Exchange magnetic field torques in YIG/Pt bilayers observed by the spin-Hall magnetoresistance

The effective field torque of an yttrium-iron-garnet film on the spin accumulation in an attached Pt film is measured by the spin-Hall magnetoresistance (SMR). As a result, the magnetization direction of a ferromagnetic insulating layer can be measured electrically. Experimental transverse and longitudinal resistances are well described by the theoretical model of SMR in terms of the direct and inverse spin-Hall effect, for different Pt thicknesses [3, 4, 8 and 35nm]. Adopting a spin-Hall angle of Pt ${\theta }_{SH}=0.08$, we obtain the spin diffusion length of Pt ($\lambda =1.1\pm 0.3$nm) as well as the real ($G_r=(7\pm 3)\times {10}^{14}{\mathrm{\Omega }}^{-1}$m${}^{-2}$) and imaginary part ($G_i=(5\pm 3)\times {10}^{13}{\mathrm{\Omega }}^{-1}$m${}^{-2}$) of the spin-mixing conductance and their ratio ($G_r\mathrm{/}{G}_i=16\pm 4$).