Magnetic relaxation due to spin pumping in thick ferromagnetic films in contact with normal metals

Spin pumping is the most important magnetic relaxation channel in ultrathin ferromagnetic layers in contact with normal metals (NMs). Recent experiments indicate that in thick films of insulating yttrium iron garnet (YIG) there is a large broadening of the ferromagnetic resonance (FMR) lines with deposition of a thin Pt layer which cannot be explained by the known damping processes. Here we present a detailed study of the magnetic relaxation due to spin pumping in bilayers made of a ferromagnetic material (FM) and a NM. Two alternative approaches are used to calculate the transverse and longitudinal relaxation rates used in the Bloch-Bloembergen formulation of damping. In one we consider that the dynamic exchange coupling at the interface transfers magnetic relaxation from the heavily damped conduction electron spins in the NM layer to the magnetization of the FM layer while the other utilizes spin currents and the concept of the spin-mixing conductance at the interface. While in thin FM films, the relaxation rates vary with the inverse of the FM layer thickness; in thick films, they become independent of the thickness because in the FM/NM structure the FMR excitation has a surface mode character. Regardless of the thickness range the longitudinal relaxation rate is twice the transverse rate resulting in damping of the magnetization with constant amplitude characterizing a Gilbert process. The enhanced spin-pumping damping explains the experimental observations in YIG/Pt bilayers.