  Strong experimental evidences of the formation of quasi-equilibrium
Bose-Einstein condensation (BEC) of magnons at room temperature in a film of
yttrium iron garnet (YIG) excited by microwave radiation have been recently
reported. Here we present a theory for the magnon gas driven by a microwave
field far out of equilibrium showing that the nonlinear magnetic interactions
create cooperative mechanisms for the onset of a phase transition leading to
the spontaneous generation of quantum coherence and magnetic dynamic order in a
macroscopic scale. The theory provides rigorous support for the formation of a
BEC of magnons in a YIG film magnetized in the plane. We show that the system
develops coherence only when the microwave driving power exceeds a threshold
value and that the theoretical result for the intensity of the Brillouin light
scattering from the BEC as a function of power agrees with the experimental
data. The theory also explains quantitatively experimental measurements of
microwave emission from the uniform mode generated by the confluence of BEC
magnon pairs in a YIG film when the driving power exceeds a critical value.
