Abstract
We suggest a new mechanism of Bose condensation of excitons in a quantum well with semimagnetic barriers. Attraction of excitons is due to their exchange interaction with semimagnetic environment. The long exciton lifetime needed for formation of a condensed phase is provided due to exchange-induced displacement of the hole into one of the barriers leading to formation of a long-living spatially indirect state. The resulted condensed state is a collective exciton magnetic polaron.
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