  We propose a mechanism for destabilizing or stabilizing Bose-Einstein
condensation (BEC) of interacting magnons in an antiferromagnet. We study how
the interaction between magnons affects the magnon BEC in a two-sublattice
antiferromagnet without and with an external magnetic field. We show that in
the absence of the magnetic field the magnon BEC is destabilized by the
attractive interband interaction, which is larger than the repulsive intraband
interaction. We also show that in the presence of the magnetic field the magnon
BEC is stabilized only if the magnetic field is large enough to make the
intraband interaction larger than the interband interaction. Our results
provide the first step for understanding the interaction effects on the magnon
BEC in antiferromagnets and may open interaction physics of multicomponent BEC
of magnons in magnets.
