Spin transport parameters in Ni 80 Fe 20 /Ru and Ni 80 Fe 20 /Ta bilayers

We present a systematic study of the spin transport properties in two different bilayer systems, ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/\mathrm{Ru}$ and ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}/\mathrm{Ta}$, combining ferromagnetic resonance (FMR) and inverse spin Hall effect (ISHE) voltage measurements. We have estimated the effective spin mixing conductance ${g}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ by analyzing the permalloy (Py) thickness dependence of the FMR linewidth obtaining ${g}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}=(3.8\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ and ${g}^{\ensuremath{\uparrow}\ensuremath{\downarrow}}=(1.3\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ for Py/Ru and Py/Ta, respectively. Analyzing the Ta thickness dependence of the ISHE voltage, we have been able to extract the spin diffusion length, ${\ensuremath{\lambda}}_{SD}=1.5\ifmmode\pm\else\textpm\fi{}0.5$ nm, and spin Hall angle, ${\ensuremath{\Theta}}_{SH}=\ensuremath{-}0.03\ifmmode\pm\else\textpm\fi{}0.01$, of Ta. From the two series of Py/Ta bilayers---with thickness variation of ferromagnetic and nonmagnetic layers, respectively---we demonstrate a path to estimate the spin diffusion length from the experimental data, independent of the spin Hall angle and the microwave field amplitude.