  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.
