Spin-wave damping in ferromagnetic stripes with inhomogeneous magnetization

A theory is presented for the interactions between the dipole-exchange spin waves in ferromagnetic nanowires with a stripe geometry. A Hamiltonian-based approach is used in order to extend earlier results for the linear (or noninteracting) spin waves to include the leading nonlinear processes due to three-magnon and four-magnon effects in a stripe. As well as the magnetic dipole-dipole and exchange terms in the Hamiltonian, the role of an applied magnetic field that can be either parallel or perpendicular to the stripe axis is considered. Within a diagrammatic perturbation method the contributions to the frequency shift and damping of the quantized spin waves are deduced. Numerical calculations are presented for Permalloy stripes, and it is shown that the damping in the transverse field case, where the magnetization may become strongly inhomogeneous, can be larger than that in the longitudinal field case. Comparisons are made with recent damping measurements for Permalloy stripes in a longitudinal field.