Spin waves in magnetic quantum wells with Coulomb interaction and sd exchange coupling

We theoretically describe the spin-excitation spectrum of a two-dimensional electron gas embedded in a quantum well with localized magnetic impurities. Compared to the previous work published in [ Phys. Rev. B 70 45205 (2004)] and [ Phys. Rev. B 79 045306 (2009)], we introduce equations that allow us to consider the interplay between the Coulomb interaction of delocalized electrons and the sd exchange coupling between electrons and magnetic impurities. Strong qualitative changes are found: mixed waves propagate below the single-particle continuum, an anticrossing gap is open at a specific wave vector, and the kinetic damping due to the electron motion [ Phys. Rev. B 81 100403 (2010)] strongly influences the coupling strength between electrons and impurities spins