Quantifying Spin Hall Effects in Gold Hall Bars*

Spin Hall effects manifest the fundamental interdependence between charge and spin transport. We studied these effects experimentally by measuring the non-local resistance,$ R_{nl}$, in mesoscopic Au Hall bars where spin current generation and detection are spatially separated in two side arms, while a bridging arm acts as the spin conduit. The measured $R_{nl}$ decreases monotonically with decreasing temperature, changing sign from positive to negative. This can be understood by modeling $R_{nl}$ as a sum of two components; a positive, ohmic component, arising from the charge current, and a negative component, due to spin Hall effects and spin diffusion. By varying the spacing between the side arms, the components can be separated. We determined the spin diffusion length, the$_{ }$spin Hall angle and the spin Hall conductivity. We found spin Hall angles of order 0.1, with a temperature dependence proportional to the resistivity, while the spin Hall conductivity was almost temperature independent.