Full first-principles theory of spin relaxation in group-IV materials

We present a generally applicable parameter-free first-principles method to determine electronic spin relaxation times and apply it to the technologically important group-IV materials silicon, diamond and graphite. We concentrate on the Elliott-Yafet mechanism, where spin relaxation is induced by momentum scattering off phonons and impurities. In silicon, we find a $\sim T^{-3}$ temperature dependence of the phonon-limited spin relaxation time T$_1$ and a value of 4.3 ns at room temperature, in agreement with experiments. For the phonon-dominated regime in diamond and graphite, we predict a stronger $\sim T^{-5}$ and $\sim T^{-4.5}$ dependence that limits $T_1$ (300 K) to 180 and 5.8 ns, respectively. A key aspect of this study is that the parameter-free nature of our approach provides a method to study the effect of {\em any} type of impurity or defect on spin-transport. Furthermore we find that the spin-mix amplitude in silicon does not follow the $E_g^{-2}$ band gap dependence usually assigned to III-V semiconductors but follows a much weaker and opposite $E_g^{0.67}$ dependence. This dependence should be taken into account when constructing silicon spin transport models.