Strong magneto-optical responses of an ensemble of defect-bound excitons in ambient exposed WS$_{2}$ and WSe$_{2}$ monolayers
Transition metal dichalcogenide (TMD) monolayers present a singular coupling in their spin and valley degrees of freedom. Moreover, by applying an external magnetic field it is possible to break the energy degeneracy between their K and $-$K valleys. This valley Zeeman effect opens the possibility of controlling and distinguishing the spin and valley characters of charge carriers in TMDs by their optical transition energies, making these materials promising for the next generation of spintronic and photonic devices. However, the free excitons of pristine TMD monolayers present a moderate valley Zeeman splitting of $\approx 0.23$ meV/T. Therefore, alternative excitonic states with higher magnetic responses are mandatory for application purposes. Here, we investigate the magneto-optical properties of ambient exposed WS$_2$ and WSe$_2$ monolayers by circularly polarized magneto-photoluminescence experiments at cryogenic temperatures. A broad lower energy photoluminescence emission related to an ensemble of defects is observed, presenting remarkable valley-related splittings of $\approx 1.45$ meV/T and $\approx 1.11$ meV/T for WS$_2$ and WSe$_2$ monolayers, respectively. In addition, we report a significant valley polarization of charge carriers in the defect mid-gap states induced by the external magnetic field. We explain this valley-polarized population and enhanced valley-related splitting in terms of imbalanced intervalley relaxations, leading to a magnetic field-dependent distribution of charge carriers in multiple defect levels. This effect, together with the individual Zeeman shiftings of the mid-gap states, explains the strong magneto-optical responses observed. Our work uncovers the singular potential of manipulating the light emission of ambient exposed TMD monolayers by an external magnetic field.