  Using the charge-conserving Floquet-Green function approach to open quantum
systems driven by external time periodic potential, we analyze how spin current
pumped (in the absence of any dc bias voltage) by the precessing magnetization
of a ferromagnetic (F) layer is injected {\em laterally} into the interface
with strong spin-orbit coupling (SOC) and converted into charge current flowing
in the same direction. In the case of metallic interface with the Rashba SOC
used in experiments [Nature Comm. {\bf 4}, 2944 (2013)], both spin
$I^{S_\alpha}$ and charge $I$ current flow within it where $I/I^{S_\alpha}
\simeq$ 2--8\% (depending on the precession cone angle), while for
F/topological-insulator (F/TI) interface employed in related experiments
(arXiv:1312.7091) the conversion efficiency is greatly enhanced $I/I^{S_\alpha}
\simeq$ 40--60\% due to perfect spin-momentum locking on the surface of TI. The
spin-to-charge conversion occurs also when spin current is pumped {\em
vertically} through the F/TI interface with smaller efficiency $I/I^{S_\alpha}
\sim 0.001\%$, but with charge current signal being sensitive to whether the
Dirac fermions at the interface are massive or massless.
