Temperature dependence of the effective spin-mixing conductance probed with lateral non-local spin valves

We report the temperature dependence of the effective spin-mixing conductance between a normal metal (aluminium, Al) and a magnetic insulator (\(\text{Y}_3\text{Fe}_5\text{O}_{12}\), YIG). Non-local spin valve devices, using Al as the spin transport channel, were fabricated on top of YIG and SiO\(_2\) substrates. By comparing the spin relaxation lengths in the Al channel on the two different substrates, we calculate the effective spin-mixing conductance (\(G_\text{s}\)) to be \(3.3\times10^{12}\)~\(\Omega^{-1}\text{m}^{-2}\) at 293~K for the Al/YIG interface. A decrease of up to 84\% in \(G_\text{s}\) is observed when the temperature (\(T\)) is decreased from 293~K to 4.2~K, with \(G_\text{s}\) scaling with \((T/T_\text{c})^{3/2}\). The real part of the spin-mixing conductance (\(G_\text{r}\approx 5.7\times10^{13}~ \Omega^{-1}\text{m}^{-2}\)), calculated from the experimentally obtained \(G_\text{s}\), is found to be approximately independent of the temperature. We evidence a hitherto unrecognized underestimation of \(G_\text{r}\) extracted from the modulation of the spin signal by rotating the magnetization direction of YIG with respect to the spin accumulation direction in the Al channel, which is found to be 50 times smaller than the calculated value.