  We explore the formation and collective modes of Bose-Einstein condensate of
Dirac magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, an
employed approach is general and could be used to describe Bose-Einstein
condensates with linear quasiparticle spectrum in various systems. By using a
phenomenological multicomponent model of pumped boson population together with
bosons residing at Dirac nodes, the formation and time evolution of condensates
of Dirac bosons is investigated. The condensate coherence and its
multicomponent nature are manifested in the Rabi oscillations whose period is
determined by the gap in the spin-wave spectrum. A Dirac nature of the
condensates could be also probed by the spectrum of collective modes. It is
shown that the Haldane gap provides an efficient means to tune between the
gapped and gapless collective modes as well as controls their stability.
