  Optical orientation of localized/bound excitons is shown to be effectively
enhanced by the application of magnetic fields as low as 20 mT in monolayer
WS$_2$. At low temperatures, the evolution of the polarization degree of
different emission lines of monolayer WS$_2$ with increasing magnetic fields is
analyzed and compared to similar results obtained on a WSe$_2$ monolayer. We
study the temperature dependence of this effect up to $T=60$ K for both
materials, focusing on the dynamics of the valley pseudospin relaxation. A rate
equation model is used to analyze our data and from the analysis of the width
of the polarization deep in magnetic field we conclude that the competition
between the dark exciton pseudospin relaxation and the decay of the dark
exciton population into the localized states are rather different in these two
materials which are representative of the two extreme cases for the ratio of
relaxation rate and depolarization rate.
