Absence of unstable zero-field intersubband spin excitations of dilute electron bilayers

Low-energy spin-density intersubband excitations of electron bilayers in GaAs double quantum wells have been investigated by inelastic light scattering in the search for unstable modes. Excitonic vertex corrections due to exchange Coulomb interactions were thus determined down to very low electron densities. The experiments are interpreted within the time-dependent local-density approximation (TDLDA) and with a nonlocal theory. The pronounced softening at zero magnetic field (a vertex-correction driven instability) predicted by the TDLDA for densities n<${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$ was not observed. At these lower densities we achieve better agreement with experiment using the nonlocal theory.