Effect of spin diffusion on Gilbert damping for a very thin permalloy layer in Cu/permalloy/Cu/Pt films

Ferromagnetic resonance (FMR) was measured for Cu/permalloy (Py) (20, 30, 40 Å)/Cu (d_Cu)/Pt (0, 50 Å) films with various d_Cu to clarify the effect of spin diffusion driven by the precession of magnetization on Gilbert damping. The peak-to-peak linewidth ΔH_pp of the FMR spectra for Cu/Py/Cu/Pt films was very large at d_Cu=0Å, and decreased remarkably at d_Cu=30Å. Above d_Cu=30Å, it decreased gradually with increasing d_Cu in the anomalously wide range of d_Cu. The out-of-plane angular dependence of the FMR of Cu/Py(30 Å)/Cu (d_Cu)/Pt (0, 50 Å) films was measured and analyzed using a Landau-Lifshitz-Gilbert equation that took into account the local variation of the effective demagnetizing field. The Gilbert damping coefficient G obtained from the analysis for Cu/Py/Cu/Pt films was about twice as large as that for Cu/Py/Cu films even at d_Cu=100Å and decreased gradually as d_Cu increased. At d_Cu=2000–3000Å, G for Cu/Py/Cu/Pt and Cu/Py/Cu films has the same value. We discussed the influence of spin diffusion driven by the precession of magnetization in FMR on G using a previously proposed model. The calculated G vs d_Cu fitted well to the experimental one, and the other features of the experimental results are well explained by the model.