Enhanced Gilber damping in thin ferromagnetic films

The precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This pumping of spins slows down the precession corresponding to an enhanced Gilbert damping constant in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnetic layer, which is accessible to model and fist-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.