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We show that the formation of a magnon condensate in thin ferromagnetic filmscan be explained within the framework of a classical stochastic non-MarkovianLandau-Lifshitz-Gilbert equation where the properties of the random magneticfield and the dissipation are determined by the underlying phonon dynamics. Wehave numerically solved this equation for a tangentially magnetizedyttrium-iron garnet film in the presence of a parallel parametric pumpingfield. We obtain a complete description of all stages of the nonequilibriumtime evolution of the magnon gas which is in excellent agreement withexperiments. Our calculation proves that the experimentally observedcondensation of magnons in yttrium-iron garnet at room temperature is a purelyclassical phenomenon which should be called Rayleigh-Jeans rather thanBose-Einstein condensation.

Rayleigh-Jeans condensation of pumped magnons in thin film ferromagnets