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

Abstract

Ferromagnetic resonance (FMR) was measured for Cu/permalloy (Py) (20, 30, 40 \AA{})/Cu ${(d}_{\mathrm{Cu}})/\mathrm{Pt}$ (0, 50 \AA{}) 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 $\ensuremath{\Delta}{H}_{\mathrm{pp}}$ of the FMR spectra for Cu/Py/Cu/Pt films was very large at ${d}_{\mathrm{Cu}}=0\mathrm{\AA{}},$ and decreased remarkably at ${d}_{\mathrm{Cu}}=30\mathrm{\AA{}}.$ Above ${d}_{\mathrm{Cu}}=30\mathrm{\AA{}},$ 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 \AA{})/Cu ${(d}_{\mathrm{Cu}})/\mathrm{Pt}$ (0, 50 \AA{}) 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 ${d}_{\mathrm{Cu}}=100\mathrm{\AA{}}$ and decreased gradually as ${d}_{\mathrm{Cu}}$ increased. At ${d}_{\mathrm{Cu}}=2000--3000\mathrm{\AA{}},$ 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.