excellent agreement with experiment data for a broad range of materials, including metals and semiconductors with inversion symmetry (silicon and iron), and materials without inversion symmetry (MoS$_2$ and MoSe$_2$). We find strong magnetic field dependence of electron and hole spin relaxation in MoS$_2$ and MoSe$_2$. As a function of temperature, we find the spin relaxation time to be proportional to carrier/momentum relaxation time in all cases, consistent with experiments but distinct from the commonly-quoted inverse relation for simplified models of the DP mechanism. We emphasize that first-principles spin-orbit coupling and electron-phonon scattering is crucial for general, accurate prediction of spin relaxation in solids.