We have observed a large spin splitting between "spin" \(+1\) and \(-1\) heavy-hole excitons,
having unbalanced populations, in undoped GaAs/AlAs quantum wells in the absence of
any external magnetic field. Time-resolved photoluminescence spectroscopy, under excitation
with circularly polarized light, reveals that, for high excitonic density and short
times after the pulsed excitation, the emission from majority excitons lies above
that of minority ones. The amount of the splitting, which can be as large as 50% of
the binding energy, increases with excitonic density and presents a time evolution
closely connected with the degree of polarization of the luminescence. Our results
are interpreted on the light of a recently developed model, which shows that, while
intra-excitonic exchange interaction is responsible for the spin relaxation processes,
exciton-exciton interaction produces a breaking of the spin degeneracy in two-dimensional
semiconductors.