Theory of coherence in Bose-Einstein condensation phenomena in a microwave-driven interacting magnon gas

Strong experimental evidences of the formation of quasiequilibrium 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 dynamics of the magnon gas driven by a microwave field far out of equilibrium that provides rigorous support for the formation of a BEC of magnons in a YIG film magnetized in the plane. We show that if the microwave driving power exceeds a threshold value 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 theoretical results agree with the experimental data for the intensity and the decay rate of the Brillouin light scattering from the BEC as a function of power and for the microwave emission from the uniform mode generated by the confluence of BEC magnon pairs.