Specific heat ofA15Nb3Sn in fields to 18 tesla

Abstract

For the first time, the low-temperature specific heat of $A15\mathrm{}$ ${\mathrm{Nb}}_3$Sn has been measured in a magnetic field (18 T) high enough to significantly suppress the superconducting transition temperature, $T_c$. All previous extrapolations to $T=0\mathrm{}$ of the normal-state specific heat, $C_n$, to determine $\gamma$ and $N\left(0\right)\mathrm{}$ are shown by the measured $C_n$ data to be incorrect. The Debye temperature, ${\Theta }_D$, has previously been assumed to vary smoothly with temperature from its low-temperature value [${\Theta }_D (T<\mathrm{}4\mathrm{} \mathrm{K})=208\mathrm{}$ K] to its higher-temperature value [${\Theta }_D(T>\mathrm{}{T}_c)=270\mathrm{}$ K]. The high-field measurement of ${\Theta }_D\mathrm{}\left(T\right)\mathrm{}$ shows that it remains constant upon cooling until 11 K, where it abruptly changes to its low-temperature value. The rather short extrapolation of the high-field normal-state data to $T=0\mathrm{}$ from $T>\mathrm{}{T}_c$ (18 T) yields a $\gamma$ of 35±3 mJ/mole ${\mathrm{K}}^2$ compared to the previously accepted value of 52 mJ/mole ${\mathrm{K}}^2$. Using this lower value for $\gamma$, and taking $\gamma =1.75\mathrm{}$ from tunneling results, implies $N\left(0\right)=1.35\mathrm{}\pm 0.1$ states/eV atom, in excellent agreement with recent band-structure calculations of Klein et al. who obtained 1.46 states/eV atom for $A15\mathrm{}$ ${\mathrm{Nb}}_3$Sn. The present work calls into question all other extrapolations of $C_n$ data in high-$T_c$ materials where ${\Theta }_D$ is known to change significantly between $T_c$ and 0 K, e.g., $A15\mathrm{}$ ${\mathrm{V}}_3$Si.