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We clarify the condition for the occurrence of magnon Bose-Einsteincondensation (BEC) in spin pumping systems without using external pumpingmagnetic fields. The Goldstone model is generalized and the stability of thevacuum is closely investigated. By applying the generalized Goldstone model tospin pumping systems, the condition for the experimental realization of thestable magnon BEC in spin pumping systems is theoretically proposed.

Bose-Einstein condensation of magnons in spin pumping systems