Magnetization measurements of high-mobility two-dimensional electron gases

De Haas--van Alphen (dHvA) oscillations are observed for Landau levels (LLs) with filling factors between 4 and 52, at temperatures in the range 50 mK to 1 K, in experiments on high-mobility GaAs/(Al, Ga)As heterojunctions. The oscillations become sawtooth-shaped at low filling factors, and theoretical fits to the data, assuming the two-dimensional electron gas to be a non-interacting Fermi system, show the shape of LLs to be close to a {δ} function. The small residual width ({~}0.4 meV or less) fits equally well to either a Gaussian or a Lorentzian density-of-states model. In almost all cases, a constant background density of states has to be included to obtain a satisfactory fit. Weak odd-filling-factor dHvA peaks are detected at high fields, from which a g-factor enhancement of 15 can be inferred. Comparison of the scattering time derived from the fits before and after illumination, with the momentum relaxation time derived from transport, reveals a counterintuitive behavior in the bulk-modulation-doped sample.