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Exchange processes are responsible for the stability of elementary bosoncondensates with respect to their possible fragmentation. This remains true forcomposite bosons when single fermion exchanges are included but spin degrees offreedom are ignored. We here show that their inclusion can produce a"spin-fragmentation" of a condensate of dark excitons, i.e., an unpolarizedcondensate with equal amount of dark excitons with spins (+2) and (-2). Quitesurprisingly, for spatially indirect excitons of semiconductor bilayers, wepredict that the condensate polarization can switch from unpolarized to fullypolarized, depending on the distance between the layers confining electrons andholes. Remarkably, the threshold distance associated to this switching lies inthe regime where experiments are nowadays carried out.

Effects of fermion exchanges on the polarization of exciton condensates