High-Magnetic-Field Specific Heat of a Low-Dislocation-Density Alloy Superconductor

Abstract

The Specific heat $C$ of a well-annealed alloy V-5 at.% Ta, measured at $1.4\ensuremath{\le}T\ensuremath{\le}5$ \ifmmode^\circ\else\textdegree\fi{}K in steady magnetic fields, displays sharp, bulk, superconducting transitions at upper critical fields ${H}_{c2}$ a factor $\ensuremath{\approx}10$ larger than the calorimetrically derived thermodynamic critical fields ${H}_{c}$. The transitions are similar to those observed earlier by Morin ${\mathit{et}\mathit{al}.}^{1}$ in ${\mathrm{V}}_{3}$Ga, but in the present case it is unlikely that the bulk nature of the high-field transitions can be attributed to a nearly complete occupation of the specimen volume by dislocation-centered high-field superconducting filaments of diameter comparable to the penetration depth, since electron transmission microscopy studies on an identically prepared specimen indicate that in at least 95% of the specimen volume the mean separation between dislocations is greater than 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ cm. However, the present data are explicable on the basis of the Ginzburg-Landau-Abrikosov-Gor'kov theory with a parameter $\ensuremath{\kappa}\ensuremath{\approx}\frac{{H}_{c2}}{\sqrt{2}{H}_{c}}\ensuremath{\approx}7$. The transition specific heat jumps $\frac{\ensuremath{\Delta}C({T}_{s})}{\ensuremath{\gamma}{T}_{s}}=1.44,1.15,1.10,0.94$ occur at ${T}_{s}=4.30,4.09,3.85,3.37$ \ifmmode^\circ\else\textdegree\fi{}K in fields $H=0,1,2,4$ kG, respectively, where $\ensuremath{\gamma}\ensuremath{\equiv}$ normal state electronic specific heat coefficient = 9.20 mJ/mole ${(\mathrm{K}\mathrm{\ifmmode^\circ\else\textdegree\fi{}})}^{2}$. The $\ensuremath{\Delta}C({T}_{s})$ values are in fair agreement with those calculated via Ehrenfest's equation for second-order phase transitions using Abrikosov's theoretical value of ${(\frac{\ensuremath{\partial}I}{\ensuremath{\partial}H})}_{T}$ at ${T}_{s}$ for $\ensuremath{\kappa}=7$, where $I\ensuremath{\equiv}$ magnetization. For $(\frac{{T}_{s}}{T})\ensuremath{\ge}1.8$, $\frac{{C}_{\mathrm{es}}}{\ensuremath{\gamma}{T}_{s}}=a \mathrm{exp}(\ensuremath{-}\frac{b{T}_{s}}{T})$ with $a=8.95,6.24,5.01,4.7;b=1.48,1.28,1.17,1.1$; for $H=0,1,2,4$ kG, respectively, where ${C}_{\mathrm{es}}$ is the electronic contribution to the specific heat. The exponential temperature dependence of ${C}_{\mathrm{es}}$ down to 1.4\ifmmode^\circ\else\textdegree\fi{}K suggests an essentially everywhere finite, field-dependent, high-field energy gap in accord with Abrikosov's vortex model.