Magnon condensation and spin superfluidity

We consider the Bose-Einstein condensation (BEC) of quasi-equilibrium magnons which leads to spin superfluidity, the coherent quantum transfer of magnetization in magnetic material. The critical conditions for excited magnon density in ferro- and antiferromagnets, bulk and thin films, are estimated and discussed. It was demonstrated that only the highly populated region of the spectrum is responsible for the emergence of any BEC. This finding substantially simplifies the BEC theoretical analysis and is surely to be used for simulations. It is shown that the conditions of magnon BEC in the perpendicular magnetized YIG thin film is fulfillied at small angle, when signals are treated as excited spin waves. We also predict that the magnon BEC should occur in the antiferromagnetic hematite at room temperature at much lower excited magnon density compared to that of ferromagnetic YIG. Bogoliubov's theory of Bose-Einstein condensate is generalized to the case of multi-particle interactions. The six-magnon repulsive interaction may be responsible for the BEC stability in ferro- and antiferromagnets where the four-magnon interaction is attractive.