Intrinsic Damping Phenomena From Quantum To Classical Magnets: An Ab Initio Study Of Gilbert Damping In A Pt/Co Bilayer

A fully quantum-mechanical description of the precessional damping of a Pt/Co bilayer is presented in the framework of the Keldysh Green's function approach using ab initio electronic structure calculations. In contrast to previous calculations of classical Gilbert damping (αGD), we demonstrate that αGD in the quantum case does not diverge in the ballistic regime due to the finite size of the total spin S. In the limit of S→∞ we show that the formalism recovers the torque correlation expression for αGD which we decompose into spin-pumping and spin-orbital torque correlation contributions. The formalism is generalized to take into account a self-consistently determined dephasing mechanism which preserves the conservation laws and allows the investigation of the effect of disorder. The dependence of αGD on Pt thickness and disorder strength is calculated, and the spin-diffusion length of Pt and the spin mixing conductance of the bilayer are determined and compared with experiments.