  Diluted magnetic semiconductors are materials well known to exhibit strong
correlations which typically manifest in carrier-mediated magnetic ordering. In
this Rapid Communication, we show that the interaction between excitons and
magnetic impurities in these materials is even strong enough to cause a
significant deviation from the bare exciton picture in linear absorption
spectra of quantum well nanostructures. It is found that exciton-impurity
correlations induce a characteristic fingerprint in the form of an additional
feature close to the exciton resonance in combination with a shift of the main
exciton line of up to a few meV. We trace back these features to the form of
the self-energy and demonstrate that reliable values of the average correlation
energy per exciton can be extracted directly from the spectra. Since the only
requirement for our findings is sufficiently strong correlations, the results
can be generalized to other strongly correlated systems.
