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The Giant Spin Hall Effect at Optical Frequencies

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.