Evolution of ground state and upper critical field in R$_{1-x}$Gd$_x$Ni$_2$B$_2$C (R = Lu, Y): Coexistence of superconductivity and spin-glass state*

We report effects of local magnetic moment, Gd$^{3+}$, doping ($x \leq 0.3$) on superconducting and magnetic properties of the closely related Lu$_{1-x}$Gd$_x$Ni$_2$B$_2$C and Y$_{1- x}$Gd$_x$Ni$_2$B$_2$C series. The superconducting transition temperature decreases and the heat capacity jump associated with it drops rapidly with Gd-doping; qualitative changes with doping are also observed in the temperature-dependent upper critical field behavior, and a region of coexistence of superconductivity and spin-glass state is delineated on the $x - T$ phase diagram. The evolution of superconducting properties can be understood within the Abrikosov-Gor'kov theory of magnetic impurities in superconductors taking into account the paramagnetic effect on upper critical field and the details of the $x - T$ phase diagrams.