Quantitative study of the spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids

We experimentally investigate and quantitatively analyze the spin Hall magnetoresistance effect in ferromagnetic insulator/platinum and ferromagnetic insulator/nonferromagnetic metal/platinum hybrid structures. For the ferromagnetic insulator, we use either yttrium iron garnet, nickel ferrite, or magnetite and for the nonferromagnet, copper or gold. The spin Hall magnetoresistance effect is theoretically ascribed to the combined action of spin Hall and inverse spin Hall effect in the platinum metal top layer. It therefore should characteristically depend upon the orientation of the magnetization in the adjacent ferromagnet and prevail even if an additional, nonferromagnetic metal layer is inserted between Pt and the ferromagnet. Our experimental data corroborate these theoretical conjectures. Using the spin Hall magnetoresistance theory to analyze our data, we extract the spin Hall angle and the spin diffusion length in platinum. For a spin-mixing conductance of $4\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.28em}{0ex}}{\ensuremath{\Omega}}^{\ensuremath{-}1}{\mathrm{m}}^{\ensuremath{-}2}$, we obtain a spin Hall angle of $0.11\ifmmode\pm\else\textpm\fi{}0.08$ and a spin diffusion length of $(1.5\ifmmode\pm\else\textpm\fi{}0.5)\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ for Pt in our thin-film samples.