Thermal-expansion studies of superconducting U1-xThxBe13 (0 ≤ x ≤ 0.052): Implication for the intepretation of the T-x phase diagram

We report on high-resolution measurements of the coefficient of thermal expansion \ensuremath{\alpha} of the heavy-fermion superconductor ${\mathrm{U}}_{1\ensuremath{-}x}{\mathrm{Th}}_{x}{\mathrm{Be}}_{13}$ for temperatures $0.05\mathrm{K}<~T<~6\mathrm{K}$ and magnetic fields $B<~8\mathrm{T}.$ Particular attention is paid to the properties of the low-temperature normal state and their evolution as a function of thorium concentration. By exploring a wide concentration range, $0<~x<~0.052,$ that encompasses the region ${x}_{c1}=0.019{T}_{c2},$ our study discloses features in the T-x plane that have been overseen by all other techniques applied to this system so far: (i) The substitution of uranium by thorium in ${\mathrm{UBe}}_{13}$ induces an anomaly that manifests itself in a negative $\ensuremath{\alpha}(T)$ contribution to the low-temperature normal-state expansivity. Its distinct field dependence signals a magnetic origin. Analyzing the relative lengths changes associated with this anomaly and that of the phase transition at ${T}_{c2}$ suggests a common (presumably magnetic) nature of both features. (ii) The linear concentration dependence of the second low-energy scale ${T}_{\mathrm{max}},$ which gives rise to a pronounced maximum in $\ensuremath{\alpha}(T)$ of ${\mathrm{UBe}}_{13}$ at 2 K (at $B=0)$ could be followed up---by applying a magnetic field---to concentrations $x>0.03.$ Most remarkably, ${T}_{\mathrm{max}}(x)$ vanishes at $x\ensuremath{\approx}0.043,$ i.e., almost exactly at ${x}_{c2}.$ (iii) Upon increasing x to above 0.03 the normal- to superconducting-state transition at ${T}_{c1}$ progressively loses its signatures in \ensuremath{\alpha}. Our measurements, together with recent specific-heat results by Schreiner et al. [Schreiner et al., Europhys. Lett. 48, 568 (1999)] indicate that superconductivity becomes gapless for $\stackrel{\ensuremath{\rightarrow}}{x}{x}_{c2}.$ Hence, the phase transition seen in specific heat as well as thermal-expansion measurements for samples with $x>{x}_{c2}$ has to be attributed to the ${T}_{c2}$ transition. Concomitant investigations of the ac susceptibility indicate that the normal- to superconducting-state transition for $x>{x}_{c2}$ now coincides with ${T}_{c2}.$ As for the implications of our observations for the interpretation of the various low-temperature anomalies, we discuss two possible scenarios both of which imply an intimate interrelation of superconductivity with the symmetry broken state that forms below ${T}_{c2}.$