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Khan Rajwali, Mao Qianhui, Wang Hangdong, Yang Jinhu, Du Jianhua, Xu Binjie, Zhou Yuxing, Zhang Yannan, Chen Bing, Fang Minghu. Quantum critical behavior in an antiferromagnetic heavy-fermion Kondo lattice system (Ce 1 − x La x )2Ir3Ge5 . Chinese Physics B, 2017, 26(1): 017401  
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Quantum critical behavior in an antiferromagnetic heavy-fermion Kondo lattice system (Ce 1 − x La x )2Ir3Ge5
Khan Rajwali1, Mao Qianhui1, Wang Hangdong2, Yang Jinhu2, Du Jianhua1, Xu Binjie1, Zhou Yuxing1, Zhang Yannan1, Chen Bing2, Fang Minghu1, 3, †
Department of Physics, Zhejiang University, Hangzhou 310027, China
Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China

 

† Corresponding author. E-mail: mhfang@zju.edu.cn

Abstract

The measurements on temperature dependences of magnetic susceptibility , specific heat , and electrical resistivity were carried out for the antiferromagnetic (AFM) (Ce La x )2Ir3Ge5 ( ) system. It was found that the Neel temperature decreases with increasing La content , and reaches 0 K near a critical content . A new phase diagram was constructed based on these measurements. A non-Fermi liquid behavior in and a relationship in were found in the samples near , indicating them to be near an AFM quantum critical point (QCP) with strong spin fluctuation. Our finding indicates that (Ce La x )2Ir3Ge5 may be a new platform to search for unconventional superconductivity.

PACS: 74.40.kb;75.50.Ee;74.25.F–;75.20.Hr
Keyword:quantum critical point;antiferromagnetic Kondo lattice system; La x )2Ir3Ge5 " target=_blank>(Ce 1 − x La x )2Ir3Ge5
1. Introduction

Quantum criticality has become one of the most fascinating subjects in condensed matter physics for the last two decades. As a system reaches a certain threshold point, quantum fluctuations at 0 K are so strong that the metallic state of the system is broken. Quantum critical fluctuations are the strongest disturbances that can be exerted on the metallic state, which are the top candidates to explain the mysterious behaviors of heavy fermions,[1,2] high-temperature superconductivity in cuprates,[3,4] and doped ferromagnetic and antiferromagnetic (AFM) systems.[1,5] Heavy-fermion compounds have played the key role in the study of the AFM quantum critical behavior. Recently, AFM Kondo-lattice systems have been tuned to the quantum critical point (QCP) by modifying the external parameters, such as the magnetic field, pressure, and chemical doping,[6] and many exotic quantum phenomena have been found near QCP. In CeColn5,[7–9] CeCu Ag ,[10] and YbRh2Si2,[11,12] AFM QCP can be realized by modifying the magnetic field. While in CeRh2Si2,[13] CeCu2Ge2,[14] Celn3, and CePd2Si2[15] systems, the Neel temperature can be driven to 0 K by an external applied pressure. There are a few examples for the realization of AFM QCP by chemical substitution in the Ce-based heavy-fermion Kondo lattice systems, such as in Ce(Cu Au x )6 ( )[16] and (CeIn Sn x ),[17] which are close to AFM QCP.

Ce2Ir3Ge5 is an AFM Kondo-lattice system with Neel temperature K.[18] It crystallizes in the tetragonal (U2Co3Si5) structure ( ). While La2Ir3Ge5 is a non magnetic compound,[19] which crystallizes in the same structure as that of Ce2Ir3Ge5. Yuan and his coworkers[20] found that the magnetic order in Ce2Ir3Ge5 can be easily suppressed by applying a hydrostatic pressure. Here we show that the AFM order can be suppressed by the partial substitution of La for Ce in the (Ce La x )2Ir3Ge5 system. It is found that the decreases with increasing La content and reaches 0 K near a critical content . A new phase diagram is constructed based on our measurements for this system. The non-Fermi liquid behavior in and the relationship in of the samples near demonstrate that strong spin fluctuation emerges in these samples, indicating them to be near AFM QCP.

2. Experimental method

Polycrystalline samples of the solid solutions (Ce La x )2Ir3Ge5 ( ) were prepared by a conventional arc-melting method. The starting materials were cut from pieces of Ce (Alfa Aesar, 99.9%), La (Alfa Aesar, 99.9%), Ir (Alfa Aesar, 99.9%), and Ge (Alfa Aesar Puratronic, 99.9999%). After melting, each sample was flipped over and re-melted several times for homogeneity. The resulting samples were sealed inside evacuated quartz tubes and annealed at 930 °C for one week. It was found that the net weight loss was less than 1% for each sample during these processes. Powder x-ray diffraction patterns for all the samples were recorded at room temperature by a PANalytical x-ray diffractometer (Model EMPYREAN) with monochromatic Cu radiations. Analysis of the x-ray powder-diffraction data was made by using the High ScorePlus software. The DC magnetic susceptibility was measured at a magnetic field of 1000 Oe using a Quantum Design MPMS (SQUID). The heat capacity and resistivity measurements were carried out by using a Quantum Design physical properties measurement system (PPMS).

3. Results and discussion

Figure 1(a) shows the powder x-ray diffraction (XRD) pattern of the un-doped Ce2Ir3Ge5 sample, together with its Rietveld refinement (weighted profile factor and the goodness-of-fit ). All the peaks can be indexed by a U2Co3Si5 orthorhombic structure,[21] with a space group of Ibam. Figure 1(b) shows the XRD patterns of the (Ce La x )2Ir3Ge5 ( , 0.3, and 0.6) samples, indicating that all the samples ( ) are a single phase. The lattice parameters were obtained by fitting the XRD data, as shown in Figs. 1(c)–1(e). For example, for the pure Ce2Ir3Ge5 ( ) sample, Å, Å, and Å, which are the same as those reported by Hossain et al.[18] With increasing La content , the lattice parameters , , and increase monotonically, which is consistent with the fact that the ionic radius of La (1.061 Å) is larger than that of Ce (1.034 Å). These results demonstrate that La can uniformly substitute for Ce in the (Ce La x )2Ir3Ge5 ( ) system.

Fig. 1. (color online) (a) X-ray diffraction patten of Ce2Ir3Ge5 and its Rietveld refinement. (b) Powder XRD patterns of (Ce La x )2Ir3Ge5 ( , 0.3, and 0.6) samples. Lattice parameters (c) , (d) , and (e) as functions of the La content for (Ce La x )2Ir3Ge5 ( ).

Figure 2(a) shows the temperature dependence of the magnetic susceptibility, , for the (Ce La x )2Ir3Ge5 ( ) samples below 20 K in a magnetic field of 1000 Oe. For the pure Ce2Ir3Ge5 sample, the AFM transition is characterized by a little decrease in at Neel temperature K as reported by Hossain et al.[18] With increasing La content, decreases and becomes invisible for . A similar behavior has been discovered in Ce2Ir3Ge5 under an external pressure.[20] Figure 2(b) displays the temperature dependence of the inverse magnetic susceptibility, , for the (Ce La x )2Ir3Ge5 ( ) samples. It is clear that the curves exhibit a linear behavior above 100 K. To fit the data above 100 K, we used the modified Curie–Weiss law[18]

(1)
where represents the temperature-independent susceptibility, is the Curie constant, and θ is the Curie–Weiss temperature. For the pure Ce2Ir3Ge5 ( ) sample, the effective moment was estimated by this fitting, which is close to that for a free Ce ion (2.54 ). It was also found that the effective moment for all the (Ce La x )2Ir3Ge5 ( ) samples is almost independent of the La content, as shown in the inset of Fig. 2(b), indicating that there is no effect on the delocalization of the 4f electron from the partial substitution of La for Ce. The negative Curie–Weiss temperature, K for the sample, indicates the presence of the Kondo interaction. As shown in the inset of Fig. 2(b), it is clear that θ increases with increasing La content, from −158 K ( ) to −78 K ( ), which is related to the Ruderman–Kittel–Kasuya–Yoshida (RKKY) coupling. It is clear that the distance between the Ce-ions increases with the La doping, then the RKKY coupling becomes weaker, as discussed by Lora-Serrano et al. for Nd La x RhIn5.[22]

Fig. 2. (color online) (a) Temperature dependence of magnetic susceptibility, , for (Ce La x )2Ir3Ge5 ( ), under an applied magnetic field of 1000 Oe. (b) The inverse susceptibility fitted with the Curie–Weiss law for (Ce La x )2Ir3Ge5 ( ). The inset shows effective moment and Curie–Weiss temperature θ for the samples.

Figure 3(a) shows the temperature dependence of the resistivity, , for the (Ce La )2Ir3Ge5 ( ) samples. The curves for the samples show a typical behavior of the AFM Kondo-lattice system. For the pure Ce2Ir3Ge5 ( ) sample, with decreasing temperature, the resistivity decreases monotonously to cm at 9.5 K, then drops sharply to cm at 2 K, which is associated with the AFM transition. For the (Ce La x )2Ir3Ge5 ( ) samples, their resistivity decreases at first with decreasing temperature, reaches a minimum at about 38 K, then increases to a maximum, finally it drops sharply at . In the paramagnetic state, the minimum in originates from the existence of the Kondo effect in the sample as discussed by Gignoux et al.[24] As shown in Fig. 3(b), the Neel temperature decreases with increasing La content. Only for the and 0.66 samples, their exhibit a metallic behavior in the whole measuring temperature range (2–300 K). In order to explore the evolution of the behavior with the partial substitution of La for Ce, we first fitted the data in the AFM state by using the following expression:[25,26]

(2)
where is the residual resistivity, is the coefficient of the Fermi-liquid T 2 term, involves the electron–magnon scattering, and is the magnitude of the gap. It is clear that in the AFM state for all the samples can be well described by Eq. (2), as shown in Figs. 3(c)–3(f). By this fitting, we obtained cm, 58 cm, 85 cm, 98 cm, 116 cm, and 119 cm and cm/K2, 2.1 cm/K2, 2.7 cm/K2, 3.5 cm/K2, 4.1 cm/K2, and 4.9 cm/K2 for the , 0.1, 0.2, 0.3, 0.4, and 0.5 samples, respectively. Both the and values increase with increasing La content. The energy gap decreases from K for to K for . On the other hand, for the and 0.66 samples, their cannot be described by either the Fermi-liquid behavior or Eq. (2). Then we used a power law expression to fit the data at lower temperatures for both samples, as shown in Figs. 3(g) and 3(h), where is the temperature coefficient and n is the power exponent. It was estimated that n is 1.3 and 1.5 for the and 0.66 samples, which is smaller than 2, indicating that their deviate from the Fermi-liquid behavior. At the same time, we also found that both and values reach a maximum for the sample (see Figs. 5(b) and 5(d)).

Fig. 3. (color online) (a) Temperature dependence of electrical resistivity in (Ce La x )2Ir3Ge5 ( ). (b) Resistivity in the low-temperature range around (marked by an arrow). (c)–(h) in the lower temperature range for , 0.1, 0.2, 0.3, 0.6, and 0.66 samples fitted by Eq. (2) or , as discussed in the text.

Figure 4(a) shows the temperature dependence of the heat capacity, , for the (Ce La x )2Ir3Ge5 ( ) samples. It is clear that a λ-type anomaly in corresponding to the AFM transition emerges at for the (Ce La x )2Ir3Ge5 ( ) samples, and decreases with increasing La content. For the and 0.66 samples, no λ-type anomaly in is observed above 0.5 K. In order to obtain more information from the data, we re-plotted the data as vs. in Fig. 4(b). First we analyze the data in the AFM state for the (Ce La x )2Ir3Ge5 ( ) samples. As discussed by Coqblin et al.,[27] should be described by the expression

(3)
where the first term represents the specific heat from the electrons, the second term is the contribution from the lattice vibration, and the third term represents the contribution of the magnons with a gap. For clarity, Figure 4(b) only shows the fitting line (red) below 9 K for the Ce2Ir3Ge5 sample. In fact, the data below for all the samples can be well described by Eq. (3). Table 1 lists the electronic specific heat coefficient , the lattice specific heat coefficient β, the magnon specific heat coefficient α, and the corresponding gap for the , 0.1, 0.2, 0.3, and 0.4 samples. It is obvious that increases while α and decrease with increasing La content, indicating that the partial substitution of La for Ce results in the enhancement of the electronic specific heat and the reduction in the magnon specific heat. However, the specific heat below 9 K for the and 0.66 samples, in which the AFM order disappears, exhibits a behavior. We used the expression[28,29]
(4)
to fit the data for both and 0.66 samples, where δ is a coefficient and T 0 presents a characteristic temperature related to the spin fluctuation term. For clarity, Figure 4(b) only shows the fitting (yellow) line for the sample. The fitting parameters for both and 0.66 samples to Eq. (4) are listed in Table 2. From the results listed in Tables 1 and 2, it can be concluded that the electronic specific heat coefficient increases with increasing La content and reaches a maximum 101.1 mJ/mol·K2 in the sample, then drops a little in the sample. Especially, the behavior emerges in the and 0.66 samples, which is a typical behavior for the system with strong spin fluctuation,[30,31] indicating that the sample is located near AFM QCP. No obvious change in β was found for all the samples, indicating that the partial substitution of La for Ce has little influence on their Debye temperature. For example, by using the fitted β values in the Debye expression , the Debye temperature was estimated to be 240 K, 238 K, and 242 K for the , 0.3, and 0.6 samples, respectively.

Fig. 4. (color online) (a) Temperature dependence of specific heat and (b) C/T as a function of for the (Ce La x )2Ir3Ge5 ( ) samples. Red line: fitting to the data of the sample by Eq. (3), deep yellow line: fitting to the data of the sample by Eq. (4).
Table 1.

Fitting parameters , β, α, and of the data below for the samples with Eq. (3).

.
Table 2.

Fitting parameters , β, δ, and T 0 of the data in the low temperature range for the and 0.66 samples with Eq. (4).

.

Based on the results of , , and measurements, we constructed the phase diagram of Néel-temperature as a function of La content for the (Ce La x )2Ir3Ge5 system, as shown in Fig. 5(a). With increasing La content, decreases and reaches 0 K at a critical content . Figure 5(b)–5(e) show the ( ), , , and as functions of La content . It is obvious that all the fitting parameters with Eq. (2)–(4) and the power law exhibit an anomalous near . For example, the power exponent n = 2 in the samples, indicating that the Fermi-liquid behavior occurs in this region, i.e., there are two kinds of electrons: itinerant and localized ones. Whereas for the and 0.66 samples, n is less than 2.0, and reaches a minimum of 1.3 in the sample, signaling that a non-Fermi liquid behavior emerges in these samples (see Fig. 5(c)). All the A, , and values reach to maximum at , as shown in Figs. 5(b), 5(d), and 5(e), respectively. All the anomalous in n, A, , and at , in addition to the behavior near , indicate that a strong spin-fluctuation emerges in the samples near , which is similar to that in the doping induced AFM QCP UCo Fe x Ge[32] and YbNi2(P As x )2[33] systems. Our finding implies that (Ce La x )2Ir3Ge5 may provide another platform to study AFM quantum fluctuation near QCP. We are looking forward to finding some exotic quantum states, such as superconductivity after obtaining a high quality single crystal in the future.

Fig. 5. (color online) La concentration dependence of (a) AFM Neel temperature as estimated from the , , and of (Ce La x )2Ir3Ge5 ( ), (b) the temperature coefficient A, (c) the power exponent n, (d) the residual resistivity , which are the fitting parameters to , see the text. (e) The electronic specific heat coefficient obtained from the data, as discussed in the text.
4. Conclusion

We synthesized successfully AFM (Ce La x )2Ir3Ge5 ( ) heavy-fermion alloys. Based on the measurements of magnetization, resistivity, and specific heat, the magnetic phase diagram was obtained for this system. It was found that the Neel temperature decreases with increasing La content , and reaches 0 K near . The non-Fermi liquid behavior in and the relationship in the samples near demonstrate that an AFM quantum phase transition occurs at . These results imply that (Ce La x )2Ir3Ge5 provides a platform for searching for the new exotic collective phases, such as unconventional superconductivity.

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