Superconductivity in Ce$3$PdIn${11}$ single crystals – intrinsic phenomenon or parasitic effect?

Cerium-based intermetallics belong to the most investigated compounds in solid state physics. It is mainly due to intriguing electronic properties they exhibit. Among a large variety of phenomena observed in those compounds one may enlist complex magnetic ordering, non-Fermi liquid features, heavy-fermion behavior, spin and valence fluctuations, superconductivity, etc.
In recent years, much attention has been paid to cerium indides with general formula Ce$_{\rm m}$T$_{\rm n}$In$_{\rm 3m+2n}$, where T = ${\it d}$-electron transition element. A member of this family, Ce$_3$PdIn$_{11}$, was reported as an antiferromagnet with two consecutive magnetic transitions at ${\it T}_{\rm N1}$ = 1.67 K and ${\it T}_{\rm N2}$ = 1.53 K, which becomes superconducting below ${\it T}_{\rm c}$ = 0.42 K [1, 2]. The coexistence of superconductivity and magnetism in this compound makes it an attractive platform for investigation of mutual relationship between these two phenomena. Unfortunately, thus far, majority of essential experiments have not been performed, due to the lack of sufficient amount of good quality samples.
Up to now, the only applied method of obtaining Ce$_3$PdIn$_{11}$ single crystals is the growth from indium flux. This technique usually leads to forming crystals of small dimensions, not exceeding 1mm$^3$. Moreover, it often yields crystals with macroscopic inhomogeneities [3]. This drawback may be caused by several factors: i) from one initial stoichiometry it is possible to grow several different phases (CeIn$_3$, Ce$_2$PdIn$_8$, Ce$_3$PdIn$_{11}$) depending on the temperature range used during the synthesis; ii) the growth of the ternary phases takes place only in a very limited temperature interval (different for each compound); iii) due to the similar crystal structure of all the Ce$_{\rm m}$T$_{\rm n}$In$_{\rm 3m+2n}$ compounds and almost perfect match of the lattice parameter ${\it a}$ (= 4.6894 Å [4], 4.6931 Å [5] and 4.6846 Å [6] for CeIn$_3$, Ce$_2$PdIn$_8$ and Ce$_3$PdIn$_{11}$, respectively), previously grown crystals of one compound may constitute a seed and substrate for the growth of another of these phases.
The complications in the growth of Ce$_3$PdIn$_{11}$ crystals led us to ask a fundamental question: Is the superconductivity observed in this compound an intrinsic property or rather a result of the presence of an impurity phase? To address this issue, we performed extensive studies of heat capacity and electrical resistivity of several Ce$_3$PdIn$_{11}$ crystals grown in different batches with varying growth recipes. The results were confronted with powder x-ray diffraction and energy-dispersive spectroscopy data collected for the measured specimens. In this contribution, we present the results of our investigations and discuss the most plausible scenarios for the intrinsic physical behavior in single-crystalline Ce$_3$PdIn$_{11}$.

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