Electronic states of CeT₂X₂₀ (T:transition metal, X=Zn and Cd)

CeT₂X₂₀ (T: transition metals, X=Al, Zn, Cd) crystallizes in the cubic CeCr₂Al₂₀ type crystal structure. In these systems, the ground state of 4f electron in Ce atom strongly depends on X atom. For example, CeT₂Al₂₀ show the paramagnetic ground state with a temperature independent and small magnetic susceptibility,¹ while CeIr₂Zn₂₀ and CeRu₂Zn₂₀ exhibit an intermediate valence state and heavy fermion state, respectively.^2–4 The localized character of the 4f electrons has been observed in CeT₂Cd₂₀, showing a Curie-Weiss type magnetic susceptibility at low temperatures.^5,6 The hybridization strength between the 4f electron and conduction electrons gets weaker in the order of X=Al, Zn, and Cd, where the lattice parameters for X=Al, Zn, and Cd are approximately 14.7, 14.3, and 15.6 Å.

In the present study, we controlled the hybridization strength between 4f electron and conduction electrons in the intermediate valence compound CeIr₂Zn₂₀ by substituting Zn with Cd to expand the lattice constant. The electrical resistivity ρ, and specific heat C of CeIr₂(Zn_1−xCd_x)₂₀ were measured, to see if CeT₂X₂₀ approaches quantum critical point due to the substitution effect. The ground state of the Cd-rich compounds, CeT₂Cd₂₀ are not clear yet. In these CeT₂Cd₂₀ compounds, the Ce atom possesses a cubic site symmetry. The crystal electric field (CEF) potential splits the 2J + 1 degenerate states into two levels namely, a Γ₇-doublet and a Γ₈-quartet.⁷ From our low temperature specific heat measurement, we could determine the ground state of CePt₂Cd₂₀.

Additionally, the relationship between the hybridization strength and 4f valence state is one of the interesting topics of research. For example, Yb valence in YbT₂Zn₂₀ decreases with decreasing temperature and becomes constant below the Kondo temperature,⁸ indicating the hybridization strength. In order to study the relation between Ce valence and hybridization strength in CeT₂X₂₀, we have performed high-resolution X-ray absorption experiment using partial fluorescence yield (PFY) at Ce L₃-edge.

Single crystals of CeIr₂(Zn_1−xCd_x)₂₀ and CePt₂Cd₂₀ have been grown by Zn-Cd and Cd self flux method, respectively. Figures 1(a) and 1(b) display the powder X-ray diffraction (PXRD) patterns of CeIr₂(Zn_1−xCd_x)₂₀ and photos of corresponding single crystals, respectively. The results of PXRD reveal that all samples crystallize in the cubic CeCr₂Al₂₀ type crystal structure. The actual concentrations of Cd in CeIr₂(Zn_1−xCd_x)₂₀ for x = 0.1, 0.2, and 0.4 were determined to be 0.09, 0.13, and 0.16, respectively, by microprobe analysis. As x increases, the lattice parameter becomes larger and tends to saturate for x > 0.1. Here, Cd could occupy three different Zn sites of 16c, 48f, and 96g. The PXRD analyses reveal that Cd tends to occupy mainly 16c site. A similar behavior was observed in YMn₂(Zn_1−xIn_x)₂₀.⁹ 

The electrical resistivity ρ was measured by the standard four-probe method in the temperature range from 0.8 to 300 K. The specific heat C was measured by the thermal relaxation technique using the physical properties measurement system, PPMS (Quantum Design Co. Ltd.). High-energy resolution X-ray absorption (PFY-XAS) spectra at Ce L₃-edge of CeIr₂(Zn_1−xCd_x)₂₀ and CePt₂Cd₂₀ were measured at BL39XU of SPring-8 by using five Ge 331 spherically-bent crystals. The PFY-XAS is obtained by using 3d − 2p resonant X-ray emission spectroscopy suppressing core-hole lifetime-broadening effect in the final states. Therefore, both Ce³⁺ and Ce⁴⁺ components are clearly resolved and small variation of spectrum is distinguished.

Figure 2(a) depicts the temperature dependence of ρ of CeIr₂(Zn_1−xCd_x)₂₀. ρ of CeIr₂Zn₂₀ shows a shoulder-like behavior around 150 K, which is consistent with the previous study.² As x increases, the value of ρ at 300 K decreases. Simultaneously, the shoulder-like structure is shifted towards lower temperatures and for x = 0.16 is located at around 50 K. A similar behavior was observed in CeNi₂(Si_1−yGe_y)₂,¹⁰ where y = 0 and 1 are intermediate valence and heavy-fermion compounds, respectively. At low temperatures, ρ(T) follows the relation, ρ = ρ₀ + AT², below a characteristic temperature T_FL, as shown by solid lines in the inset of Fig. 2(a), where ρ₀ is the residual resistivity, and A^1/2 corresponds to the effective mass. With increasing x, A increases and T_FL decreases. Similar behavior was reported in the pressure study of YbIr₂Zn₂₀.¹¹ In the case of YbIr₂Zn₂₀, the shoulder-like structure in ρ(T) has been transformed into a peak around the critical pressure, where A is extremely enhanced and T_FL is reduced to almost 0 K. Our experimental results of CeIr₂(Zn_1−xCd_x)₂₀ imply that the hybridization effect becomes weaker due to the Cd substitution.

Figure 2(b) shows the specific heat divided by temperature C/T versus T² of CeIr₂(Zn_1−xCd_x)₂₀. The solid line in Fig. 2(b) represents the curve calculated by the Debye approximation for CeIr₂Zn₂₀ expressed as C/T = γ + βT² with γ = 35 mJ/(K²⋅mol) and β = 1.3 mJ/(K⁴⋅mol). The values of C/T at low temperatures, which corresponds to γ, is enhanced by substituting Zn with Cd. The enhancement of γ is consistent with the enhanced A value, as discussed above. C/T for x = 0 and 0.09 almost follows a linear relation with T². In contrast, C/T for x = 0.13 and 0.16 deviates from linearity and exhibits a small upturn at low temperatures which is something similar to that observed in CeNi₂(Si_1−yGe_y)₂¹⁰ for y ≥ 0.8. In particular, CeNi₂Ge₂ shows a non-Fermi liquid behavior as the 4f contribution C_4f/T is proportional to − ln T. In analogy with CeNi₂(Si_1−yGe_y)₂, CeIr₂(Zn_1−xCd_x)₂₀ might approach the quantum critical point and the upturn could be the sign of non-Fermi liquid behavior. The upturn in C/T was also explained by the Kondo model with a small Kondo temperature.¹² We need to measure C(T) at lower temperatures and subtract with lattice contribution to get more insight on the upturn.

Figure 3(a) shows the low temperature part of the heat capacity of CePt₂Cd₂₀ and LaPt₂Cd₂₀ along with the calculated entropy S_4f on the right axis. $CCePt2Cd20$ gradually increases below 2 K with decreasing temperature, which might be due to some short-range order, and shows a clear λ-type jump at 0.3 K due to a phase transition. Correspondingly, an abrupt change of slope in ρ of CePt₂Cd₂₀ is observed at 0.26 K, as indicated by an arrow in Fig. 3(b).

The magnetic entropy S_4f has been estimated from 4f contribution C_4f, $C4f=CCePt2Cd20−CLaPt2Cd20$ (not shown here for brevity). Here, we used the calculated lattice contribution $CLaPt2Cd20$ below 2 K by the Debye approximation with γ = 20 mJ/(K²⋅mol) and β = 4.5 mJ/(K⁴⋅mol),¹³ as shown by the solid line in Fig. 3(a). S_4f reaches almost R ln 2 at 2 K and remains almost flat up to 4 K, which implies that the ground state is the Γ₇ doublet and the transition may be due to a magnetic ordering. Here, S_4f at 0.1 K is determined as 0.48 J/(K⋅mol) by assuming that C_4f linearly decreases toward 0 for T → 0 K. Note that the γ value of CePt₂Cd₂₀ can not be estimated correctly due to the extremely large magnetic component. However, the γ value of CePt₂Cd₂₀ should be small similar to that of CeNi₂Cd₂₀ whose γ value is 25 mJ/(K²⋅mol),⁵ thus indicating that the hybridization strength of CeT₂Cd₂₀ is much smaller compared to that of CeIr₂Zn₂₀.

Figure 4(a) shows the PFY-XAS spectra for three different samples of CeIr₂Zn₂₀, CeIr₂(Zn_0.91Cd_0.09)₂₀, and CePt₂Cd₂₀ at 300 K. The prominent peak observed at 5.726 keV and the broad hump around 5.737 keV are assigned to 4f¹(Ce³⁺) and 4f⁰(Ce⁴⁺) components, respectively. Spectral intensity of the main peak for CeIr₂Zn₂₀ seems to be enhanced by Cd substitution, while for CeIr₂(Zn_1−xCd_x)₂₀ it is much smaller than that of CePt₂Cd₂₀. A similar behavior was observed in heavy fermion compounds UIr₂Zn₂₀ and UPd₂Cd₂₀, which exhibit a non-magnetic ground state and a phase transition, respectively.^14,15 In the case of UPd₂Cd₂₀ a sharper peak was observed compared to that of UIr₂Zn₂₀.¹⁶ Note that since self-absorption effect, which can reflect the spectral shape, is not excluded in the present study hence the observed different spectra among CeIr₂(Zn_1−xCd_x)₂₀ and CePt₂Cd₂₀ can originate not only from different hybridization strength but also from different constituent atoms.

The PFY-XAS spectrum of CePt₂Cd₂₀ does not change between 3.0 K and 300 K, as shown in Fig. 4(b). In contrast, an apparent change in spectra between 300 K and 3.0 K is detected in CeIr₂Zn₂₀ and Cd-doped one. With decreasing temperature, the main peak of 4f¹ component is suppressed and the hump of 4f⁰ one is enhanced, thus indicating 4f⁰ configuration is more stable at low temperature. This result originates from thermal variation of Ce valence. A similar behavior is observed in mixed valence Kondo lattice compounds, for example, CeT₂(Si_1−xGe_x)₂.¹⁷ The variation of Ce valence between two temperatures is reduced by substituting Zn with Cd, implying that a weak hybridization effect reduces the valence change. In the opposite side of weak hybridized compounds, a temperature dependent valence change is not observed in CeMo₂Al₂₀ (not shown here). The hybridization effect of CeIr₂Zn₂₀ is incidentally strong enough to observe the Ce valence change in the measured temperature range. In order to elucidate the mechanism of Ce valence change with temperature, PFY-XAS experiment for Ce compounds with a similar γ value of CeIr₂Zn₂₀ should be performed.

We succeeded in growing single crystals of CeIr₂(Zn_1−xCd_x)₂₀ which are confirmed to crystallize in the CeCr₂Al₂₀-type structure. The actual x values are found to be around 0.1, which are smaller than nominal x, implying that the 16c site Zn is relatively easier to substitute. The experimental results of PXRD, electrical resistivity, and specific heat reveal that the electronic state of CeIr₂Zn₂₀ changes from intermediate valence state to moderately heavy fermion state by the negative chemical pressure, indicating that the hybridization effect is suppressed by Cd substitution. It is necessary to measure low temperature C and grow crystals for x > 0.16 to look for quantum critical phenomena in the CeT₂X₂₀ system.

The low temperature specific heat and electrical resistivity measurements of CePt₂Cd₂₀ confirms a magnetic transition below 0.3 K with the Γ₇ doublet ground state. This is the first compound exhibiting a clear phase transition among a series of CeT₂X₂₀.

From PFY-XAS experiment, the temperature dependent spectra are clearly observed in CeIr₂Zn₂₀, which directly correspond to thermal variation of Ce valence state. Cd substitution seems to suppress the variation of spectra between 3.0 K and 300 K. In CePt₂Cd₂₀, the spectra is almost temperature independent.

This work was carried out under the Joint-Research Program of the International Research Center for Nuclear Materials Science, Institute for Materials Research, Tohoku University. A.T. and R.K. thank Department of Science and Technology, Government of India for the financial assistance (Grant: DST/INT/JSPS/P-196/2015). This study was partially supported by Grants-in-Aid for Scientific Research (C) (Grant No. 15K05195) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan. The PFY-XAS experiments were performed at the BL39XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal Nos. 2016B1961, 2017A1857, 2017B1066, 2018A1047).