The circular polarization of cw photoluminescence as a function of applied magnetic field has been measured at 1.8 K for excitons in a series of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As and GaAs/AlAs type-I quantum wells having well widths between 2.5 and 8.0 nm. The results show evidence of level crossings, which have been analyzed to give the short-range, spin-dependent exchange interaction. The associated experimental exchange splittings between optically allowed and nonallowed exciton states are of the order of 0.15 meV for the narrowest wells and fall monotonically with increasing width. Simulations of the data using solutions of rate equations for the exciton-level populations show that the optically nonallowed exciton states lie below the allowed states and give insight into the field dependence of the spin-relaxation rates of excitons and of holes and electrons in an exciton. Calculations of the enhancement of exchange interaction due to carrier confinement relative to the bulk value give agreement between the quantum-well and bulk-exchange values, and confirm that exchange is particularly sensitive to barrier height and other details of the structure. The data also show evidence for eigenstate-polarization changes, which indicate a much smaller zero-field splitting due to departure of the quantum-well symmetry from the ideal ${\mathit{D}}_{2\mathit{d}}$. The simulation indicates that only a fraction (up to 20%) of excitons in these samples actually experiences a nonideal, distorted environment.

• Received 3 June 1994

DOI:https://doi.org/10.1103/PhysRevB.50.14246