Single layer transition metal dichalcogenides are 2D semiconducting systems with unique electronic band
structure. Two-valley energy bands along with strong spin-orbital coupling lead to valley-dependent carrier spin
polarization, which is the basis for recently proposed valleytronic applications. These systems also exhibit
unusually strong many body effects, such as strong exciton and trion binding, due to reduced dielectric
screening of Coulomb interactions. Not much is known about the impact of strong many particle correlations on
spin and valley polarization dynamics. Here we report direct measurements of ultrafast valley specific relaxation
dynamics in single layer MoS<sub>2</sub> and WS<sub>2</sub>. We found that excitonic many body interactions significantly
contribute to the relaxation process. Biexciton formation reveals hole valley/spin relaxation time in MoS<sub>2</sub>. Our
results suggest that initial fast intervalley electron scattering and electron spin relaxation leads to loss of valley
polarization for holes through an electron-hole spin exchange mechanism in both MoS<sub>2 </sub>and WS<sub>2</sub>.
We derive an evolutional equation incorporating the processes of spin-polarization transfer from an electron to a magnetic ion subsystem of a diluted magnetic semiconductor along with spin-lattice relaxation and spatial spin diffusion. Above equation has been obtained for nonequilibrium magnetization due to exchange scattering of photoexcited charge carriers by magnetic ions. We show that the mechanism of a band gap narrowing due to exchange scattering requires relatively low optical power to reach an optical bistability for pump frequency range close to crystal band gap. In a bulk crystal, only relatively small local area with essential magnetization enhancement can absorb optical power, thus forming a photoinduced magnetization wave. Spatial spin diffusion can be responsible for a motion of such
magnetization wave. We solve above derived equation both analytically for one-dimensional case and numerically otherwise and perform its stability analysis. We also evaluate numerically possible threshold of photoinduced magnetization wave excitation for typical diluted magnetic semiconductor A<sub>1-x</sub><sup>II</sup>Mn<sub>x</sub>B<sup>VI</sup> and estimate its length and velocity of propagation.