Modification of spin-wave resonance spectra for the case of an asymmetric surface pinning of spins in films with damping

Solutions to the Landau-Lifshitz equations with general boundary conditions for the magnetization and an expression for the complex high-frequency sus ceptibility perpendicular to the magnetization of the ferromagnetic layer w ere obtained with allowance for damping in the spin system. Based on a nume rical analysis of the imaginary part of the susceptibility, a modification of the spectrum of the spin-wave resonance and shifts and broadening of the bulk and surface modes are investigated for various types and extents of t he surface pinning of spins and various degrees of damping.