In monolayer Transition Metal Dichalcogenides (TMDs) the valence and conduction bands are spin split because of the strong spin-orbit interaction. In tungsten-based TMDs the spin-ordering of the conduction band is such that the so-called dark exciton, consisting of an electron and a hole with opposite spin orientation, has lower energy than the A exciton. A possible mechanism leading to the transition from bright to dark excitons involves the scattering of the electrons from the upper to the lower conduction band state in K. Here we exploit the valley selective optical selection rules and use two-color helicity-resolved pump-probe spectroscopy to directly measure the intravalley spin-flip relaxation dynamics of electrons in the conduction band of single-layer WS$_2$. This process occurs on a sub-ps time scale and it is significantly dependent on the temperature, indicative of a phonon-assisted relaxation. These experimental results are supported by time-dependent ab-initio calculations which show that the intra-valley spin-flip scattering occurs on significantly longer time scales only exactly at the K point. In a realistic situation the occupation of states away from the minimum of the conduction band leads to a dramatic reduction of the scattering time.
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