Magnetic and physical properties of new hexagonal compounds PrPt$_4X$ ($X$ = Ag, Au)

TL;DR

This study reports the synthesis and characterization of two new hexagonal compounds PrPt4X (X=Ag, Au), revealing distinct low-temperature behaviors including possible multipolar ordering and non-Fermi liquid characteristics near a quantum critical point.

Contribution

First synthesis and detailed physical property analysis of PrPt4Ag and PrPt4Au, demonstrating structural preservation and novel low-temperature electronic behaviors.

Findings

PrPt4Ag shows an anomaly at 7.6 K suggesting multipolar order.

PrPt4Au exhibits non-Fermi liquid behavior near a quantum critical point.

Both compounds have significantly enhanced quasiparticle masses.

Abstract

We have synthesized PrPt$_4$Ag and PrPt$_4$Au compounds for the first time and report their crystal structure, as well as magnetic and physical properties in the temperature range of 1.9~K to 300~K. Both compounds are derived from the substitution of Pt with Ag and Au, respectively in the parent compound PrPt$_5$ which crystallizes in the hexagonal CaCu$_5$-type structure. Here we observed the preservation of the hexagonal CaCu$_5$-type structure under such substitutions, which is in contrast to the observations in PrCu$_4$Ag and PrCu$_4$Au adopting the cubic MgCu$_4$Sn-type structure upon substitution on parent hexagonal PrCu$_5$. The temperature dependences of specific heat $C_p(T)$, and electrical resistivity $\rho(T)$ of PrPt$_4$Ag show an anomaly at 7.6~K. This is absent in the magnetic susceptibility $\chi(T)$, thus suggesting a possible multipolar ordering of the Pr$^{3+}$ moment. PrPt$_4$Au on the other hand does not show any anomaly but an upturn in $C_p(T)/T$ below about 10~K and attains 1.23~J/(mol K$^2$) at 1.9~K. In addition, $\rho(T)$ $\sim T$ for nearly a decade in temperature. These observations for PrPt$_4$Au are the hallmark of a non-Fermi liquid (nFL) behavior and is characteristic of a system near a quantum critical point. The analyses of the low-temperature $C_p(T)$ for PrPt$_4$Ag and PrPt$_4$Au give values of the Sommerfeld coefficient, $\gamma = 728.5~$mJ/(mol K$^2$) and 509.1~mJ/(mol K$^2$), respectively, indicating a significant enhancement of the quasiparticle mass in the two compounds.

Tables

Table 1. Table 1: Lattice parameters of PrPt 4 Ag and PrPt 4 Au obtained from the Rietveld refinements of their XRD patterns.

Compound	$a$ (Å)	$c$ (Å)	$V$ (Å3)	$R_p$ (%)	$R_{wp}$(%)	${\chi }^2$
PrPt4Ag	5.344(2)	4.399(2)	108.8(9)	9.597	12.25	4.596
PrPt4Au	5.343(3)	4.378(5)	108.3(8)	8.957	11.89	4.875

Table 2. Table 2: A collection of estimated characteristic HF parameters of PrPt 4 Ag and PrPt 4 Ag.

Compound	$\gamma$ (mJ/(molPr K2))	$A$ ($\mu \Omega$cm/K2)	$A/{\gamma }^2$ ( $\times$ 10-5$\mu \Omega$cm(molPr K/mJ)2)	$R_w$
PrPt4Ag	728.50	0.010	0.00188	1.38
PrPt4Au	509.10	0.117	0.0449	1.62

Full text

1 Introduction

PrPt5 is a Van-Vleck paramagnet that has been studied mostly for nuclear cooling by adiabatic demagnetization [1]. This technique profits from the high nuclear spin ($I$ = 5/2) of the only known stable 141Pr isotope. It crystallizes in the hexagonal CaCu5-type structure with space group $P$6/$mmm$ (No. 191) [2]. It has been observed that the lack of magnetic ordering in PrPt5 is associated with its weak exchange interaction [3]. In addition, magnetization studies have revealed a nuclear spontaneous ferromagnetic Weiss temperature, $\theta_{p}$ = 2 mK, which is attributed to nuclear hyperfine enhancement in the system [4]. In a substitution study by Malik et al. [5], the $R$Pt4In ($R$ = La-Tm) compounds, which represent a doping of 20% on the Pt site, were reported to adopt the cubic MgCu4Sn-type structure with the exception of TmPt4In which forms in the Cu3Au-type structure. Also, ErPt4In and HoPt4In were observed to possess a mixture of MgCu4Sn and Cu3Au phases as evidenced from the X-ray diffraction patterns. PrPt4In was reported to remain paramagnetic down to 4.2 K [5]. Here we report the synthesis, as well as the magnetic and physical properties of the new compounds PrPt4Ag and PrPt4Au. Interestingly, it was found that both compounds crystallize in the same hexagonal CaCu5 parent structure. This is in contrast with the observations in PrCu4Ag and PrCu4Au [6, 7] which adopt the cubic MgCu4Sn-type structure similar to those of $R$Pt4In compounds reported by Malik et al. [5].

2 Experimental methods

Polycrystalline samples of PrPt4Ag and PrPt4Au were prepared by arc melting stoichiometric amounts of high-purity elements (wt.% $\geq$ 99.9) on a water-cooled Cu plate under a purified static argon atmosphere in an Edmund Buehler arc furnace. The weight losses for both compounds were $\sim$ 0.09%. The arc-melted pellets were then wrapped in Ta foil, placed in an evacuated quartz tube and annealed at 800∘C for 14 days so as to improve the quality of the samples. Room temperature powder X-ray diffraction (XRD) patterns were recorded on pulverized samples using a Rigaku diffractometer employing Cu-K$\alpha$ radiation. The XRD patterns with the Rietveld refinements [8] employing the FullProf suite of programs [9] are shown in Fig. 1. The lattice parameters obtained from the Rietveld refinements are presented in Table 1. For both compounds, the XRD results confirm phase formation of the desired compounds. For the case of PrPt4Au, a spurious peak, barely resolved above the background noise was detected at 2$\Theta$ = 48*∘*. It was verified that this peak does not have its origin in any of the elements Pr, Pt or Au thus the origin of this peak remains unknown.

Magnetic properties were measured using the Magnetic Property Measurement System (Quantum Design Inc., San Diego) between 1.8 K and 300 K with an external magnetic field up to 7 T. The four-probe DC electrical resistivity, specific heat and thermal transport between 1.9 K and 300 K were measured using the Physical Property Measurement System also from Quantum Design.

3 Magnetic properties

The temperature dependences of magnetic susceptibility $\chi(T)$ of both compounds in an external field of 0.1 T are shown in Fig. 2 (a) and (b). From the plots, $\chi(T)$ of both compounds are qualitatively similar and show no visible anomaly down to 1.9 K. For temperatures above 100 K, $\chi(T)$ for both compounds follow a Curie-Weiss behavior based on the expression: $\chi(T)=N_{A}\mu_{\mathrm{eff}}^{2}/(3k_{B}(T-\theta_{p}))$, where $\mu_{\mathrm{eff}}$ is the effective magnetic moment, $\theta_{p}$ is the Weiss temperature, NA is the Avogadro number and kB is the Boltzmann constant. From the least-square fits shown as white lines in Fig. 2 (a) and (b), values of $\mu_{\mathrm{eff}}=3.30\mu_{B}$/Pr, $\theta_{P}=95.10~{}$K and $\mu_{\mathrm{eff}}=3.15~{}\mu_{B}$/Pr, $\theta_{P}=99.16~{}$K for PrPt4Ag and PrPt4Au, respectively are obtained. These values of $\mu_{\mathrm{eff}}$ are slightly reduced in comparison to the value of 3.58 $\mu_{B}$/Pr calculated for a free Pr3+ ion. Such reduction in $\mu_{\mathrm{eff}}$ can be attributed to the crystalline electric field (CEF) effect on the Pr3+ moment. The isothermal magnetization for both compounds measured at temperatures of 1.8 K and 10 K are shown in the insets to Fig. 2 (a) and (b). The magnetization trend shows a little curvature at 10 K which becomes more pronounced at 1.8 K for both compounds. PrPt4Ag and PrPt4Au attain magnetization of $\approx$ 1.8 $\mu_{B}$/Pr at 7 T, which is about 50% reduced compared to the value of 3.2 $\mu_{B}$/Pr expected for a free Pr3+ ion. Assuming that at a temperature of 1.8 K no higher-lying levels of the $J$ = 4 multiplet of Pr are occupied, we attribute this deficiency in the extracted magnetization to the effects of magneto-crystalline anisotropy in both compounds.

4 Specific heat

The temperature dependence of the specific heat $C_{p}(T)$ between 1.9 K and 300 K for PrPt4Ag and PrPt4Au are shown in Fig. 3 (a) and (b). Values of $\approx$ 150 J/(mol K) are observed at room temperature for both compounds, which correspond to the Dulong-Petit value. In inset (i) of Fig. 3 (a), the low-$T$ plot of $C_{p}/T$ against $T$ for PrPt4Ag is shown. At 7.6 K an anomaly with a broad feature is observed. The electrical resistivity results to be presented in Section 5 also reveal an anomaly around the same temperature. No such an anomaly is however observed in $\chi(T)$ presented in the previous section, thus suggesting a possible multipolar ordering of the Pr3+ moment in PrPt4Ag. This is supported by the Van-Vleck paramagnetism observed in $\chi(T)$ indicating that spins or dipolar order do not play a detectable role in the anomaly. In the absence of a long-range magnetic order in Pr systems, the 4$f$-electrons orbitals are the only effective degrees of freedom and multipolar ordering of the Pr3+ moment can be realized [10, 11]. Also shown is the plot of the calculated entropy. At $T_{Q}$ only an amount of 0.3R$\ln(6)$ is released which is only about one third of the total entropy expected. The plot of $C_{p}/T$ against $T$ on a semi-log scale for PrPt4Au shown in inset (i) of Fig. 3 (b) shows an upturn below 10 K reaching a value of 1.23 J/(mol K2) at 1.9 K. We have also observed a linear-in-$T$ behavior of $\rho(T)$ which is discussed in Section 5. These observations in PrPt4Au are the hallmark of a non-Fermi liquid (nFL) behavior. Among many other reasons, proximity to a quantum critical point or possible spin/elemental disorder such as in doped systems could be responsible for such behavior [12]. The calculated entropy is also presented in the same plot. At 8 K, the recovered entropy is about 0.9R$\ln(6)$ which is close to the full entropy expected.

We further analyzed the low-$T$ behavior by plotting of $C_{p}/T$ against $T^{2}$ for both compounds as shown in inset (ii) of Fig. 3 (a) and inset (ii) of Fig. 3 (b). Least-square fits to both sets of data (represented as red lines) based on the expressions: $C_{p}/T=\gamma+\beta T^{2}$ and $\beta=12\pi^{4}nR/(5\theta^{3}_{D}$), where $n$ and R are the number of atoms per formula unit and universal gas constant, respectively, $\gamma$ is the Sommerfeld coefficient and $\theta_{D}$ is the Debye temperature are shown. From the fits, $\gamma$ = 728.50 J/(mol K2) and 509.10 J/(mol K2) are obtained for PrPt4Ag and PrPt4Au, respectively. The observed $\gamma$ values for these two compounds are more than two orders of magnitude greater than what is expected for an ordinary metal and qualitatively similar to those of the heavy fermion (HF) systems, where significant enhancement of the quasiparticles mass have been observed [13].

5 Electrical transport

The temperature dependence of the electrical resistivity $\rho(T)$ for PrPt4Ag and PrPt4Au investigated between 1.9 K and 300 K are presented in Fig. 4 (a) and (b), respectively. The observed values of residual resistivity are $\approx$6 and $\approx$3 for PrPt4Ag and PrPt4Au, respectively. Both compounds show typical metallic behavior down to low temperatures. A broad curvature is observed at intermediate temperatures in PrPt4Ag, which is common to rare-earth intermetallic systems; possibly associated to thermal de-population of the crystal field levels as temperature is lowered. A plot of $\rho(T)$ against $T^{2}$ presented in the inset of Fig. 4 (a) indicates a power law behavior based on the expression: $\rho(T)$ = $\rho_{0}$ + $AT^{2}$. A fit of the expression to the data is shown as the red line. The residual resistivity, $\rho_{0}=10.46~{}\mu\Omega$cm and the coefficient of the quadratic term, $A=0.010~{}\mu\Omega$cm/K2 are obtained. The Kadowaki-Woods ratio (KWR) [14], $A/\gamma^{2}=1.88\times 10^{-8}~{}\mu\Omega$cm(mol K/mJ)2 is obtained by using $\gamma$ = 728.5 mJ/(mol K2) obtained from $C_{p}(T)$ analysis. The relationship between $\chi(T)$ and $\gamma$ is also evaluated using the Wilson ratio [15] given as: $R_{w}=\pi^{2}k_{B}^{2}\chi(T\longrightarrow 0)/(\mu^{2}_{\mathrm{eff}}\gamma)$. Using the observed low-$T$ values of $\chi(T\longrightarrow 0)$ = 0.5025 emu/mol, $\gamma$ = 728.5 mJ/(mol K2) and $\mu_{\mathrm{eff}}$ = 3.30 $\mu_{B}$/Pr yields $R_{w}=1.38$ which is comparable to a value of unity expected for HF systems. Also, a little anomaly is noticeable in the low-$T$ plot at $\sim$ 7.6 K which coincides with the anomaly observed in $C_{p}(T)$ around the same temperature.

PrPt4Au on the other hand is quasi-linear in nature down to low temperatures. In the inset of Fig. 4 (b), the low-$T$ behavior of PrPt4Ag is shown together with a fit (shown as red line) using the expression; $\rho(T)$ = $\rho_{0}$ + $AT^{n}$. From the fit, the residual resistivity, $\rho_{0}$ = 14.58 $\mu\Omega$cm, $n$ = 1 and $A$ = 0.117 $\mu\Omega$cm/K are obtained. Such a temperature dependence of $\rho(T)$ deviates from the Fermi-liquid behavior expected at low temperatures for normal metals. Results from $C_{p}(T)$ of PrPt4Au discussed in Section 4 have also shown a temperature dependence that deviates from those of ordinary metals. Using the values of $A=0.117~{}\mu\Omega$cm/K2 and 509.10 mJ/(mol K2), yields KWR = 4.49 $\times$ 10*-7* $\mu\Omega$cm(mol K/mJ)2. Also, using the values of $\chi(T\longrightarrow 0)$ = 0.3743 emu/mol, $\gamma$ = 509.10 mJ/(mol K2) and $\mu_{\mathrm{eff}}=3.15~{}\mu_{B}$/Pr yields $R_{w}$ = 1.62. The parameters observed in PrPt4Ag and PrPt4Ag reveal both compounds as new HF systems.

6 Discussion and conclusion

The existence of the hexagonal PrPt4Ag and PrPt4Au compounds are reported together with their physical and magnetic properties. PrPt4Ag shows a putative multipolar ordering at $T_{Q}=7.6~{}$K. From the crystal field levels permitted for the $J$ = 4 multiplet in a $D_{6h}$ local symmetry, one would expect to have 3 $\Gamma_{3}$ non-Kramers doublets and another 3 $\Gamma_{1}$ singlets. However, the observation of such an anomaly at $T_{Q}$ makes $\Gamma_{3}$ the likely ground state in PrPt4Ag. In contrast, the low-$T$ region of PrPt4Au shows a logarithmic divergence of $C_{p}(T)/T$, and a linear-in-$T$ behavior of $\rho(T)$ below 10 K which is typical of a non-Fermi liquid behavior. These behaviors are likely associated with spin scatterings observed for a system in the proximity of a quantum critical point. Further analyses of $C_{p}(T)$ of both compounds reveal $\gamma$ = 728.50 J/(mol K2) and 509.10 J/(mol K2) for PrPt4Ag and PrPt4Au, respectively. In Table 2, a collection of characteristic HF parameters are presented for easy comparison with the observations in this work. The observation of enhanced $\gamma$ value in systems with a $\Gamma_{3}$ non-Kramers ground state are often associated to the quadrupolar Kondo effect [10, 11]. Future studies will focus on experiments below 2 K in order to further unravel the physics involved in the ground state of these two non-Kramers-ion systems.

Acknowledgment

MOO acknowledges the UJ-URC bursary for doctoral studies in the Faculty of Science. AMS thanks the SA-NRF (93549) and UJ-URC for financial support.