Using a low-temperature molecular-beam epitaxy growth procedure, Ga 1Ϫx Mn x As -a III-V diluted magnetic semiconductor -is obtained with Mn concentrations up to xϳ9%. At a critical temperature T c ͑T c Ϸ50 K for xϭ0.03-0.05͒, a paramagnetic to ferromagnetic phase transition occurs as the result of the interaction between Mn-h complexes. Hole transport in these compounds is strongly affected by the antiferromagnetic exchange interaction between holes and Mn 3d spins. A model for the transport behavior both above and below T c is given. Above T c , all materials exhibit transport behavior which is characteristic for systems near the metal-insulator transition. Below T c , due to the rising spontaneous magnetization, spin-disorder scattering decreases and the relative position of the Fermi level towards the mobility edge changes. When the magnetization has reached its saturation value ͑below ϳ10 K͒ variable-range hopping is the main conduction mechanism. The negative magnetoresistance is the result of the expansion of the hole wave functions in an applied magnetic field. ͓S0163-1829͑97͒04044-7͔

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Magnetic breakdown phenomena have been investigated in the longitudinal magnetoresistance of the quasi-two-dimensional (Q2D) superconductor in magnetic fields of up to 50 T, well above the characteristic breakdown field. The material is of great interest because its relatively simple Fermi surface, consisting of a closed Q2D pocket and an open Q1D band, is almost identical to the initial hypothetical breakdown network proposed by Pippard. Two frequencies are expected to dominate the magnetoresistance oscillations: the frequency, corresponding to orbits around the closed pocket, and the frequency, corresponding to the simplest classical breakdown orbit. However, a frequency is in fact found to be the dominant high-frequency oscillation in the magnetoresistance. Numerical simulations, employing standard theories for calculating the density of states, indicate that a significant presence of the frequency (forbidden in the standard theories) can result simply from the frequency-mixing effects associated with the pinning of the chemical potential in a quasi-two-dimensional system. While this effect is able to account for the previous experimental observation of frequency oscillations of small amplitude in the magnetization, it cannot explain why such a frequency dominates the high-field magnetotransport spectrum. Instead we have extended the numerical simulations to include a quantum interference model adapted for longitudinal magnetoresistance in a quasi-two-dimensional conductor. The modified simulations are then able to account for most of the features of the experimental magnetoresistance data.

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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.