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A fully quantum mechanical description of the precessional damping of Pt/Cobilayer is presented in the framework of the Keldysh Green function approachusing {\it ab initio} electronic structure calculations. In contrast toprevious calculations of classical Gilbert damping ($\alpha_{GD}$), wedemonstrate that $\alpha_{GD}$ in the quantum case does not diverge in theballistic regime due to the finite size of the total spin, $S$. In the limit of$S\rightarrow\infty$ we show that the formalism recovers the torque correlationexpression for $\alpha_{GD}$ which we decompose into spin-pumping andspin-orbital torque correlation contributions. The formalism is generalized totake into account a self consistently determined dephasing mechanism whichpreserves the conservation laws and allows the investigation of the effect ofdisorder. The dependence of $\alpha_{GD}$ on Pt thickness and disorder strengthis calculated and the spin diffusion length of Pt and spin mixing conductanceof the bilayer are determined and compared with experiments.

Intrinsic Damping Phenomena from Quantum to Classical Magnets:An ab-initio Study of Gilbert Damping in Pt/Co Bilayer