  The valley degree of freedom and the possibility of spin-valley coupling of
solid materials have attracted growing interest, and the relaxation dynamics of
spin- and valley-polarized states has become an important focus of recent
studies. In spin-orbit-coupled inversion-asymmetric two-dimensional materials,
such as MoS_{2} it has been found that the spin randomization is
characteristically faster than the time scales for inter- and intra-valley
scatterings. In this study, we examined the ultrafast non-collinear spin
dynamics of an electron valley in monolayer MoS_{2} by using real-time
propagation time-dependent density functional theory. We found that the spin
precession of an electron in the valley is sharply coupled with the
lowest-lying optical phonon that release the in-plane mirror symmetry. This
indicates that the spin randomization of MoS_{2} is mainly caused by
spin-phonon interaction. We further suggest that flipping of spins in a
spin-orbit-coupled system can be achieved by the control over phonons.
