Temperature dependence of the spin Hall effect in mixed-valent YbAl$_{\mathrm{3}}$

The spin Hall effect results in a spin current that flows transverse to an applied electric field in non-magnetic materials, and that can be used to apply an efficient spin-transfer torque in magnetic memory devices. Theoretical predictions suggest that the strength of the spin Hall effect might be enhanced by rare-earth $f$-electron elements, if the $f$ levels are hybridized with itinerant states and are sufficiently close in energy to the Fermi level. YbAl$_{\mathrm{3}}$ is a rare-earth mixed-valence system, where Yb 4$f$ states become increasingly itinerant at low temperatures. This is accompanied by a shift in binding energy of the 4$f$ derived heavy bands towards the Fermi level and an enhanced 4$f$ contribution to the YbAl3 Fermi surface, as temperature is lowered. We report on temperature dependent measurements of the spin Hall effect using spin-torque ferromagnetic resonance in YbAl3/Fe bilayers, and discuss implications for the spin Hall effect of increasing 4$f$ density of states at the Fermi level.