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 ${(d}_{\mathrm{Cu}})/\mathrm{Pt}$ (0, 50 Å) films with various $d_{\mathrm{Cu}}$ to clarify the effect of spin diffusion driven by the precession of magnetization on Gilbert damping. The peak-to-peak linewidth $\Delta H_{\mathrm{pp}}$ of the FMR spectra for Cu/Py/Cu/Pt films was very large at $d_{\mathrm{Cu}}=0\mathrm{}\mathrm{\AA },$ and decreased remarkably at $d_{\mathrm{Cu}}=30\mathrm{}\mathrm{\AA }.$ Above $d_{\mathrm{Cu}}=30\mathrm{}\mathrm{\AA },$ it decreased gradually with increasing $d_{\mathrm{Cu}}$ in the anomalously wide range of $d_{\mathrm{Cu}}.$ The out-of-plane angular dependence of the FMR of Cu/Py(30 Å)/Cu ${(d}_{\mathrm{Cu}})/\mathrm{Pt}$ (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 $d_{\mathrm{Cu}}=100\mathrm{}\mathrm{\AA }$ and decreased gradually as $d_{\mathrm{Cu}}$ increased. At $d_{\mathrm{Cu}}=2000\mathrm{}–3000\mathrm{\AA },$ 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 $d_{\mathrm{Cu}}$ fitted well to the experimental one, and the other features of the experimental results are well explained by the model.