Specific heat anomalies in the magnetic borocarbide superconductors ${\mathrm{Y}}_{1-x}{R}_x{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ $(R=\mathrm{Gd},$ Dy, Ho, and Er)

The specific heat anomalies associated with the superconducting transition of ${\mathrm{Y}}_{1-x}{R}_x{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ $(R=\mathrm{Gd},$ Dy, Ho, and Er) show a common correlation between the specific heat jump $\Delta C$ and the transition temperature $T_c$ with an almost quadratic relation $\Delta C\propto T_c^2$ in all these solid solutions. The antiferromagnetic superconductor ${\mathrm{DyNi}}_2{\mathrm{B}}_2\mathrm{C}$ with $T_N>T_c$ as well as Ho and ${\mathrm{ErNi}}_2{\mathrm{B}}_2\mathrm{C},$ which are paramagnetic at $T_c,$ fit into the same scheme of $\Delta C$ versus $T_c$ as the pseudoquaternaries. A simple description which combines the weak-coupling results of magnetic pair breaking theory with strong-coupling corrections explains reasonably well the quadratic relation between $\Delta C$ and $T_c.$ The overall agreement between this model and our experimental results indicates that the Sommerfeld value $\gamma$ and hence the electronic density of states are almost constant within these heavy rare-earth solid solutions and their boundary compounds.