Quantum mechanism of nonlocal Gilbert damping in magnetic trilayers

A fully quantum-mechanical calculation of the Gilbert damping constant alpha in magnetic trilayers is done by employing the torque-correlation formula within a realistic tight-binding model. A remarkable enhancement of alpha in Co/NM sub(1)/NM sub(2) trilayers is obtained due to adding the caps NM sub(2)=Pd, Pt, and it decays with the thickness of the spacers NM sub(1) =Cu, Ag, Au in agreement with experiment. Nonlocal origin of the Gilbert damping is visualized with its atomic layer contributions, it is shown that magnetization in Co is damped remotely by strong spin-orbit coupling in NM sub(2) via quantum states with large amplitude in both Co and NM sub(2).