The exciton recombination and spin dynamics are investigated both experimentally and theoretically in an ensemble of indirect band gap (In,Al)As/AlAs quantum dots (QDs) with type-I band alignment. The magnetic-field-induced circular polarization of the time-integrated photoluminescence changes sign across the emission spectrum with a width reflecting the QD size. It is negative on the low energy side, i.e. for emission from large QDs, but positive on the high energy side, i.e. for emission from small QDs. However, the exciton g factor, measured by spin-flip Raman scattering, is positive across the whole QD ensemble. The magnetic-field-induced circular polarization of the photoluminescence dynamics is studied as function of the magnetic field strength and direction. The dynamics are non-monotonic over a time range up to milliseconds. The time dependence of the photoluminescence circular polarization degree and sign strongly depends on the emission energy and changes with magnetic field orientation. The observed nonmonotonic behavior is provided by the interplay of bright and dark exciton states, contributing to the emission. The experiment is interpreted using a kinetic theory, which accounts for the dynamics of the spin states in the exciton level quartet in longitudinal and tilted magnetic fields, the radiative recombination processes, and the redistribution of the excitons between these states as result of spin relaxation. The model allows us to evaluate the electron and heavy hole spin relaxation times in QDs with different sizes.
Шамирзаев et al. (Fri,) studied this question.