  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.
