Quantum Mechanism Of Nonlocal Gilbert Damping In Magnetic Trilayers

A fully quantum-mechanical calculation of the Gilbert damping constant a in magnetic trilayers is done by employing the torque-correlation formula within a realistic tight-binding model. A remarkable enhancement of a in Co/NM1/NM2 trilayers is obtained due to adding the caps NM2=Pd, Pt, and it decays with the thickness of the spacers NM1=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 NM2 via quantum states with large amplitude in both Co and NM2.