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Superconductivity, Kondo physics and magnetic order: Tuning the groundstate in the La$_{1-x}$Ce$_x$FeSiH solid solution through the interplay between $3d$ and $4f$ correlated electrons

We report a study of the La$_{1-x}$Ce$_x$FeSiH solid solution ($0 \leq x \leq 1$), a family of intermetallic hydrides of ZrCuSiAs-type structure, with space group $P4/nmm$. For low cerium concentrations $x \leq 0.20$, we observe the presence of superconductivity, which originates from the correlated $3d$ electrons of iron. The superconducting regime is progressively suppressed by the cerium substitution. For moderate cerium concentration $0.07 \leq x \leq 0.50$, we observe evidence of the single-ion Kondo effect and no magnetic phase transition down to 2 K. For $0.07 \leq x \leq 0.20$, the single-ion Kondo effect coexists with a superconducting ground state at low temperatures. From $x > 0.50$, we observe signatures of Kondo coherence and a heavy Fermi liquid regime at low temperature. Finally, at high cerium concentration $x \geq 0.85$, we observe signatures of magnetic ordering at low temperatures. We discuss our results by introducing temperature scales related to superconductivity, the Kondo effect, and magnetic order, which permits building a rich phase diagram temperature versus cerium content $x$. This shows that using the cerium concentration $x$ as a unique control parameter, we can explore the Kondo entanglement between correlated $3d$ and $4f$ electrons, which suggests an unusual change between the superconducting state related to the $3d$ electrons and the Kondo coherent state involving both $3d$ and $4f$ electrons.