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We compare resonant electronic Raman scattering and photoluminescencemeasurements for the characterization of a spin-polarized two-dimensionalelectron gas embedded in $\text{Cd}_{1-x}\text{Mn}_x\text{Te}$ single quantumwells. From Raman scattering by single-particle excitations in a zero magneticfield, we measure the Fermi velocity and then obtain the Fermi energy (as wellas the electron density), which is comparable to that extracted fromphotoluminescence for moderate electron densities, assuming a bare band-edgemass. At large electron densities, the Fermi energies derived from Ramanscattering and photoluminescence differ. For an applied in-plane magnetic fieldand zero wave vector transferred to the electron gas, Raman scattering spectrashow peaks at both the Zeeman energy $Z$, resulting from collective excitationsof the spin-polarized electron gas, and the one electron spin-flip energy$Z^*$. Magneto-photoluminescence spectra show conduction band splitting thatare equivalent to $Z$, suggesting that collective effects are present in thephotoluminescence spectra. Assuming (as before) an uncorrected mass, the degreeof spin polarization $\zeta$ determined from the magneto-photoluminescencelineshape is found to differ from that derived from the magnetic fielddependent Raman scattering measurements for large electron densities. Weattribute the discrepancy in measuring $\zeta$ and the Fermi energy to therenormalized mass resulting from many-body electron-electron interactions.

Measuring the spin polarization and Zeeman energy of a spin-polarized electron gas: Comparison between Raman scattering and photoluminescence