The compound Sr$_{0.5}$Ce$_{0.5}$FBiS$_{2}$ belongs to the intensively studied family of layered BiS$_2$ superconductors. It attracts special attention because superconductivity at $T_{sc} = 2.8$ K was found to coexist with local-moment ferromagnetic order with a Curie temperature $T_C = 7.5$ K. Recently it was reported that upon replacing S by Se $T_C$ drops and ferromagnetism becomes of an itinerant nature (Thakur et al., Sci. Reports 6, 37527 (2016)). At the same time $T_{sc}$ increases and it was argued superconductivity coexists with itinerant ferromagnetism. Here we report a muon spin rotation and relaxation study ($mu$SR) conducted to investigate the coexistence of superconductivity and ferromagnetic order in Sr$_{0.5}$Ce$_{0.5}$FBiS$_{2-x}$Se$_x$ with $x=0.5$ and $1.0$. By inspecting the muon asymmetry function we find that both phases do not coexist on the microscopic scale, but occupy different sample volumes. For $x=0.5$ and $x=1.0$ we find a ferromagnetic volume fraction of $sim , 8 %$ and $sim , 30 %$ at $T=0.25$ K, well below $T_{C} = 3.4$ K and $T_C = 3.3$ K, respectively. For $x=1.0$ ($T_{sc} = 2.9$ K) the superconducting phase occupies the remaining sample volume ($sim , 70 %$), as shown by transverse field experiments that probe the Gaussian damping due to the vortex lattice. We conclude ferromagnetism and superconductivity are macroscopically phase separated.
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