Anisotropic effect of Cd-doping on superconducting phase in CeCoIn$_{5}$ at high fields

Unconventional superconductor CeCoIn$_{5}$ at high magnetic field displays first order superconducting (SC) transition, and an additional high field-low temperature SC phase (previously proposed to be an inhomogeneous superconducting FFLO state). We have studied Cd-doping effect on the FFLO state and the first order SC transition by measuring specific heat $C$(T) of CeCo(In$_{1-x}$Cd$_{x})_{5}$ (x=0.01, 0.02 and 0.03) at low temperatures and high fields. Our data show that the FFLO state is already destroyed by 1{\%} Cd-doping. The effect of Cd doping on the first order SC transition is anisotropic. The cross-over temperature $T_{0}$, where the superconducting transition changes its nature from first to second order, decreases rapidly with increasing doping for $H$//[100] and disappears already at x=0.02, while it remains rather temperature-independent for $H$//[001] up to x=0.03.