Superconductivity, Kondo physics, and magnetic order: Tuning the ground state in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>La</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:m

We report a study of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>La</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mo>−</a:mo> <a:mi>x</a:mi> </a:mrow> </a:msub> <a:msub> <a:mi>Ce</a:mi> <a:mi>x</a:mi> </a:msub> <a:mi>FeSiH</a:mi> </a:mrow> </a:math> solid solution <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mo>(</b:mo> <b:mn>0</b:mn> <b:mo>≤</b:mo> <b:mi>x</b:mi> <b:mo>≤</b:mo> <b:mn>1</b:mn> <b:mo>)</b:mo> </b:mrow> </b:math> , a family of intermetallic hydrides of ZrCuSiAs-type structure, with space group <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>P</c:mi> <c:mn>4</c:mn> <c:mo>/</c:mo> <c:mi>n</c:mi> <c:mi>m</c:mi> <c:mi>m</c:mi> </c:mrow> </c:math> . For low cerium concentrations <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>x</d:mi> <d:mo>≤</d:mo> <d:mn>0.20</d:mn> </d:mrow> </d:math> , we observe the presence of superconductivity, which originates from the correlated <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>3</e:mn> <e:mi>d</e:mi> </e:mrow> </e:math> electrons of iron. The superconducting regime is progressively suppressed by the cerium substitution. For moderate cerium concentration <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mn>0.07</f:mn> <f:mo>≤</f:mo> <f:mi>x</f:mi> <f:mo>≤</f:mo> <f:mn>0.50</f:mn> </f:mrow> </f:math> , we observe evidence of the single-ion Kondo effect and no magnetic phase transition down to 2 K. For <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mn>0.07</g:mn> <g:mo>≤</g:mo> <g:mi>x</g:mi> <g:mo>≤</g:mo> <g:mn>0.20</g:mn> </g:mrow> </g:math> , the single-ion Kondo effect coexists with a superconducting ground state at low temperatures. From <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>x</h:mi> <h:mo>&gt;</h:mo> <h:mn>0.50</h:mn> </h:mrow> </h:math> , we observe signatures of Kondo coherence and a heavy Fermi liquid regime at low temperature. Finally, at high cerium concentration <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>x</i:mi> <i:mo>≥</i:mo> <i:mn>0.85</i:mn> </i:mrow> </i:math> , 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 <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>x</j:mi> </j:math> . This shows that using the cerium concentration <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>x</k:mi> </k:math> as a unique control parameter, we can explore the Kondo entanglement between correlated <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mn>3</l:mn> <l:mi>d</l:mi> </l:mrow> </l:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>4</m:mn> <m:mi>f</m:mi> </m:mrow> </m:math> electrons, which suggests an unusual change between the superconducting state related to the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mn>3</n:mn> <n:mi>d</n:mi> </n:mrow> </n:math> electrons and the Kondo coherent state involving both <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mn>3</o:mn> <o:mi>d</o:mi> </o:mrow> </o:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:mn>4</p:mn> <p:mi>f</p:mi> </p:mrow> </p:math> electrons.