We report an unusual enhancement of the magnetic induction in single crystals of the magnetic superconductor RbEuFe$_4$As$_4$ , highlighting the interplay between superconducting and magnetic subsystems in this material. Contrary to the conventional Meissner expulsion of magnetic flux below the superconducting transition temperature, we observe a substantial boost of the magnetic flux density upon approaching the magnetic transition temperature, Tm. Direct imaging of the flux evolution with a magneto-optical technique, shows that the magnetic subsystem serves as an internal magnetic flux pump, drawing Abrikosov vortices from the surface, while the superconducting subsystem controls their conveyance into the bulk of the magnetic superconductor via a peculiar self-organized critical state.
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