  Recently, magnons, which are quasiparticles describing the collective motion
of spins, were found to undergo Bose-Einstein condensation (BEC) at room
temperature in films of Yttrium Iron Garnet (YIG). Unlike other quasiparticle
BEC systems, this system has a spectrum with two degenerate minima, which makes
it possible for the system to have two condensates in momentum space. Recent
Brillouin Light scattering studies for a microwave-pumped YIG film of thickness
d=5 $\mu$m and field H=1 kOe find a low-contrast interference pattern at the
characteristic wavevector $Q$ of the magnon energy minimum. In this report, we
show that this modulation pattern can be quantitatively explained as due to
non-symmetric but coherent Bose-Einstein condensation of magnons into the two
energy minima. Our theory predicts a transition from a high-contrast symmetric
phase to a low-contrast non-symmetric phase on varying the $d$ and $H$, and a
new type of collective oscillations.
