  We combined a spin-resolved photoemission spectrometer with a high-harmonic
generation (HHG) laser source in order to perform spin-, time- and
angle-resolved photoemission spectroscopy (STARPES) experiments on the
transition metal dichalcogenide bulk WTe$_2$, a possible Weyl type-II
semimetal. Measurements at different femtosecond pump-probe delays and
comparison with spin-resolved one-step photoemission calculations provide
insight into the spin polarization of electrons above the Fermi level in the
region where Weyl points of WTe$_2$ are expected. We observe a spin
accumulation above the Weyl points region, that is consistent with a
spin-selective bottleneck effect due to the presence of spin polarized
cone-like electronic structure. Our results support the feasibility of STARPES
with HHG, which despite being experimentally challenging provides a unique way
to study spin dynamics in photoemission.
