Influence of the conductivity on spin wave propagation in a Permalloy waveguide

The influence of the electrical conductivity of a Permalloy waveguide on the spin wave propagation was investigated using the finite-element solution of the combined system of quasistatic electromagnetic potential and linearized LLG (Landau–Lifshitz–Gilbert) equations. The difference in the group velocity between the conductive and nonconductive waveguides becomes large for films over 300 nm thick, and the difference is very small for film thicknesses less than 100 nm. The observed enhancement of the group velocity with increasing film thickness is attributed to the damping caused by the electrical conductivity, which leads to narrowing of the spin wave packet envelope and shorter arrival times of propagating waves. The basic characteristics of the dispersion relations do not change between conductive and nonconductive films for small film thicknesses less than 300 nm. The simulated dispersion relations indicate shift of their maximum intensity toward lower wavenumbers and, therefore, increase in the group velocity with increasing thickness. The simulated decay length of the spin waves for conductive films initially increases but then decreases with increasing thickness, which agrees well with the experimental results. The extracted damping coefficients from both simulations and the experiment agree very well and increase proportionally with d2, where d is the film thickness, due to the additional eddy current damping. The observed thickness and conductivity dependence of spin wave propagation is crucial for magnonics research and toward the development of future spin wave devices using metal films.