  Transition-metal dichalcogenides (TMDCs) are an aspiring class of materials
with unique electronic and optical properties and potential applications in
spin-based electronics. Here, we use terahertz emission spectroscopy to study
spin-to-charge current conversion (S2C) in the TMDC NbSe$_2$ in
ultra-high-vacuum-grown F|NbSe$_2$ thin-film stacks, where F is a layer of
ferromagnetic Fe or Ni. Ultrafast laser excitation triggers an ultrafast spin
current that is converted into an in-plane charge current and, thus, a
measurable THz electromagnetic pulse. The THz signal amplitude as a function of
the NbSe$_2$ thickness shows that the measured signals are fully consistent
with an ultrafast optically driven injection of an in-plane-polarized spin
current into NbSe$_2$. Modeling of the spin-current dynamics reveals that a
sizable fraction of the total S2C originates from the bulk of NbSe$_2$ with the
same, negative, sign as the spin Hall angle of pure Nb. By quantitative
comparison of the emitted THz radiation from F|NbSe$_2$ to F|Pt reference
samples and the results of ab-initio calculations, we estimate that the spin
Hall angle of NbSe$_2$ for an in-plane polarized spin current lies between
-0.2% and -1.1%, while the THz spin-current relaxation length is of the order
of a few nanometers.
