  Bose-Einstein condensation of quasi-equilibrium magnons is one of few
macroscopic quantum phenomena observed at room temperature. Since its
discovery, it became an object of intense research, which led to the
observation of many exciting phenomena such as quantized vortices, second
sound, and Bogolyubov waves. However, for a long time it remained unclear, what
physical mechanisms can be responsible for the spatial stability of the magnon
condensate. Indeed, since magnons are believed to exhibit attractive
interaction, it is generally expected that the magnon condensate should be
unstable with respect to the real-space collapse, which contradicts all the
experimental findings. Here, we provide direct experimental evidence that
magnons in a condensate exhibit repulsive interaction resulting in the
condensate stabilization and propose a mechanism, which is responsible for the
interaction inversion. Our experimental conclusions are additionally supported
by the theoretical model based on the Gross-Pitaevskii equation. Our findings
solve a long-standing problem and provide a new insight into the physics of
magnon Bose-Einstein condensates.
