Neutral and positively charged excitons: A magneto-optical study of a p-doped ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ quantum well

We present a systematic study of optical transitions in a modulation doped ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ quantum well with variable concentration of the hole gas. Using a semimagnetic semiconductor as the quantum well material allowed us to control independently the total hole concentration and its distribution between the two spin subbands (by a small magnetic field). Therefore, in transmission experiment we analyze population effects and distinguish the influence of spin-independent effects (screening) from spin-dependent ones (phase-space filling and intensity stealing). The observed variation of the exciton (X) and charged exciton ${(X}^{+})$ oscillator strengths can be accounted for assuming that the influence of phase-space filling is negligible and the variation of oscillator strength due to screening is found to be similar for both exciton species. We also show that the $X^{+}$ dissociation energy significantly increases with the population of preexisting carriers with the appropriate spin.