Elastic properties of SmPt₂Cd₂₀ probed by ultrasound measurements

A series of RTr₂X₂₀ (R = rare-earth element, Tr = transition metal element, X = Al, Zn, Cd) of intermetallic compound crystallizes in the cubic CeCr₂Al₂₀ -type structure with a space group Fd$3¯$m (No. 227). In this structure, the rare-earth atoms occupy the 8a site with cubic T_d symmetry located at the center of an X16 cage (CN 16 Frank-Kasper polyhedron), forming a diamond structure sublattice.¹ Among the series, Sm-based systems SmTr₂X₂₀ exhibit often unusual magnetic-field-insensitive heavy fermion (HF) behavior, being markedly different from those of Ce-based HF ones. In fact, it was found recently that SmTr₂X₂₀ exhibits anomalous field-insensitive phase transition and HF state in the ordered state.^2,3 Since SmTr₂Al₂₀ shows a weak temperature dependence of the magnetic susceptibility and the field-insensitive nature of physical properties, the valence fluctuation of Sm ions is expected to play a crucial role in these systems. The present research aims to gain more insight into the behavior of magnetic-field insensitive HF systems. SmPt₂Cd₂₀ undergoes a magnetic phase transition at 0.64 K to a ferromagnet (FM) state.² The effective magnetic moment μ_eff and paramagnetic Curie temperature Θ were determined to be 0.46 μ_B/Sm and 0.53K, respectively. The positive value of Θ suggests that ferromagnetic interaction is predominant in this system. The temperature dependence of the electrical resistivity shows a shoulder-like structure around 10 K, possibly indicating the reduction of crystalline electric field (CEF) excitation of 4f electrons. Furthermore, the magnetic resistivity, determined by subtraction of the non-magnetic reference LaPt₂Cd₂₀ shows a gradual increase below around 200 K, followed by a sharp decrease below around 50 K with decreasing temperature. It should be noted that the specific heat divided by temperature increases with decreasing temperature even below T_c and attains 4.5 J/mol K² at 0.26 K, suggesting formation of the HF state and possibly strong magnetic quantum fluctuations. In cubic symmetry, the CEF splits the sixfold degenerate ⁶H_5/2 multiplet of the Sm³⁺ 4f⁵ state into a Γ₇ doublet and a Γ₈ quartet. The estimated magnetic entropy from the specific heat suggests the Γ₇ doublet to be the ground state and the Γ₈ quartet the excited state at around 30 K above. Although much effort has been devoted to experimental and theoretical studies of the Sm-based HF systems so far, the mechanism to form the magnetic-field-insensitive HF state is poorly understood. We have carried out the ultrasound investigations of SmPt₂Cd₂₀ in a wide temperature range and at applied external magnetic field. In this short communication, we report the low-temperature property of SmPt₂Cd₂₀ proved by ultrasound measurements.

Single crystals of SmPt₂Cd₂₀ were prepared by Cd self-flux method. Typical size of obtained single crystals is approximately 1 × 1×2 mm³, but only with the crystallographic ⟨110⟩ axis. In consequence, the C_E = (C₁₁ -C₁₂)/2 was possible in this study. For sample quality evaluation, we have performed elemental analysis using an x-ray fluorescence spectrometer JSX-1000S (JEOL). No impurity elements have been detected. The details have been described elsewhere.² For ultrasound measurements, single crystalline LiNbO₃ transducers were employed to generate and detect ultrasound in a frequency range between 10 and 50 MHz. A phase comparison and phase sensitive method was used in our experiments. We performed the ultrasound measurements on SmPt₂Cd₂₀ in the extremely low temperature ranges covering the magnetic transition temperature T_c = 0.64 K, using a ⁴He refrigerator down to 1.4 K and a ³He-⁴He dilution refrigerator down to 80 mK. Superconducting magnets equipped with the refrigerators were employed for the ultrasonic measurements in applied magnetic fields.

Figure 1 shows the relative change of the transverse elastic constant ΔC(T)/C₀ as a function of temperature in SmPt₂Cd₂₀. One observes a slight elastic softening effect below around 2 K. The softening is gradually suppressed with increasing a magnetic field. Here let us attempt to describe the softening effect in terms of CEF effect. The CEF level scheme for SmPt₂Cd₂₀ was proposed from the magnetic entropy result as Γ₇ (0 K) - Γ₈ (30 K).² In this case, a characteristic minimum structure is expected in ΔC(T)/C₀ at around 15 K. In fact, it is difficult to obtain the good-fitted results taking only CEF effect into account. Thus, it is likely that the CEF effect is not primary origin to cause the observed elastic softening in the ΔC(T)/C₀. This point directs attention to something else to explain the softening effect. If a system has a large density of states of quasiparticles in the vicinity of Fermi level formed by the hybridization, a coupling constant d between the quasiparticles and their relevant elastic strain induced by sound waves becomes significantly strong.^4–6 This often causes elastic anomalies at low temperatures, so-called deformation-potential approximation which is described by,

where, $CΓ(0)$⁠, d and W denote the background elastic constant, the coupling constant and a total band width, respectively. β denotes 1/k_BT. Dotted lines in Fig. 1 show the calculated results by using the above formula. The results are in a good agreement between theory and experiment above T_c. This is consistent with the simple model that the coupling between the strongly mass-enhanced mobile electrons and the lattice through the deformation-potential leads to the elastic anomaly. Figure 2 shows the field dependence of the d and W. The d increases while the W decreases gradually by applying the magnetic field. Thus, it is likely that itinerant to localized view on 4f-electron of Sm ions would be tuned by external magnetic field in this field range. That is to say, our observations suggest that the magnetic fluctuation i.e., Kondo screening is suppressed, and reduction of itinerant 4f state would occur under magnetic field in SmPt₂Cd₂₀.

As a summary, we have investigated the elastic properties of the Sm-based 1-2-20 system SmPt₂Cd₂₀. A distinct elastic softening toward the transition temperature was observed in the ΔC(T)/C₀. This softening would be possibly ascribed to the coupling between the quasiparticles with a highly enhanced effective mass and the relevant elastic strain, suggesting the formation of a coherent many-body, heavy fermion state at low temperatures.

The measurements have been performed in the Cryogenic Division of the Center for Instrumental Analysis, Iwate University. This work was supported by JSPS KAKENHI Grant Number JP15H05883 (J-Physics).