In-NQR study of heavy fermion superconductor Ce2PdIn8 under pressure

115In nuclear quadrupole resonance measurements were performed in the normal state of the heavy fermion superconductor Ce2PdIn8 under hydrostatic pressure up to about 2.3 GPa. The observed behavior of the spin-lattice relaxation rate revealed a systematic suppression of antiferromagnetic critical fluctuations with increasing pressure.


Introduction
It has been theoretically recognized that dimensionality plays a key role in unconventional superconductivity (SC) emerging near a quantum critical point (QCP) [1], and Ce-based heavyfermion intermetallics with the general formula Ce n T In 3n+2 (n = 1, 2, ∞, T = Co, Rh, Ir, Pd, Pt) have been revealed good candidates for systematic experimental study of this problem [2]. The quasi-two-dimensional (2D) compounds CeCoIn 5 and CeRhIn 5 are superconductors with T c = 2.3 K (0 GPa) [3] and T c = 2.2 K (2.5 GPa) [4], respectively, while the most 3D phase CeIn 3 becomes superconducting under pressure of P ≃ 2.7 GPa with T c = 0.2 K [5]. These findings are fully in line with the expectation that the critical temperature in spin-fluctuation-driven superconductors decreases with increasing the system dimensionality.
The compounds Ce 2 T In 8 crystallizing with the crystal structure of the Ho 2 CoGa 8 type are believed to have a character intermediate between 2D-and 3D-like [2,6]. Recently, ambient pressure SC was discovered in Ce 2 PdIn 8 with T c ≃ 0.7 K [7]. The electronic specific heat coefficient is approximately 1.5 J/K 2 mol-fu [7,8,9,10], which implies a heavy-fermion ground state. The electrical resistivity of the compound exhibits a logarithmic temperature dependence above 40 K, with a local maximum at approximately 30 K(∼ T coh ), marking a crossover between the coherent and incoherent dense Kondo regimes, and a linear temperature dependence below about 10 K down to T c , evidencing a non-Fermi-liquid (NFL) behavior near QCP [7,8,9]. Moreover, it has been clarified that QCP can be tuned by magnetic field and pressure [10,11,12,13,14]. As for the superconductivity, it has been shown that d-wave is the most probable candidate for the SC gap symmetry. The thermal conductivity data have revealed the presence of residual density of states (R-DOS) at the Fermi level [12]. Penetration depth measurements [15] and nuclear quadrupole resonance (NQR) studies [16] have also indicated a nodal-line structure in the superconducting gap. The SC properties of Ce 2 PdIn 8 are thus quite similar to those reported for CeCoIn 5 . However, T c and the upper critical field H c2 (0) of Ce 2 PdIn 8 are considerably lower than the values found for CeCoIn 5 . The difference is probably associated with the fact that the crystal structure of the latter system is much more twodimensional than that of Ce 2 PdIn 8 .
The high-pressure electrical resistivity measurements have revealed that both the superconductivity and the NFL character in Ce 2 PdIn 8 are gradually suppressed with increasing pressure. To shed more light on the quantum critical behavior of the compound, it is vital to perform microscopic and site-selective experiments under pressure. In this paper, we report on our high-pressure 115 In NQR studies on the normal state of Ce 2 PdIn 8 , and compare the results with the bulk property data.

Experiments
A polycrystalline sample of Ce 2 PdIn 8 was synthesized by arc melting and characterized for its quality, as described in Ref. [9]. The 115 In NQR studies were performed in the frequency range of 7−60 MHz using a phase-coherent pulsed NQR spectrometer. Measurements were carried out above 1.5 K using a 4 He cryostat. The spin-lattice relaxation time T 1 was obtained from the recovery of the nuclear magnetization after a saturation pulse. The high pressure was generated using a BeCu/NiCrAl piston-cylinder cell filled with Daphne 7373 oil. The NQR frequency of the 63 Cu resonance in Cu 2 O at 4.2 K was used as an indicator of the pressure value inside the cell [17,18]. (Color online) In-NQR spectra of Ce 2 PdIn 8 at the In(1) site for the 3ν Q line (the transition between |I z = ±5/2⟩ and |I z = ±7/2⟩). For the sake of comparison, the spectra obtained at different pressures were shifted to 0 MHz. Figure 1 shows the typical NQR spectra of Ce 2 PdIn 8 taken at 4.2 K under pressures of 0, 1.58, 2.29 GPa (the site index and the NQR line number are the same as those defined in Ref. [16]). Narrow NQR lines (∼160 kHz) and their nearly identical shape indicate high quality of the sample and good hydrostatic pressure homogeneity inside the cell. A broad shoulder around f − f 0 ∼ 0.3 MHz is originating from the signal of 113 In nuclei as previously reported at ambient pressure in Ref. [16]. This also confirms the quality of the specimen. The frequency position f 0 of the NQR line center at a given temperature increases with increasing pressure (the same trend was observed for all the other NQR lines measured), and this feature can be ascribed to the compression of the unit cell volume. At ambient pressure, the spin-lattice relaxation time T 1 in Ce 2 PdIn 8 was derived over the temperature range 0.075−300 K at the frequency f 0 of the spectral center at the In(1) site. The nuclear magnetization recovery curves were analyzed in terms of the quadruple exponential function, appropriate for the nuclear spin I = 9/2 of the 115 In nuclei [19]. For example, for the 4ν Q line with the asymmetry parameter η = 0 the following formula was applied

Results and Discussion
where m(t) and m 0 denote the nuclear magnetization after a time t from the NMR saturation pulse and the thermal equilibrium magnetization, respectively. Figure 2 shows the temperature dependencies of the spin-lattice relaxation rate 1/T 1 in Ce 2 PdIn 8 measured under pressures of 0, 1.58, 2.29 GPa. 1/T 1 was evaluated from the 2ν Q , 3ν Q and 4ν Q lines. The results were found to perfectly coincide at 4.2 K for the 2ν Q and 3ν Q lines and at 100 K for the 3ν Q and 4ν Q lines. It is worth noting that the new data derived at ambient pressure at temperatures above 1.5 K were found in perfect agreement with the previous results obtained on a different sample, reported in Ref. [16]. This finding proves the reliability of our determination of 1/T 1 for Ce 2 PdIn 8 .
At ambient pressure, 1/T 1 nearly saturates between T coh (≃ 30 K) and about 150 K. This behavior indicates that the 4f electrons of the Ce ions are nearly localized above T coh . Actually, above 60 K, one can approximate the experimental data by the function where the first term corresponds to the Korringa contribution due to correlation-free conduction electrons and the second term accounts for the condribution due to localized 4f electrons. The fit parameters are α = 4.3 1/sK and β = 1.5 × 10 3 1/s. It is note worthy that the picture of localized 4f electrons at higher temperatures is valid because the value β is dominant in the fitting. The general property of heavy fermion compounds is that the correlation-free conduction electron term is much smaller than the term due to the conduction electrons hybridized at low temperatures with the 4f electrons (1/T 1 ) f . Indeed, in the case of Ce 2 PdIn 8 , e.g. at 10 K, αT = 43 1/s is negligibly small in relation to the measured value 1/T 1 = 1000 1/s. Therefore, one can estimate the relaxation rate originating from the coherent 4f electrons at low temperatures (1/T 1 ) f by subtracting the Korringa term from the 1/T 1 data obtained below T coh ( 1 Assuming that αT is independent of pressure [20], one obtains from the above formula (1/T 1 ) f that is close to the raw 1/T 1 values, yet different enough to discuss the electronic state in Ce 2 PdIn 8 more precisely. At a given temperature, the magnitude of (1/T 1 ) f systematically decreases with increasing pressure. In the range 1.5-20 K, the slope of (1/T 1 ) f versus T becomes steeper with increasing pressure. Altogether, these features indicate a gradual suppression of the antiferromagnetic fluctuations with rising pressure. In order to describe this effect quantitatively one can use the self consistent renormalization (SCR) theory [21]. Within the SCR approach, depending on the effective dimensionality of the systems, the following relationships should be observed where the staggered susceptibility χ Q (T ) with the propagation vector Q follows the Curie-Weiss law with a positive Curie-Weiss temperature θ.
Applying the SCR theory to the NQR data of Ce 2 PdIn 8 in the range between 1.5 and 15 K one obtains the values of θ collected in Table 1. For both models, the Curie-Weiss temperature increases with increasing pressure. Taking into account that θ is a measure of the distance from the quantum critical point [21], one can conclude that hydrostatic pressure systematically drives the compound away from its QCP. However, one should notice that up to 2.29 GPa, the value of θ remains small, which means that the spin fluctuations keep significant even at that high pressure. These findings are fully consistent with the main result of the electrical resistivity measurements under pressure [13].
As can be inferred from the θ uncertainty values given in Table 1, a better fit to the NQR experimental data of Ce 2 PdIn 8 was achieved within the 3D SCR model. This result is at odds with the analyzes of the low-temperature heat capacity data, which led to the preference of the 2D scenario [10]. It seems reasonable to expect that the character of spin fluctuations in Ce 2 PdIn 8 is neither as much 2D as found for CeCoIn 5 nor as 3D as evidenced for UIn 3 . In an intermediate situation, bulk property techniques and microscopic probes may appear more sensitive to somewhat different aspects of the dimensionality, and thus lead to seemingly contradictory results. Pressure (GPa) 0 1.58 2.29 θ (K): 2D model 3.3(2) 7.9(4) 11.3(7) θ (K): 3D model 0.0(1) 1.0(2) 2.3(3)

Summary
The heavy fermion superconductor Ce 2 PdIn 8 was studied by means of In-NQR measurements under pressure up to about 2.3 GPa. The results indicated a gradual suppression of the antiferromagnetic spin fluctuations with increasing pressure, which manifests a gradual shift of the system away from the quantum critical magnetic instability. The terminal pressure reached in our experiments was however too low to stabilize the Fermi liquid state, hence further NQR investigations of Ce 2 PdIn 8 at much higher pressures are needed.