Specific-heat analysis of rare-earth transition-metal borocarbides: An estimation of the electron-phonon coupling strength

We analyzed the superconducting and normal-state heat capacity of superconducting ${\mathrm{YNi}}_2$ ${\mathrm{B}}_2$C, ${\mathrm{LuNi}}_2$ ${\mathrm{B}}_2$C, ${\mathrm{LaPt}}_{1.5}$ ${\mathrm{Au}}_{0.5}$ ${\mathrm{B}}_2$C and the nonsuperconducting reference compounds ${\mathrm{LaNi}}_2$ ${\mathrm{B}}_2$C, ${\mathrm{YCo}}_2$ ${\mathrm{B}}_2$. The deviations of the thermodynamic ratios as ΔC/γ${\mathit{T}}_{\mathit{c}}$, γ${\mathit{T}}_{\mathit{c}}^2$/${\mathit{H}}_{\mathit{c}}^2$(0), ${\mathit{H}}_{\mathit{c}}^{\prime }$(${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{cH}\mathit{c}}$(0), and Δ(0)/${\mathit{k}}_{\mathrm{B}}$ ${\mathit{T}}_{\mathit{c}}$ from their BCS values give an estimate for the strong-coupling parameter ${\mathit{T}}_{\mathit{c}}$/${\mathrm{\omega }}_{\mathrm{}\ln \mathrm{}}$ which is in the range of 0.06–0.1 and indicates that the phonon mediated superconductivity can be classified in the moderately strong-coupling limit. From the normal-state specific heat between 2 and 300 K we constructed model phonon spectra to determine the moments of the phonon density of states F(ω) and calculated the electron-phonon enhancement factor λ with the Allen and Dynes formula which yields λ values in the range of 0.95–1.15 for the three superconducting compounds. The comparison of these λ values with the electron mass enhancement derived from the ratio of the Sommerfeld parameter γ and the calculated density of states at the Fermi level, N(${\mathit{E}}_{\mathit{F}}$), shows that band structure calculations overestimate N(${\mathit{E}}_{\mathit{F}}$). Furthermore we determined the upper critical field ${\mathit{H}}_{\mathit{c}2}$(T) from specific-heat measurements up to 11 T and the normalized Ginzburg-Landau parameter k(T) which both show BCS-type behavior for ${\mathrm{LaPt}}_{1.5}$