  We measure the inverse spin Hall effect of Cu$_{1-x}$Ir$_{x}$ thin films on
yttrium iron garnet over a wide range of Ir concentrations ($0.05 \leqslant x
\leqslant 0.7$). Spin currents are triggered through the spin Seebeck effect,
either by a DC temperature gradient or by ultrafast optical heating of the
metal layer. The spin Hall current is detected by, respectively, electrical
contacts or measurement of the emitted THz radiation. With both approaches, we
reveal the same Ir concentration dependence that follows a novel complex,
non-monotonous behavior as compared to previous studies. For small Ir
concentrations a signal minimum is observed, while a pronounced maximum appears
near the equiatomic composition. We identify this behavior as originating from
the interplay of different spin Hall mechanisms as well as a
concentration-dependent variation of the integrated spin current density in
Cu$_{1-x}$Ir$_{x}$. The coinciding results obtained for DC and ultrafast
stimuli show that the studied material allows for efficient spin-to-charge
conversion even on ultrafast timescales, thus enabling a transfer of
established spintronic measurement schemes into the terahertz regime.
