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We have studied the low-temperature photoluminescence of the two-dimensional electron gas in a single GaAs quantum well in magnetic fields up to 50 T over four orders of magnitude of illumination intensity. At the very highest illumination powers, where the recombination is excitonic at zero field, we find that the binding energy of both the singlet and triplet states of the negatively charged exciton (X Ϫ ) increase monotonically with the applied field above 15 T. This contradicts recent calculations for X Ϫ , but is in agreement with adapted calculations for the binding energy of negative-donor centers. At low-laser powers we observe a strong transfer of luminescence intensity from the singlet ͑ground͒ state to the triplet ͑excited͒ state as the temperature is reduced below 1 K. This is attributed to the spin polarization of the two-dimensional electron gas by the applied magnetic field.

We have used a torque magnetometer to measure de Haas - van Alphen oscillations in the magnetization of two-dimensional electrons in GaAs/AlGaAs heterostructures and multiple-quantum-well systems for temperatures ranging from 0.125 K to 4.2 K and in magnetic fields of up to 15 T. Our results indicate that for high magnetic fields the density of states can be described by a series of Lorentzian-broadened Landau levels with a broadening that is independent of the magnetic field, B, and Landau level index, n. However, at low magnetic fields the Lorentzian-broadened density of states becomes indistinguishable from a Gaussian one with a broadening that is proportional to . The high-field behaviour of the Landau level line-shape is shown to differ appreciably from the low-field case as reported by other workers using both magnetization and other experimental methods. The reliability of this and other experimental techniques is discussed.

De Haas-van Alphen ͑dHvA͒ oscillations are observed for Landau levels ͑LLs͒ with filling factors between 4 and 52, at temperatures in the range 50 mK to 1 K, in experiments on high-mobility GaAs/͑Al, Ga͒As 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 ␦ function. The small residual width ͑ϳ0.4 meV or less͒ 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.

Abstract. The high magnetic field, low-temperature magnetic properties of lowdimensional electron and hole systems reveal a wealth of fundamental information. Quantum oscillations of the thermodynamic equilibrium magnetization yield the total density of states, a central quantity in understanding the quantum Hall effect in 2D systems. The magnetization arising from non-equilibrium circulating currents reveals details, not accessible with traditional measurements, of the vanishingly small longitudinal resistance in the quantum Hall regime. We review how the technique of magnetometry has been applied to these systems, the most important discoveries that have been made, and their theoretical significance.