On the Magnon Bose Einstein Condensation in Ferromagnetic Film
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Bose-Einstein condensation (BEC) is one of the most intriguing macroscopic quantum phenomena. It has been observed in a variety of different systems, including ultracold atoms and ensembles of quasiparticles. In this work we concentrate on the magnon Bose-Einstein condensation observed in ferromagnetic yttrium iron garnet (YIG) film. In contrast to the cold atomic system, the magnon BEC proceeds at room temperature. We first review the basic theory of magnons in ferromagnetic film and discuss the recent experimental results on magnon BEC. The magnon spectrum in YIG film has two minima of energy at nonzero wavevectors Q and -Q. Therefore, in principle two condensates can appear. It is very important for observable condensation phenomena how the condensed magnons are distributed between the two minima and whether two condensates are coherent. Previous theoretical and experimental studies ignored both these problems. In this dissertation we address these important questions. Starting from the microscopic model describing the ferromagnetic film, we analytically calculate the interaction of condensates. It depends on thickness of the film d and external magnetic field H0. In comparatively thick films (1-5 ?m) the magnons of the same condensate attract each other, whereas the magnons of different condensate repulse. It leads to spontaneous violation of the mirror symmetry predicted by our theory. As a consequence, the numbers of condensed magnons in the two minima are not equal. This result explains the rather low contrast in the interference pattern observed in experiments by the real space Brillouin light scattering methods. We also find that the dipolar interaction that does not conserve the magnon number generates a special type of interaction that leads to the coherence between two condensates and to the existence of two types of condensates with sum of their phase equal to either 0 or ?. The existence of the interference pattern violates also the translational symmetry of the condensate. The corresponding excitations are Goldstone modes that we call "zero sound'. We calculated its spectrum. We also calculated how the condensate depends on the thickness of film and external magnetic field and discovered that, in the range of thickness 0:1 - 03 ?m the phase transition to the phase with equal condensate densities proceeds. This transition as well as transition between 0- and ?- phases can be driven by external magnetic field. Next we study the relaxation rate of condensed magnons. There are two important time scales in the formation of magnon BEC, that is, the thermalization time ?th and the life time ?l. In order to generate and observe BEC, the condition ?th >> ?l must be fulfilled. Experimentally the thermalization time is of the order of 100 ns. The relaxation is due to the magnon-magnon interaction conserving the magnon numbers. The lifetime is found to be of the order of 1 ?s, and was thought to be due to the magnon-phonon interaction which doesn't conserve the magnon numbers. However the calculation of lifetime due to magnon-phonon interaction disagrees with the experimental values. Here we calculate the lifetime due to three magnon processes in a ferromagnetic film with finite thickness. Our calculation gives a lifetime of the order of 10 ?s, which is almost of the same order of magnitude with the one provided by magnon-phonon interaction. This means that the three magnon processes provide an important channel for the relaxation of condensed magnons.