Collective Spin-Flip Excitations in the Quantum Hall Regime

Abstract

In an external magnetic field, the electron inversion layer in GaAs heterojunctions supports collective charge and spin density oscillations, i.e., magnetoplasmons and spin-waves, which, at long wavelengths, can be probed by cyclotron resonance and electron spin resonance experiments. To first order, electron-electron interactions only affect these modes at finite wave vectors and, hence, their effect is not directly probed by such experiments. Recently, inelastic light scattering methods have been used with great success to probe these collective excitations at finite wave vectors. Very recently, a strong feature in these spectra, near filling factor v = 1, has been identified with a collective spin-flip excitation, which involves excitations where an electron is both promoted from the lowest Landau level to the second level and its spin is reversed. At long wavelengths, such excitations are shifted away from the sum of the cyclotron energy and the Zeeman energy, hωc + gμB, by a Coulomb exchange energy. At filling factor v = 1, the value of this exchange energy calculated in the time-dependent Hartree Fock approximation gives excellent agreement with the value extracted from the experimental spectra. The dispersion of collective spin-flip excitations has been calculated at integral and fractional Landau level filling within the time-dependent Hartree Fock and generalized single-mode approximations. These results are discussed, with emphasis on the features that could be probed experimentally.