Phase Diagram for Magnon Condensate in Yttrium Iron Garnet Film

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.