This paper presents a novel mechanism for enhanced Gilbert damping in thin ferromagnetic films. The damping arises from spin pumping, where the precession of magnetization transfers spin angular momentum into adjacent normal metal layers. This process is described by the Landau-Lifshitz-Gilbert (LLG) equation, with the damping constant enhanced by the scattering matrix of the ferromagnetic layer. The damping constant α' = α - α₀ is expressed in terms of the scattering matrix at the Fermi energy, which can be calculated using model or first-principles methods. The results are consistent with recent experimental data on permalloy films. The mechanism is the inverse of spin-current induced magnetization switching. Spin current generated by magnetization precession is transferred into the normal metal, leading to a spin pump that transfers angular momentum from the ferromagnet to the normal metal. This effect is mathematically formulated using the scattering matrix of the ferromagnetic layer and the precession of the magnetization direction. The paper analyzes the spin current pumped into normal metal layers and derives expressions for the damping constant α' in terms of the scattering matrix parameters. For permalloy films, the damping constant α' is found to be proportional to 1/d, where d is the film thickness. This result is supported by experimental data on N-Py-N sandwiches, showing a systematic dependence of the damping parameter on the permalloy film thickness. The paper also discusses the role of spin-flip relaxation times and interface conductance in determining the effectiveness of spin pumping. For Cu, the spin-flip relaxation time is long, leading to poor spin current dissipation and no enhancement of the Gilbert damping constant. In contrast, Pt, Ta, and Pd have shorter spin-flip relaxation times, leading to significant damping enhancement. The results are consistent with previous theoretical models and experimental observations, and the paper concludes that the spin-pump mechanism is a key factor in enhancing Gilbert damping in thin magnetic films. The findings have important implications for the development of magnetic recording technologies and other applications involving spintronics.This paper presents a novel mechanism for enhanced Gilbert damping in thin ferromagnetic films. The damping arises from spin pumping, where the precession of magnetization transfers spin angular momentum into adjacent normal metal layers. This process is described by the Landau-Lifshitz-Gilbert (LLG) equation, with the damping constant enhanced by the scattering matrix of the ferromagnetic layer. The damping constant α' = α - α₀ is expressed in terms of the scattering matrix at the Fermi energy, which can be calculated using model or first-principles methods. The results are consistent with recent experimental data on permalloy films. The mechanism is the inverse of spin-current induced magnetization switching. Spin current generated by magnetization precession is transferred into the normal metal, leading to a spin pump that transfers angular momentum from the ferromagnet to the normal metal. This effect is mathematically formulated using the scattering matrix of the ferromagnetic layer and the precession of the magnetization direction. The paper analyzes the spin current pumped into normal metal layers and derives expressions for the damping constant α' in terms of the scattering matrix parameters. For permalloy films, the damping constant α' is found to be proportional to 1/d, where d is the film thickness. This result is supported by experimental data on N-Py-N sandwiches, showing a systematic dependence of the damping parameter on the permalloy film thickness. The paper also discusses the role of spin-flip relaxation times and interface conductance in determining the effectiveness of spin pumping. For Cu, the spin-flip relaxation time is long, leading to poor spin current dissipation and no enhancement of the Gilbert damping constant. In contrast, Pt, Ta, and Pd have shorter spin-flip relaxation times, leading to significant damping enhancement. The results are consistent with previous theoretical models and experimental observations, and the paper concludes that the spin-pump mechanism is a key factor in enhancing Gilbert damping in thin magnetic films. The findings have important implications for the development of magnetic recording technologies and other applications involving spintronics.