Transport and thermodynamic properties of the novel compound Nd₅CuSn₃

Rare-earth-based intermetallic compounds exhibit various magnetic and electrical properties that arise from 4f electrons, such as magnetic ordering, higher-rank multipole ordering, and unconventional superconductivity.^1–3 Ternary intermetallic compounds R₅TX₃ (R=Ce, Yb, T=Cu, Ag, X=Sn, Pb) have been observed to crystallize in the hexagonal Hf₅CuSn₃-type structure.⁴ In this structure, rare-earth ions occupy two non-equivalent crystallographic sites: R1 (4d) and R2 (6g). The interatomic distance between R1 and R1 is shorter than that between R2 and R2 and that between R1 and R2. Ce₅CuSn₃ exhibits an antiferromagnetic transition at 3.5 K and heavy-fermion behavior with the Sommerfeld coefficient γ of 270 mJ/K² mol Ce.⁵ For the La counterpart, the data for specific heat are explained as a combination of the Einstein and the Debye models.⁶ Isostructural heavy-fermion antiferromagnets Ce₅CuX₃ (X=Pb, Bi) have also been reported.⁷ Ce₅AgSn₃ orders ferromagnetically below 5 K.⁸ With the exception of Ce-based compounds, magnetic properties of Dy₅CuPb₃, Gd₅NiPb₃, and Nd₅NiPb₃ have also been studied.^9–11 Dy₅CuPb₃ undergoes the two successive transitions: ferrimagnetic order at 45 K and antiferromagnetic order at 6.5 K. Gd₅NiPb₃ is ferrimagnetic below 68 K. Nd₅NiPb₃ shows antiferromagnetic order at 42 K and undergoes a weak-ferromagnetic spin canting transition at 8 K. These complex magnetic phase transitions are related to the two non-equivalent rare-earth ion sites in the crystal structure of each compound.

To the best of our knowledge, physical properties of R₅CuSn₃ compounds have not been studied, except for Ce₅CuSn₃. In this study, we have carried out the measurements of the electrical resistance and specific heat of a polycrystalline sample of hexagonal Nd₅CuSn₃. The results show that the compound underwent a phase transition at 56.3 K and suggest that this transition is of ferromagnetic or ferrimagnetic ordering.

A polycrystalline sample of Nd₅CuSn₃ was prepared by arc-melting stoichiometric amounts of the constituent elements (purity exceeding 99.9%) under an argon atmosphere. The sample was remelted several times to ensure homogeneity and was then annealed in an evacuated quartz ampule at 600 °C for 1 week. It is worth noting that the Nd₅CuSn₃ compound easily oxidizes in air. Powder X-ray diffraction (XRD) patterns of the sample were carried out using a PANalytical X’Pert PRO with CuKα radiation. The standard four-probe method was used to measure the electrical resistance from 2 K to 300 K using a Physical Property Measurement System (PPMS, Quantum Design). Au wires were used for voltage and current leads and were attached using silver paste. Specific heat was measured using the PPMS in a temperature range of 2 ≤ T ≤ 200 K under an applied magnetic field of up to 7 T.

Figure 1 presents the XRD patterns of Nd₅CuSn₃. The diffraction peaks indicate that the hexagonal Hf₅CuSn₃-type structure is the primary phase. The impurity phase may be associated with Cu₂O. The estimated lattice constants are a=9.348 Å and c=6.684 Å, which are smaller than those of Ce₅CuSn₃. These values agree with the trend expected from the lanthanide contraction.

Figure 2 shows the temperature dependence of the electrical resistance R, normalized to the value at 300 K for Nd₅CuSn₃. Owing to micro-cracks in this sample, the geometric dimensions could not be determined exactly. This cracking phenomenon has been observed in other R₅TX₃ samples, such as Ce₅CuSn₃,⁵ Ce₅CuPb₃,⁶ and Dy₅CuPb₃.⁹ R depended only weakly on temperature above 100 K and featured a shoulder at around 60 K, as shown in the inset of Fig. 2. This shoulder indicates a phase transition. A similar maximum in the R(T) curve has been reported for RNi₅¹² and Dy₅CuPb₃.⁹ This cusp-like anomaly may be attributed to the scattering caused by critical fluctuations above the phase-transition temperature. Below T_M, R(T) decreased with decreasing temperature due to the reduction in spin-disorder scattering in the magnetically ordered state.

The data of specific heat C for Nd₅CuSn₃ in zero magnetic field are plotted against temperature in Fig. 3. At 200 K, C reached approximately 225 J/K mol, which is close to the Dulong-Petit value of 221 J/K mol. A clear jump in C(T) appeared at around 55 K as observed from R(T) measurement, indicating the bulk nature of the phase transition. The magnetic transition temperature T_M is 56.3 K, as determined from the midpoint of the jump in the C/T curve, which is shown in the inset of Fig. 3. All data for C(T) in magnetic fields up to 7 T are plotted in Fig. 4. The temperatures at which C showed a peak were shifted to higher temperatures and the peak broadened with increasing magnetic field. This result suggests that this transition is ferromagnetic or ferrimagnetic ordering at T_M. In case of a ferromagnetic metal with a non-cubic crystal structure, C below T_M is expected to obey the following equation;

where the first term represents the electronic contribution, the second represents a low temperature approximation of the lattice contribution, and the third term represents the conventional form of a magnon contribution (α, β, and γ are constants and Δ represents the magnon gap).¹⁵ The least-squares fit of the formula to the experimental results below 8 K (shown in the inset of Fig. 5) yields the following parameters: the Sommerfeld coefficient γ ∼250 mJ/K² mol (50 mJ/K² mol Nd), β ∼3 mJ/K⁴ mol, α ∼0.75 J/K^2.5 mol, and Δ ∼9 K. The Sommerfeld coefficient for Nd₅CuSn₃ is 50 mJ/K² mol Nd, which is 10 times larger than that for La₅CuSn₃ of 4.5 mJ/K² mol La ⁵ and is 5 times larger than those of other Nd-based compounds: 5 mJ/K² mol Nd for Nd₂Al¹³ and 9.5 mJ/K² mol for NdAl₂.¹⁴ The Debye temperature of the sample is estimated to be 180 K, assuming nine Debye oscillators. The magnetic specific heat C_m is estimated by subtracting the Debye specific heat C_D from the measured data. The equation for C_D is represented as

where n is the number of the Debye oscillators, N_A is the Avogadro’s number, and k_B is the Boltzmann constant. Here we use Θ_D=180 K obtained by the fitting of Eq. (1). The calculated values for C_m/T and S_m are plotted in Fig. 5. S_m was calculated by integrating C_m/T with respect to temperature. S_m reaches 5R ln 10 around 250 K.

The analysis of the magnetic specific heat indicates that the electronic contribution is very small (γ ∼0), whereas a large value of γ =50 mJ/K² mol Nd was obtained by the fitting the data at low temperatures. A large value of γ was also observed in the isostructural compound Nd₅NiPb₃¹¹ and was attributed to spin fluctuations arising from the two non-equivalent Nd sites. For Nd₅CuSn₃, a peak in C_m/T at around 20 K, as shown in Fig. 5, may be attributed to the complex magnetic interaction originated from the two non-equivalent Nd sites. The large γ may also originate in the hybridization between f-electrons and conduction electrons. To estimate the value of A/γ² (Kadowaki-Woods relationship),¹⁶ where A is the coefficient of resistivity ρ expressed as ρ∝AT², a large-grain specimen of Nd₅CuSn₃ will be needed to determine the absolute resistivity value. To study the magnetic ordering of this compound in more detail, magnetization measurements are now in progress.

We have prepared the novel Nd₅CuSn₃ compound which crystallizes in the hexagonal structure. Electrical resistance and specific heat measurements revealed that Nd₅CuSn₃ exhibited a phase transition at T_M =56.3 K. With increasing magnetic field, the peak in C(T) broadened and appeared at higher temperatures. These results suggest that the transition at T_M indicates the formation of ferromagnetic or ferrimagnetic ordering in the sample.

Electrical resistance and specific heat measurements were carried out at the Faculty of Science, Ehime University, Japan. KTM was financially supported by a tenure track program of Ehime University, Japan.