studied by scanning SQUID microscopy*

The superconductivity coexisting with ferromagnetic order has intrigued scientists for decades. RbEuFe₄As₄ is one of these cases with the superconductivity in the FeAs layers and ferromagnetic order in the Eu layers. Systematic spatially resolved studies are lacking but necessary to investigate the superconductivity, ferromagnetic order, and the relation between them. We used scanning SQUID microscopy to image the in situ diamagnetic and ferromagnetic responses of RbEuFe₄As₄ with micrometer scale resolution in both magnetometry mode and susceptometry mode. We observed homogeneous superconductivity with T_c ~ 37 K, and unexpected and inhomogeneous double ferromagnetic transitions with T_m ~ 15 K upon cooling down. The vortices coexist with the magnetic domains below T_m, but are not rearranged in the temperature cycles through T_m. The observed spatial feature of suppressed superfluid density matches well with the inhomogeneous ferromagnetic domain structure close to T_m, which is consistent with the scenario that the ferromagnetic spin fluctuations strongly suppress the superconductivity. In our study, the ferromagnetic order in RbEuFe₄As₄ is not strong enough to rearrange the vortices, but the superconductivity is strongly suppressed by the magnetic fluctuations. Our results will stimulate future investigations into the physical phenomena arising from the superconducting and magnetic subsystems by scanning probes.