(color online) (a) Schematic diagram of the TRFR experiment. The red and blue arrows represent the spin of the photo-excited electrons and holes (b) Kerr rotation dynamics at 4 K for a σ⁺ and σ⁻ pump beam. The laser excitation energy is 1.735 eV. The inset indicates optical selection rules of the excitons in K± valleys and their coupling induced by the long-range exchange interaction. (c) Temperature dependence of Kerr rotation dynamics after a σ⁺ polarized pump pulse excitation (d) Temporal evolution of θ_F(t) in semi logarithmic scale measured at 77 K. The black line is a bi-exponential fit to the data (red line). (e) Schematic illustration of a simple single-electron picture of the conduction and valence bands at the K and K′ valleys of MoS₂ together with the relevant optical selection rules and scattering processes. The conduction bands are separately drawn as spin-up (K) and spin-down (K′) components with slightly different curvature and small splitting. The n_↑, n↓, , and are densities of the resident electrons, and γ_s is electron spin relaxation and γ_v is spin-conserving inter-valley scattering. (f) Temperature dependence (red for 5 K and black for 40 K) of time-resolved Kerr rotation dynamics with pump pulse at 635 nm and 100 ps duration, and probe pulse at 672 nm and 250 fs duration. (g) Probe energy dependence of time-resolved Kerr rotation dynamics, the pump energy is kept at ~ 12 meV higher than probe photon energy (h) The sketch of Kerr signal intensities at (green, solid triangles) and (blue, solid circles) with the PL spectrum (grey curves) for comparison. The emission peaks of neutral exciton (X) and positive trion (X⁺) are indicated by vertical dotted lines. Panels (a) and (d) are reproduced from Ref. [39]; panels (b) and (c) are reproduced from Ref. [38]; panels (e) and (f) are reproduced from Ref. [42]; and panels (g) and (h) are reproduced from Ref. [41].