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

Abstract

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}$. The deviations of the thermodynamic ratios as \ensuremath{\Delta}C/\ensuremath{\gamma}${\mathit{T}}_{\mathit{c}}$, \ensuremath{\gamma}${\mathit{T}}_{\mathit{c}}^{2}$/${\mathit{H}}_{\mathit{c}}^{2}$(0), ${\mathit{H}}_{\mathit{c}}^{\ensuremath{'}}$(${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{cH}\mathit{c}}$(0), and \ensuremath{\Delta}(0)/${\mathit{k}}_{\mathrm{B}}$${\mathit{T}}_{\mathit{c}}$ from their BCS values give an estimate for the strong-coupling parameter ${\mathit{T}}_{\mathit{c}}$/${\mathrm{\ensuremath{\omega}}}_{\mathrm{}\mathrm{ln}\mathrm{}}$ which is in the range of 0.06--0.1 and indicates that the phonon mediated superconductivity can be classified in the moderately strong-coupling limit. From the normal-state specific heat between 2 and 300 K we constructed model phonon spectra to determine the moments of the phonon density of states F(\ensuremath{\omega}) and calculated the electron-phonon enhancement factor \ensuremath{\lambda} with the Allen and Dynes formula which yields \ensuremath{\lambda} values in the range of 0.95--1.15 for the three superconducting compounds. The comparison of these \ensuremath{\lambda} values with the electron mass enhancement derived from the ratio of the Sommerfeld parameter \ensuremath{\gamma} and the calculated density of states at the Fermi level, N(${\mathit{E}}_{\mathit{F}}$), shows that band structure calculations overestimate N(${\mathit{E}}_{\mathit{F}}$). Furthermore we determined the upper critical field ${\mathit{H}}_{\mathit{c}2}$(T) from specific-heat measurements up to 11 T and the normalized Ginzburg-Landau parameter k(T) which both show BCS-type behavior for ${\mathrm{LaPt}}_{1.5}$${\mathrm{Au}}_{0.5}$${\mathrm{B}}_{2}$C, but a significant upward curvature for ${\mathrm{YNi}}_{2}$${\mathrm{B}}_{2}$C and especially for ${\mathrm{LuNi}}_{2}$${\mathrm{B}}_{2}$C.