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

TL;DR

This study investigates how the spin diffusion length in Pt thin films relates to out-of-plane resistivity, using broadband ferromagnetic resonance to clarify the mechanisms affecting spin relaxation and resolving previous controversies.

Contribution

It demonstrates that the spin diffusion length in Pt is determined by out-of-plane resistivity and is independent of film thickness, clarifying the relation between spin relaxation mechanisms and electrical properties.

Findings

Spin relaxation involves a superposition of DP and EY mechanisms.

Spin diffusion length correlates with out-of-plane resistivity.

The results resolve the controversy on thickness dependence of spin diffusion length.

Abstract

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}