Tilted-magnetic-field measurements of activation energies and cyclotron resonance for ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs heterojunctions

The Landau-level splitting in ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs heterojunctions has been studied in tilted magnetic fields by analyzing either the thermally activated conductance or the cyclotron-resonance absorption. For an increasing parallel magnetic field, a decrease of the activation energy is found for even filling factors. At odd filling factors the activation energy increases with the parallel magnetic field, corresponding to an increase of the spin splitting. The angular dependence of the Landau-level splitting obtained from the activated conduction at a filling factor of ν=2 is found to be in excellent agreement with the results obtained from cyclotron-resonance experiments. For higher filling factors (ν=4 and 6) only a qualitative agreement between the two methods is observed. The quantitative discrepancy is attributed to the existence of mobility edges, which result in a reduction of the gap observed in thermally activated transport.