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The compound Sr$_{0.5}$Ce$_{0.5}$FBiS$_{2}$ belongs to the intensivelystudied family of layered BiS$_2$ superconductors. It attracts specialattention because superconductivity at $T_{sc} = 2.8$ K was found to coexistwith 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 andferromagnetism becomes of an itinerant nature (Thakur et al., Sci. Reports 6,37527 (2016)). At the same time $T_{sc}$ increases and it was arguedsuperconductivity coexists with itinerant ferromagnetism. Here we report a muonspin rotation and relaxation study ($\mu$SR) conducted to investigate thecoexistence of superconductivity and ferromagnetic order inSr$_{0.5}$Ce$_{0.5}$FBiS$_{2-x}$Se$_x$ with $x=0.5$ and $1.0$. By inspectingthe muon asymmetry function we find that both phases do not coexist on themicroscopic 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 remainingsample volume ($\sim \, 70 \%$), as shown by transverse field experiments thatprobe the Gaussian damping due to the vortex lattice. We concludeferromagnetism and superconductivity are macroscopically phase separated.

Macroscopic phase separation of superconductivity and ferromagnetism in Sr0.5Ce0.5FBiS2-xSex revealed by muSR