Spin diffusion length associated to out-of-plane resistivity of Pt thin films in spin pumping experiments

We present a broadband ferromagnetic resonance study of the Gilbert damping enhancement ($\Delta \alpha$) due to spin pumping in NiFe/Pt bilayers. The bilayers, which have negligible interfacial spin memory loss, are studied as a function of the Pt layer thickness ($t_{\text{Pt}}$) and temperature (100-293 K). Within the framework of diffusive spin pumping theory, we demonstrate that Dyakonov-Perel (DP) or Elliot-Yaffet (EY) spin relaxation mechanisms acting alone are incompatible with our observations. In contrast, if we consider that the relation between spin relaxation characteristic time ($\tau_{\text{s}}$) and momentum relaxation characteristic time ($\tau_{\text{p}}$) is determined by a superposition of DP and EY mechanisms, the qualitative and quantitative agreement with experimental results is excellent. Remarkably, we found that $\tau_{\text{p}}$ must be determined by the out-of-plane electrical resistivity ($\rho$) of the Pt film and hence its spin diffusion length ($\lambda_{\text{Pt}}$) is independent of $t_{\text{Pt}}$. Our work settles the controversy regarding the $t_{\text{Pt}}$ dependence of $\lambda_{\text{Pt}}$ by demonstrating its fundamental connection with $\rho$ considered along the same direction of spin current flow. \end{abstract}