Intrasubband excitations and spin-splitting anisotropy in GaAs modulation-doped quantum wells

We present Raman-scattering measurements of intrasubband excitations in the quasi-two-dimensional electron gas (2DEG) of an n-type modulation-doped GaAs/${\mathrm{Al}}_{0.33}$${\mathrm{Ga}}_{0.67}$As quantum well. In depolarized spectra we observe spin-flip single-particle excitations between the spin-split conduction bands. Measurements with the Raman wave vector along different crystallographic orientations allow us to probe the anisotropy of this spin splitting, caused by the lack of inversion symmetry in GaAs. We discuss theoretical descriptions of the spin splitting in a 2DEG and compare calculated and measured Raman spectra. In polarized spectra we observe scattering with comparable intensity from non-spin-flip single-particle excitations and plasmons. In order to describe correctly the plasmon dispersion we have to take into account the effects on the Coulomb interaction of image charges in the sample surface.