  We generalize the spin Hall angle to laser pulses of finite frequencies in
the linear response regime and predict a giant optical spin Hall effect.
Namely, for certain transition metal elements, at particular frequencies, the
spin current can be a significant fraction of the charge current, and even
exceed it for XUV frequencies. By maximizing spin current while minimizing the
charge current, we thus minimize a major source of heating in spintronic
devices. We employ {\it ab-initio} time-dependent density functional theory
(TDDFT), and with real-time simulations calculate the conductivity and
transverse spin conductivity for all $3$d, $4$d, and $5$d transition metals for
frequencies up to $50$ eV. In the XUV frequency range we find values greater
than $1$ for the spin Hall angle, indicating spin currents larger than the
charge current can be generated.
