Dynamical Corrections to Spin Wave Excitations in Quantum Wells due to Coulomb Interactions and Magnetic Ions

We have measured dispersions of spin-flip waves and spin-flip single-particle excitations of a spin polarized two-dimensional electron gas in a CdMnTe quantum well using resonant Raman scattering. We find the energy of the spin-flip wave to be below the spin-flip single particle excitation continuum, a contradiction to the theory of spin waves in diluted magnetic semiconductors put forth in [Phys. Rev. B 70, 045205 (2004)]. We show that the inclusion of terms accounting for the Coulomb interaction between carriers in the spin wave propagator leads to an agreement with our experimental results. The dominant Coulomb contribution leads to an overall red shift of the mixed electron-Mn spin modes while the dynamical coupling between Mn ions results in a small blue shift. We provide a simulated model system which shows the reverse situation but at an extremely large magnetic field.