Slow inter-minima relaxation and its consequence for BEC of magnons

Two recent articles of the Munster University experimental team led by S.O. Demokritov displayed several important facts related to the Bose-Einstein condensation of magnons (BECM) under permanent pumping first discovered in 2006. They contradicted existing theories of this phenomenon, which predict the attractive interaction between magnons and strong spontaneous violation of the reflection symmetry. In this article, we show that these theories implicitly assumed all relaxation processes to be fast compared with the lifetime of the magnons, whereas one of them -- relaxation between two minima of energy -- is slow. We classify processes responsible for the inter-minima relaxation and present their analytic theory. We analyze how the slow inter-minima relaxation modifies the anticipated properties of a ferromagnet with the magnon condensate