The family (R, T, and X stand for rare-earth elements, transition metals, and s–p metals, respectively) provides a vast platform for studying superconductivity, heavy fermion (HF) behavior, Kondo effect, magnetic orders, and many other novel phenomena.^[1–3] The interplay between magnetic phase transitions and superconductivity in this family catches the interest of researchers. Compared to the superconductivity transition temperatures reported in the cuprate superconductors or the iron-based superconductors,^{[4, 5]} in this family is relatively low, with the highest of 6.3 K reported in the multiband superconductor Lu Fe Si .^[6,7] Remarkably, pressure induced heavy fermion superconductivity was found in the antiferromagnet Ce Ni Ge ,^[8] raising more doubt about the relation between superconductivity and magnetism in this system. The discovery of superconductivity in antiferromagnetic (AFM) compounds will definitely fulfill the magnetic-superconductivity phase diagram of this 2–3–5 family as well as the heavy fermion superconductors.^[9] Recently, Pr Pt Ge was reported to have K,^[6] which is the highest in the 2–3–5 family. At even lower temperatures, neutron scattering measurements found two AFM transitions, which are completely decoupled from the superconductivity in this compound.^[10] In addition, Kondo screening of the magnetic Pr ions was also found, indicating the possibility of heavy fermion superconductivity (HFSC) for this compound, however the electric specific heat coefficient was not reported.^[6]

Pr-based HFSCs are very rare, as the majority of heavy fermion systems are U- or Ce-based compounds.^[11,12] Therefore, the observation of superconductivity in Pr Pt Ge is particularly interesting as a potential new Pr-based HF superconductor. It is speculated that HFSC is unlikely to occur in the Pr-based compounds, as the singlet ground state does not support the degeneracy to form an HF ground state.^[11] The discovery of HFSC in PrOs Sb , with electronic specific heat coefficient , is thus very intriguing.^[13] It was proposed that has a huge hybridization among its first excited triplet crystal-electric-field (CEF) split state, the and conduction electrons, leading to the emergence of the HF behavior.^[11,14]

The reported of Pr Pt Ge is ∼8 K, which is very close to that of the recently discovered Pt–Ge skutterudite .^[15–19] Also, a low superconductivity volume fraction was obtained from the meissner effect measurements.^[6] These features raise the possibility that superconductivity occurs from the impurity filled-skutterudite phase and the doubt about whether the reported superconductivity in Pr Pt Ge is intrinsic or not.

Therefore, we systematically characterize the basic properties of ( , Ce, Pr) of the 2–3–5 family by resistivity, magnetic susceptibility, and heat capacity measurements to determine (i) whether Pr Pt Ge is a heavy fermion compound, and (ii) the source of the superconductivity. Zero-resistance is found in ( , Pr) below the reported of K.^[6] Pr Pt Ge displays quite a low superconductivity volume fraction (less than 2 %) from the magnetic susceptibility measurements. From the specific heat measurements, we find no jump near . Therefore, our results suggest that the superconductivity in Pr Pt Ge is not bulk. Moreover, the relatively small values of provide evidence that ( , Ce, Pr) are not heavy fermion compounds.

Single crystalline samples of ( ) were synthesized using the Pt–Ge self-flux method as described in Ref. [6]. The starting materials La/Ce (99.9%), Pr (99.5%) rods (Alfa Aesar), Pt shots (99.9%), and Ge pieces (Alfa Aesar 99.9999+%) were mixed with the stoichiometric ratio of 1:4:20. They were put in alumina crucibles before being sealed in a quartz tube. They were heated to 1130 °C and dwell at this temperature for 40 h before cooling down to 850 °C with a rate of 3 °C/h. X-ray diffraction (XRD) measurements were performed by using an x-ray diffractometer (D8 Advance, Bruker) with Cu- radiation. Rietveld refinements were conducted on powder XRD patterns using the softwares GSAS^[20] and EXPGUI.^[21] The dc magnetization was measured by a Quantum Design superconducting quantum interference device. Four wire electrical resistivity measurements (2 K to 300 K) and specific heat measurements (2 K to 50 K) were performed in a Quantum Design physical properties measurement system Evercool II, with the specific heat measurements employing a standard thermal relaxation technique.

For all of the samples, the x-ray measurements reveal that they form in the U Co Si -type orthorhombic structure with space group Ibam, which can be viewed as a combination of the and the structures.^[22] The x-ray data are displayed in Fig. 1. The lattice parameters are summarized in Table 1, with values close to the results in Refs. [6] and [23]. The lattice parameters of La Pt Ge , Ce Pt Ge , and Pr Pt Ge decrease as the atomic radius of the constituent rare-earth elements decreases. The single crystal XRD pattern of Pr Pt Ge with the incident beam oriented along the b-axis is displayed in Fig. 1(d).

Fig. 1.

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Fig. 1. (a)–(c) Powder XRD patterns of pulverized single crystals La Pt Ge , Ce Pt Ge , and Pr Pt Ge , respectively. Tick marks below each pattern indicate the expected Bragg peaks for the refined U Co Si -type orthorhombic crystal structure. (d) The single crystal XRD pattern of Pr Pt Ge along the b-axis. The dotted circles shown in panels (a), (b), and (d) represent the direction of the b-axis. (e) The crystal structure of ( ).

Table 1.

Table 1.

Table 1. Lattice parameters and unit cell volumes of (R = La, Ce, Pr). .   a/Å b/Å c/Å V/Å La Pt Ge 10.121(3) 11.998(1) 6.228(4) 756.28(1) Ce Pt Ge 10.102(3) 11.888(4) 6.203(2) 744.93(1) Pr Pt Ge 10.098(3) 11.852(2) 6.192(4) 741.07(1)

Table 1. Lattice parameters and unit cell volumes of (R = La, Ce, Pr). .

Figure 2 shows the temperature dependence of resistivity measured in zero magnetic field for Pr Pt Ge and Ce Pt Ge single crystals along the c-axis. For the electrical resistivity measurements, we define as the temperature at which the resistance drops to zero and find K for Pr Pt Ge , which is consistent with the previous work^[6] and is almost the same as the of .^[15] gives a residual resistivity ratio (300 K)/ (8 K), , slightly larger than that in the previous work.^[6] Zero resistance is also found in La Pt Ge at 8.2 K (not shown here) while Ce Pt Ge does not transit into the superconducting state. The resistivity data are displayed in Fig. 2(b), where Ce Pt Ge shows a local minimum around K followed by the upturn to the local maximum resistivity at K. A sharp drop occurs at K, consistent with the Néel temperature determined from the magnetization measurements (will be discussed later). Such behaviors are similar to those observed in another Ce-based 2–3–5 compound, .^[24]

Fig. 2.

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Fig. 2. (a) and (b) Temperature dependence of resistivity for Pr Pt Ge and Ce Pt Ge measured along the c-axis without an applied magnetic field, respectively. The inset in panel (a) highlights the low temperature resistivity, where the transition into the superconducting state is observed at K for Pr Pt Ge . The inset of panel (b) shows the low temperature resistivity of Ce Pt Ge , where an abrupt drop is observed at K, which is consistent with the formation of the antiferromagnetic phase.

Full diamagnetization is one of the signature properties of bulk superconductivity. Therefore magnetization measurements at low fields were performed to determine the superconducting volume fraction. Figure 3 shows the zero-field-cooled (ZFC) and field-cooled (FC) dc-susceptibility of La Pt Ge and Pr Pt Ge with the magnetic field of mT applied along the c-axis. Both La Pt Ge and Pr Pt Ge show clear diamagnetic signals at K and 7.6 K, respectively, consistent with the results in Ref. [6]. However, when converted to the superconducting volume fractions, we find that they are less than 2% for both La Pt Ge and Pr Pt Ge , indicating the absence of bulk superconductivity.

Fig. 3.

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	Fig. 3. Meissner effect in (a) La Pt Ge and (b) Pr Pt Ge , for which in terms of was measured in an applied field of H = 1 mT parallel to the c-axis. FC and ZFC stand for field-cooled and zero-field-cooled measurements, respectively. The superconductivity volume fractions in both compounds are less than 2% at 2 K.

Figure 4 shows the magnetization measurement results for Pr Pt Ge and Ce Pt Ge . Figure 4(a) is the magnetic susceptibility measured in applied magnetic fields of H = 10 mT along the ab-plane and c-axis for Pr Pt Ge . The magnetization with the magnetic field applied along the c-axis is weaker than that parallel to the ab-plane, in agreement with the anisotropy observed from neutron scattering.^[10] For the plane, two distinct downward kinks are observed at K and K, consistent with the results reported in Ref. [6].

Fig. 4.

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Fig. 4. (a) and (b) Magnetization susceptibility of Pr Pt Ge and Ce Pt Ge single crystals measured in applied magnetic fields along the ab-plane and c-axis in the low temperature region (2 K K), respectively. (c) Inverse magnetic susceptibility of Ce Pt Ge and Pr Pt Ge in a temperature range of 2 K K. Curie–Weiss fits were performed at temperatures above 150 K. (d) and (e) Field dependence of isothermal magnetization at T = 2 K and 5 K with an applied field along the c-axis for Ce Pt Ge and Pr Pt Ge single crystals, respectively.

As displayed in Fig. 4(b), Ce Pt Ge shows a clear AFM transition at K. In the normal state, the magnetization in the ab-plane is stronger than that along the c-axis. The magnetic moment orientation in the ordered state is thus likely to be lying in the ab-plane, which is different from its related compound that is oriented along the bc-plane, corresponding to the easy direction produced by the CEF.^[23]

Magnetization along the c-axis for both Pr Pt Ge and Ce Pt Ge follows the Curie–Weiss law above 150 K (Fig. 4(c)), consistent with the results in Ref. [6]. Fitting to the Curie–Weiss law, , gives the Curie–Weiss temperature K for Pr Pt Ge . The derived Curie constant gives an effective magnetic moment /Pr, smaller than the Hund rule value of 3.58 of ion. Similarly, we derive K and /Ce for Ce Pt Ge , close to Hund’s rule value of 2.54 of ion. An anomaly around 20 K in magnetization for Pr Pt Ge in the field of T is observed. The isothermal magnetization measurements of Pr Pt Ge with the applied magnetic fields along the c-axis are displayed in Fig. 4(e). At 2 K, well within the AFM state, increasing the field results in a non-linear increase in the magnetization up to 2.4 T where the magnetization clearly changes to a paramagnetic linear behavior. At 5 K, Ce Pt Ge exhibits a paramagnetic linear field dependence for all applied fields. Ce Pt Ge also exhibits a similar behavior, as shown in Fig. 4(d) with the critical field at 2 T.

Figures 5(a)–5(c) display the specific heat data for La Pt Ge , Pr Pt Ge , and Ce Pt Ge . The normal state temperature dependence of the heat capacity is well described by the expression , with the first and the second terms corresponding to the electronic and phononic contributions, respectively. The derived values of suggest that both Pr Pt Ge and Ce Pt Ge are not heavy fermion compounds. The Debye temperature is derived by the relation^[24]

Fig. 5.

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	Fig. 5. (a)–(c) Temperature dependence of specific heat of La Pt Ge , Ce Pt Ge , and Pr Pt Ge , respectively. (d) Magnetic contribution of specific heat of single crystals Pr Pt Ge and Ce Pt Ge .

Table 2.

Table 2.

Table 2. Parameters derived from specific heat measurements of (R = La, Ce, Pr) in their normal state. Fit range: 10–25 K for La Pt Ge , 15–20 K for Ce Pt Ge , and 10–20 K for Pr Pt Ge . . /mJ mol K /mJ mol K /K La Pt Ge 6.6 2.45 199.4 Ce Pt Ge 159 2.33 202.8 Pr Pt Ge 129 2.26 204.8

Table 2. Parameters derived from specific heat measurements of (R = La, Ce, Pr) in their normal state. Fit range: 10–25 K for La Pt Ge , 15–20 K for Ce Pt Ge , and 10–20 K for Pr Pt Ge . .

The magnetic contribution to specific heat of Pr Pt Ge and Ce Pt Ge is obtained by subtracting of La Pt Ge , the same treatment that has been applied for .^[25] As shown in Fig. 5(a), there are clear jumps in the specific heat at temperatures corresponding to the AFM transitions in Pr Pt Ge and Ce Pt Ge . The low-temperature regime of in the AFM ordered state of Pr Pt Ge (2–3.2 K) can be well described by . The fit gives mJ mol K and mJ mol K . The latter term represents the contribution of AFM magnons. The positive value of meV for Pr Pt Ge represents a gap in the magnon spectrum in the AFM state. The opening of such a gap in the magnon spectrum could lead to anisotropic magnetic behaviors.^[25] The presence of such anisotropy is confirmed in our magnetic susceptibility measurements (Fig. 4). A similar behavior is also observed in , indicating that they share similar AFM energy structures. The energy gap of Pr Pt Ge , however, is smaller than that of .^[25] Such a gap is not present in Ce Pt Ge as the fit does not work well.

One of the most widely accepted methods to determine bulk superconductivity is a jump in the specific heat. While previous literature shows this jump for La Pt Ge , there is no suitable data for Pr Pt Ge .^[6] Therefore, we attempted to isolate the magnetic contribution of specific heat for Pr Pt Ge by subtracting the phonon contribution . However, this analysis results in no peak, and is not as suitable as the specific heat shows a broad upward curvature due to the AFM. Therefore, we also used La Pt Ge as a non-magnetic reference compound and subtracted its specific heat from Pr Pt Ge . Even in this case, there is no peak observed near . From the detailed analysis of the specific heat, our results suggest that Pr Pt Ge might have filamentary or impurity-phase-induced superconductivity, similar to some compounds with strain-stabilized non bulk-superconductivity, such as Sn-flux synthesized single crystalline .^[26]

It is worth mentioning that the synthesis methods can affect whether bulk or non-bulk superconductivity is in certain compounds. For example, the stoiciometric iron pnictide synthesized by the furnace-cooled method does not show any diamagnetic signal while the quenched sample shows pronounced bulk superconductivity.^[27] It is thus possible that (R = La, Ce, Pr) might show bulk superconductivity with other different synthesis methods. However, it is beyond the scope of this manuscript to find new methods of making single crystalline (R = La, Ce, Pr).

Another possible origin of the observed superconductivity in La Pt Ge and Pr Pt Ge might be the superconducting 1–4–12 filled-skutterudite impurity phases. The self-flux sample synthesis reported used the atomic ratio of 1:4:20, which is the same ratio used to synthesize the filled skutterudite family of materials.^[16] and both show bulk superconductivity around 8 K,^[15] which is the same as the reported ’s in La Pt Ge and Pr Pt Ge . However, the previous work reported a tiny heat capacity jump without entropy conservation below in La Pt Ge .^[6] Moreover, La Pt Ge /Pr Pt Ge probably have similar upper critical field values as those of . The is 1.60 T for and 2.06 T for .^[15] Although there is no data reported for La Pt Ge , superconductivity can be suppressed by an applied field of 2 T.^[6] Also, the extrapolated of Pr Pt Ge at 0 K is close to that of .^[10] We therefore suggest that the origin of the observed superconductivity in Pr Pt Ge is not intrinsic according to the heat capacity measurements.

In summary, single crystalline ternary germanide compounds (R = La, Ce, Pr) were synthesized using the self-flux method. For Pr Pt Ge , non-bulk superconductivity is suggested based upon the low superconductivity volume fractions and the absence of obvious superconducting specific heat jumps around as determined from the resistivity measurements. Antiferromagnetic (AFM) transitions are observed at K and K in Pr Pt Ge , while Ce Pt Ge possess only one AFM transition at K.