Theoretical Study of Gilbert Damping Constants in Magnetic Multilayer Films

A theory is presented, describing Gilbert damping of a ferromagnetic layer by treating the outflow of the spin angular momentum to lattice and nonmagnetic systems on the same footing. The Mori formalism is applied to the entire system, including at the interface between different bulk (or film) systems. The Gilbert damping constant is determined from both Kamersky's spin-orbit-related torque correlation (TC) term and the hopping-related TC term. In addition, we confirm that the hopping-related TC term corresponds to conventional Gilbert damping enhanced by spin pumping.