We studied the effect of impurity on the first order superconducting (SC) transition and the high field-low temperature (HFLT) SC state of ${\mathrm{CeCoIn}}_5$ by measuring the specific heat of $\mathrm{CeCo}({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x{)}_5$ with $x=0.0011$, 0.0022, and 0.0033 and $\mathrm{CeCo}({\mathrm{In}}_{1-x}{\mathrm{Hg}}_x{)}_5$ with $x=0.00016$, 0.000 32, and 0.000 48 at temperatures down to 0.1 K and fields up to 14 T. Cd substitution rapidly suppresses the crossover temperature $T_0$, where the SC transition changes from second to first order, to $T=0\mathrm{K}$ with $x=0.0022$ for $H\parallel [100]$, while it remains roughly constant up to $x=0.0033$ for $H\parallel [001]$. The associated anomaly of the proposed FFLO state in Hg-doped samples is washed out by $x=0.00048$, while remaining at the same temperature, indicating high sensitivity of that state to impurities. We interpret these results as supporting the nonmagnetic, possibly FFLO, origin of the HFLT state in ${\mathrm{CeCoIn}}_5$.

• Received 15 April 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.037001