Spin-Polarization of a 2DEG in Cd$_{1-x}$Mn$_{x}$Te Quantum Wells

Low energy excitations of a spin-polarized electron gas embedded in Cd$_{1-x}$Mn$_{x}$Te quantum wells are studied by magneto-resonant Raman scattering and magneto-photoluminescence at superfluid helium temperature in the Voigt geometry. From Raman, we measured the one electron spin flip energy as a function of the bare Zeeman splitting originating from exchange interaction between $s$ electrons and localized Mn d electrons. The ratio between the spin flip energy and the bare Zeeman splitting shows a strong dependence on the electron density. From photoluminescence measurements, we extract the spin flip energy and the spin-polarization rate. Comparison of the measured spin flip energy with our theoretical model [1] shows that the Raman values are in better agreement with the theory. The photoluminescence lineshape, however, gives estimation of the spin-polarization rate that is in good agreement with our model. [1] F. Perez \textit{et al.} ACTA Physics Polonica A, \textbf{106}, 311 (2004).