Spin-flip Raman scattering of electrons and heavy-holes is studied for resonant excitation of neutral and charged excitons in a CdTe/Cd$_{0.63}$Mg$_{0.37}$Te quantum well. The spin-flip scattering is characterized by its dependence on the incident and scattered light polarization as well as on the magnetic field strength and orientation. Model schemes of electric-dipole allowed spin-flip Raman processes in the exciton complexes are compared to the experimental observations, from which we find that lowering of the exciton symmetry, time of carrier spin relaxation, and mixing between electron states and, respectively, light- and heavy-hole states play an essential role in the scattering. At the exciton resonance, anisotropic exchange interaction induces heavy-hole spin-flip scattering, while acoustic phonon interaction is mainly responsible for the electron spin-flip. In resonance with the positively and negatively charged excitons, anisotropic electron-hole exchange as well as mixed electron states allow spin-flip scattering. Variations in the resonant excitation energy and lattice temperature demonstrate that localization of resident electrons and holes controls the Raman process probability and is also responsible for symmetry reduction. We show that the intensity of the electron spin-flip scattering is strongly affected by the lifetime of the exciton complex and in tilted magnetic fields by the angular dependence of the anisotropic electron-hole exchange interaction.
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