We review experiments on the de Haas–van Alphen (dHvA) effect, i.e., the quantum oscillatory behavior of the magnetization M, in modulation‐doped AlGaAs/GaAs heterostructures at low temperature T. In particular we focus on the thermodynamic energy gaps and the density of states (DOS) of two‐dimensional electron systems (2DES's) in the integer quantum Hall regime. M as a thermodynamic quantity yields direct access to both quantities. Energy gaps due to Landau quantization at even integer filling factors ν are extracted from different samples that cover a wide range of electronic parameters. They are varied by heterostructure growth parameters. For the quantitative analysis we simulate the magnetization starting from a single‐particle model DOS. We find that a DOS consisting of, both, levels with a Gaussian broadening and a background that increases linearly with ν is essential to model magnetization data for the different heterostructures over a wide range of ns and T. In particular we discuss the correlation of the Landau level broadening with the specific sample parameters. Oscillations in M at odd filling factors resulting from the spin splitting of Landau levels are investigated as a function of magnetic field and electron density ns. We recalculate the exchange‐energy contribution to the spin splitting and find a disagreement with Hartree–Fock calculations. However, our results are consistent with previously published magnetocapacitance measurements. In the sample exhibiting the lowest level broadening we observe discontinuous jumps of M at even ν. This specific feature of the 2DES magnetization was predicted more than 70 years ago by Peierls but never reported for dHvA effect studies before. Both, the significant improvements of the measurement technique and the optimization of heterostructure growth during recent years have allowed us to observe such discontinuities in M. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

In a simultaneous experiment we studied the de Haas-van Alphen ͑dHvA͒ and the Shubnikov-de Haas ͑SdH͒ effects in a two-dimensional electron system ͑2DES͒ in a modulation-doped GaAs/ Al x Ga 1−x As heterostructure. For this, a gated 2DES mesa was monolithically integrated with a micromechnical cantilever with an interferometric fiber-optics readout. In situ measurement of the dHvA and SdH oscillations at 300 mK in a magnetic field B allowed us to directly compare the variation of the ground state energy and the nonequilibrium transport behavior, respectively. This was done on a 2DES of a small carrier density n s ranging from 5 ϫ 10 10 to 33ϫ 10 10 cm −2 . The wave forms of the dHvA oscillations were nonsinusoidal down to a magnetic field as small as 1.45 T. At the same time the zero-field mobility was as low as e =10 5 cm 2 / V s. We found that at fixed B the observed dHvA wave form and amplitude were independent of n s and e . This was unexpected and in contrast to the established picture in the literature. To understand the dHvA effect quantitatively in a disordered 2DES our data suggest that energetic details of the disorder potentials have to be considered.

We have studied experimentally the nonequilibrium currents ͑NECs͒ induced by sweeping either the magnetic field B or the carrier density n S of a two-dimensional electron system ͑2DES͒. The gated 2DES resided in a modulation-doped GaAs/ Al x Ga 1−x As heterostructure and was integrated into a micromechanical cantilever. The NECs provoke a magnetic moment which we have detected via torque magnetometry down to 300 mK. Additional electrical leads allowed for simultaneous magnetotransport measurements. We find a hysteretic behavior of the NECs and a striking asymmetry of the corresponding magnetic moment around integer filling factors = hn S / eB. Surprisingly, the shape of the hysteresis loops is the same for sweeps of B or n S if plotted versus . In a certain parameter regime each NEC signal exhibits a characteristic slope which is found to depend only on the filling factor at large B or n S . Based on a model considering capacitive coupling between 2DES and gate we attribute the slopes to the conductance quantization of the quantum Hall effect. The NECs are found to be limited by the time-dependent buildup of the radial Hall field governed by the gate capacitance. These findings are in contrast to a floating 2DES without a gate where the breakdown of the quantum Hall effect was previously reported to limit the NECs. Our model also explains the observed shape and dependence on temperature as well as sweep rate. The in situ measurement of the longitudinal resistance allows us to directly correlate the magnetic behavior with both the magnetic field and temperature-dependent resistance of the 2DES.

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