Cite this Article
Luo Jun, Yang Jie, Maeda S, Li Zheng, Zheng Guo-Qing. Structural phase transition, precursory electronic anomaly, and strong-coupling superconductivity in quasi-skutterudite (Sr1−xCax)3Ir4Sn13 and Ca3Rh4Sn13. Chinese Physics B, 2018, 27(7): 077401  
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Structural phase transition, precursory electronic anomaly, and strong-coupling superconductivity in quasi-skutterudite (Sr1−xCax)3Ir4Sn13 and Ca3Rh4Sn13
Luo Jun1, 2, Yang Jie1, †, Maeda S3, Li Zheng1, 2, Zheng Guo-Qing1, 2, 3, ‡
Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Department of Physics, Okayama University, Okayama 700-8530, Japan

 

† Corresponding author. E-mail: yangjie@iphy.ac.cn gqzheng123@gmail.com

Project supported by the National Natural Science Foundation of China (Grant Nos. 11674377 and 11634015), the National Key R&D Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300502), and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB07020200). J. Y. is supported by the Youth Innovation Promotion Association of CAS.

Abstract

The interplay between superconductivity and structural phase transition has attracted enormous interest in recent years. For example, in Fe-pnictide high temperature superconductors, quantum fluctuations in association with structural phase transition have been proposed to lead to many novel physical properties and even the superconductivity itself. Here we report a finding that the quasi-skutterudite superconductors (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3Rh4Sn13 show some unusual properties similar to the Fe-pnictides, through 119Sn nuclear magnetic resonance (NMR) measurements. In (Sr1−xCax)3Ir4Sn13, the NMR linewidth increases below a temperature T* that is higher than the structural phase transition temperature Ts. The spin-lattice relaxation rate (1/T1) divided by temperature (T), 1/T1T and the Knight shift K increase with decreasing T down to T*, but start to decrease below T*, and followed by more distinct changes at Ts. In contrast, none of the anomalies is observed in Ca3Rh4Sn13 that does not undergo a structural phase transition. The precursory phenomenon above the structural phase transition resembles that occurring in Fe-pnictides. In the superconducting state of Ca3Ir4Sn13, 1/T1 decays as exp(−Δ/kBT) with a large gap Δ = 2.21kBTc, yet without a Hebel–Slichter coherence peak, which indicates strong-coupling superconductivity. Our results provide new insight into the relationship between superconductivity and the electronic-structure change associated with structural phase transition.

PACS: 74.25.nj;74.40.-n;74.25.Dw
Keyword:nuclear magnetic resonance;antiferromagnetic fluctuation;structural phase transition;phase diagram
1. Introduction

Transition-metal compounds show diverse properties such as magnetism, superconductivity, and charge density wave, and often accompany a structural transition.[1–3] In these materials, the interplay between superconductivity and other orders is of great interest. For example, in the copper oxides,[4] heavy fermions,[5] and iron-based superconductors[6] that contain transition metal elements, superconductivity is found in the vicinity of a quantum critical point (QCP) at which other orders are completely suppressed at absolute zero temperature. In particular, in iron-based superconductors, not only a magnetic (spin density wave) QCP, but also another QCP associated with the structural phase transition exists.[7] In this case, quantum fluctuations of the electronic nematic order associated with the structural phase transition may lead to many novel physical properties such as T-linear electrical resistivity.[7–10]

Materials with the general stoichiometry R3M4X13 are a large family usually adopting a common quasi-skutterudite structure, where R is an alkaline-earth or rare-earth element, M is a transition metal, and X is a group-IV element.[11,12] Superconductivity with a fairly high transition temperature Tc ∼ 7 K was found in R3M4Sn13 more than 30 years ago,[13,14] but the physical properties were poorly understood. Recently, this class of materials received new attention because of a possible interplay between the superconductivity and the structure instability.

The electrical resistivity, susceptibility, Hall coefficient, and heat transport measurements on Ca3Ir4Sn13 found that an anomaly occurs at a temperature of 35 K, above the superconducting transition temperature Tc = 7 K.[15–17] The anomaly was ascribed to ferromagnetic spin fluctuation in early works.[15] Resistivity and susceptibility measurements on Sr3Ir4Sn13 also showed anomalies at 147 K. Subsequent x-ray diffraction and pressure effect measurements on Sr3Ir4Sn13 showed that a structural phase transition from a cubic I phase ( ) to an I′ phase ( ) takes place at Ts, with the lattice parameter doubled in the low temperature phase. Therefore, the anomalies reported earlier in this class of materials are due to the structural phase transition. By chemical or physical pressure, Ts can be suppressed to zero, while Tc increases slowly and reaches to a maximum 8.9 K.[18] A similar phase diagram has also been obtained in (Sr1−xCax)3Rh4Sn13.[19] Thus, a possible relation between the enhanced Tc and the structure instability was suggested.[18,20]

The nature of the electronic structure change due to the structural phase transition is not well understood. Neutron scattering and specific heat measurements revealed a second-order nature of the structural phase transition in (Sr1−xCax)3Ir4Sn13.[21,22] The Hall coefficient changed from a negative to a positive value and the optical measurement indicated that the Drude spectral weight is transferred to the high energy region across Ts in Sr3Ir4Sn13.[23,24] Based on these results, a reconstruction of the Fermi surface below Ts due to a charge density wave (CDW) formation was suggested.[23,24]

In this work, we grow single crystals of (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3Rh4Sn13, and perform electrical resistivity and 119Sn NMR measurements to elucidate the electronic properties change associated with the structural phase transition. (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) undergo a structural phase transition at Ts = 147 K, 85 K, and 35 K, respectively, while Ca3RH4Sn13 does not. By NMR measurements, we find that an anomaly occurs already above Ts in (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1). Such an electronic anomaly prior to the structural transition resembles an actively-investigated phenomenon in some of the Fe-based superconductors where the physical properties show an in-plane anisotropy (nematicity) above Ts below which the C4 symmetry is lowered to the C2 symmetry. However, in Ca3RH4Sn13 that does not undergo a structural transition, the Korringa relation is satisfied down to T ∼ 20 K. The electronic state properties below T* are discussed by analyzing the change in the Korringa ratio. We also measure the superconducting state property of Ca3Ir4Sn13, and find that it is a strong-coupling s-wave superconductor. We will discuss the relationship between the superconductivity, the electronic state change associated with the structural transition, and electron correlations.

2. Experiment

Single crystals of (Sr1−xCax)3Ir4Sn13 and Ca3RH4Sn13 were grown by the self-flux method, as previously reported in Ref. [13]. The composition shown in this paper is the nominal one. Excessive Sn flux was removed in concentrated HCl acid. Crystals with the proper size were picked up and polished, then the temperature dependence of the resistivity was measured by the standard four-probe method using a physical properties measurement system (PPMS, Quantum Design). The Tc was determined by both DC susceptibility using a magnetic properties measurement system (MPMS, Quantum Design) with an applied magnetic field of 10 Oe, and AC susceptibility using an in-situ NMR coil. For 119Sn NMR measurements, since the sample shows a good electrical conductivity so that the skin depth is short, we crushed the single crystals into fine powders to gain the surface area. The 119Sn nucleus has a nuclear spin I = 1/2 and gyromagnetic ratio γn/2π = 15.867 MHz/T. The 119Sn NMR spectra were obtained by scanning the rf frequency and integrating the spin echo intensity at a fixed magnetic field H0. The spin-lattice relaxation time T1 was measured by using the saturation-recovery method, and obtained by a good fitting of the nuclear magnetization M(t) to 1 − M(t)/M0 = exp(−t/T1), where M(t) is the nuclear magnetization at time t after the single saturation pulse and M0 is the nuclear magnetization at thermal equilibrium.

3. Results
3.1. Sample characterization

Figure 1(a) presents the temperature dependence of the electrical resistivity for (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13 single crystals. For (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1), the resistivity shows a distinct hump, which has been ascribed to a structure transition.[18] Figure 1(b) shows the temperature dependence of the DC magnetic susceptibility below 9 K. A sharp superconducting transition with a narrow transition width of about 0.2 K for Sr3Ir4Sn13, Ca3Ir4Sn13, and Ca3RH4Sn13 indicates the good crystal quality. The Tc is determined by the point at which the magnetic susceptibility begins to decrease. The Meissner shielding fraction is estimated to be over 90%, which proves the bulk nature of the superconductivity.

Fig. 1. (color online) (a) The temperature dependence of the electrical resistivity for (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13. The arrows indicate the structural transition temperature Ts. (b) The temperature dependence of the magnetic susceptibility for (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13 below T = 9 K. The arrows indicate the critical temperature Tc.
3.2. Precursory electronic anomaly above Ts

Since 119Sn (I = 1/2) has no quadrupole moment, the nuclear spin Hamiltonian is simply given by the Zeeman interaction , where K is the Knight shift and γn is the nuclear gyromagnetic ratio. As expected in a material with a cubic crystal structure, a single 119Sn NMR transition line (m = −1/2 ↔ m = 1/2 transition) is observed. Considering that the Sn atoms form an icosahedral cage in the crystal structure and there are two different crystallographic sites (see Fig. 2), namely, one Sn(1) in the center and twelve Sn(2) on the vertices of the icosahedron, the spectrum should have two peaks. Figure 2 shows the frequency-swept 119Sn-NMR spectra measured at T = 250 K under a fixed magnetic field for the four samples. It can be seen that the spectra indeed show two peaks. All the spectra can be fitted by two Gaussian functions with an area ratio of 12:1, so the low frequency peak and high frequency peak respectively correspond to Sn(2) and Sn(1), which have an occupancy ratio of 12:1. The typical fitting curves at 250 K are shown in Fig. 2.

Fig. 2. (color online) The crystal structure of (Sr1−xCax)3Ir4Sn13 and Ca3RH4Sn13 that contain two different Sn sites, and the 119Sn-NMR spectra for (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13 at 250 K. The horizontal coordinate represents the reduced frequency f/f0, with f0 = γH0/2π. The blue and red dotted lines are Gaussian fittings to the obtained spectra with area ratio of 1 : 12. The solid lines are the sum of the two Gaussian functions.

Below we discuss the normal-state properties inferred from the NMR measurements. Figure 3 shows the temperature dependence of the spectra for the four samples, from which the full width at half maximum (FWHM) of the spectra is obtained as shown in Fig. 4. Usually, one expects that the FWHM of the spectra increases below the structural phase transition temperature, below which four types of Sn(2) sites are formed[18] that may have slightly different K and result in broadening of the spectra. However, as can be seen in Fig. 4, the FWHM starts to increase at a temperature T* that is above Ts.

Fig. 3. (color online) The temperature dependence of the 119Sn-NMR spectra for (a)–(c) (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and (d) Ca3RH4Sn13. The two peaks marked by the blue and red arrows correspond to Sn(1) site and Sn(2) site, respectively.
Fig. 4. (color online) The temperature dependence of FWHM of the NMR spectra, 1/T1T, and the Knight shift K of (a)–(i) (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and (j)–(l) Ca3RH4Sn13. The blue and red filled circles correspond to Sn(1) and Sn(2) sites, respectively. The purple dash lines indicate structural transition temperature Ts. The black dash dot lines indicate the temperature T* below which anomalies appear.

Figure 4 also shows the temperature dependence of 1/T1T and the Knight shift K for the four samples. The K was obtained from the Gaussian fitting of the spectra. T1 was measured at the position of the respective two peaks. It can be seen that 1/T1T and K also decrease below T*, and followed by a more distinct change at Ts. For (Sr0.5Ca0.5)3Ir4Sn13 and Ca3Ir4Sn13, the anomaly is pronounced, although it is less clear for Sr3Ir4Sn13. A previous report in Ca3Ir4Sn13 that 1/T1T decreases below around 75 K is consistent with our results.[25]

The total Knight shift consists of three parts, K = Kdia + Korb + Ks, where Kdia arises from the diamagnetic susceptibility χdia, Korb from the orbital (Van-Vleck) susceptibility χorb, and Ks from the spin susceptibility χs. The χs is estimated to be 8.1 × 10−4 emu/mol according to , where N(0) = 12.5 eV−1 per formula unit is the density of states at the Fermi level.[26] The closed shells or fully occupied electronic bands contribute to the diamagnetism, which is proportional to the atomic number and the atomic radius. Since iridium has a large atomic number, the reported diamagnetic susceptibility of Sr3Ir4Sn13, which is −1.2 × 10−4 emu/mol above Ts,[18,23] is mainly due to iridium, whose contribution is −9.8 × 10−4 emu/mol.[15] The χorb is temperature-independent, and is usually much smaller than χs. After considering different contributions, the total susceptibility can be diamagnetic as reported.[18,23] However, the Ir diamagnetism has no hyperfine coupling to Sn nuclear spins. Thus the Sn Knight shift is mainly due to χs, and is positive, as found in our measurement.

In general, 1/T1T probes the transverse imaginary part of the dynamic susceptibility ( ) and can be written as

where A(q) is the hyperfine coupling constant, ω is the NMR frequency, and γe is the electronic gyromagnetic ratio. In a simple metal with no electron correlation, 1/T1T is reduced to a constant proportional to N(0)2. On the other hand, Ks due to spin susceptibility is proportional to N(0). As a result, a relation between the two quantities (Korringa relation), , is obtained. Therefore, a decrease of 1/T1T and K below Ts is usually encountered, as a reduction of the density of states (DOS) can be expected. A closer look into the data finds that 1/T1T and K decrease more rapidly at the Sn(2) site than that at the Sn(1) site. This indicates that the Sn(2) site has a closer relationship with the transition. This is consistent with the neutron and x-ray scttering experiments that have found a breathing mode of phonon due to Sn(2) atoms, which is softened at Ts.[21] In contrast to (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1), we did not detect any anomaly in the temperature dependence of 1/T1T, K, and FWHM of Ca3RH4Sn13 above 20 K, as shown in Fig. 4(j)–4(l). This is consistent with the fact that Ca3RH4Sn13 does not undergo a structural phase transition.

The anomaly seen in 1/T1T and K at T* resembles a puzzling phenomenon in the Fe-based superconductors such as BaFe2−xCoxAs2, BaFe2(As1−xPx)2, or NaFe1−xCoxAs,[27–29] where nematic properties already appear at a temperature far above Ts. In this class of Fe-based materials, a C4 to C2 structural phase transition place at Ts. It also shares some similarities with the pseudogap behaviors in underdoped copper oxide superconductors, where the DOS starts to decrease before the superconducting phase transition.[30] In any event, the precursory electronic anomaly above the Ts suggests that the structural phase transition is electronically-driven, rather than lattice-driven.

3.3. Electronic-state change below T*

Next, we examine if the electronic-state change below T* can be totally ascribed to a loss of the DOS. In Fig. 5(a), we plot K against (T1T)−1/2 for Ca3RH4Sn13. In the temperature range 20 K< T < 250 K, a good linear relation is found between K and (T1T)−1/2, as expected for a conventional metal in which both (T1T)−1/2 and Ks are proportional to the DOS. Deviation from the linear relation below T = 20 K will be discussed later. From the intercept of the relation, we obtain Korb = 0.34 ± 0.01%.

Fig. 5. (color online) (a) The relationship between (T1T)−1/2 and K for Ca3RH4Sn13, with temperature as an implicit parameter. The red solid line is a linear fitting to the data above T = 20 K. The solid violet squares and open violet squares represent points above and below 20 K, respectively. (b) The Korringa ratio as a function of temperature for (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13. The dash arrows indicate T*. The solid arrows indicate Ts. The dashed straight line is the guide to the eyes.

For (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1), however, the temperature dependence of (T1T)−1/2 and K is weak at high temperatures so that a similar plot does not yield meaningful information. Instead we plot the so-called Korringa ratio S as a function of temperature in Fig. 5(b), where S is defined as For a conventional metal, S = 1. As one can see, S is constant for Ca3RH4Sn13 above T = 20 K within the experimental error, which is also true for (Sr1−xCax)3Ir4Sn13 above T*. However, S shows a distinct decrease below T* for (Sr1−xCax)3Ir4Sn13, which suggests that the reduction of 1/T1T and K cannot simply be ascribed to a loss of the DOS. Below, we discuss possibilities for the decrease of S.

Firstly, a second-order phase transition often accompanies the development of a short-range correlation just above the transition temperature, thus the structural instability may be responsible for the anomaly seen in our NMR data. Theoretical calculations of phonon dispersion suggest that imaginary phonon modes exist in Sr3Ir4Sn13 and the lattice instabilities lie at some wave vectors.[26] Neutron scattering data have shown the softening of phonon mode towards Ts.[21] Specific heat measurements on Sr3Ir4Sn13 also show that ΔC/T starts to increase at 160 K (Ts = 147 K) and the critical fluctuation model can fit the specific heat data well, which leads to the proposal of short-range correlation above Ts.[22] Therefore, the NMR quantities may also be affected by such structural short-range correlation through magneto–elastic coupling, resulting in the deviation from the Korringa relation below T*. On the other hand, we note that, for a CDW case, the quantity 1/T1T will increase with decreasing temperature towards the transition temperature,[31,32] in contrast to a decrease of 1/T1T observed in the present case.

Secondly, we discuss the possibility of magnetic correlations. To explore this issue in more detail, we turn to the data at temperatures below T = 20 K. In Fig. 6, we compare 1/T1T of the four samples. Above 160 K, 1/T1T for all samples has the same value and shows a similar temperature variation. Below 160 K, 1/T1T of Ca3RH4Sn13 increases all the way down to 4.2 K, while that of (Sr1−xCax)3Ir4Sn13 is reduced below T*. Interestingly, we note that, in all samples, there exists an upturn at a low temperature below T = 20 K, as indicated by the black arrows. Such upturn is quite pronounced particularly in Ca3RH4Sn13. It can be seen from Fig. 4 that 1/T1T shows a clear upturn for (Sr1−xCax)3Ir4Sn13, while the Knight shift is T-independent in such a temperature range. For Ca3RH4Sn13, the temperature dependencies of 1/T1T and K also deviate from the Korringa relation below T = 20 K due to the additional increase of 1/T1T. Therefore, the upturn is clearly not due to a change in the DOS or the structural instability, since the upturn is away from Ts and Ca3RH4Sn13 even does not undergo a structural phase transition. Previously, anharmonic phonons due to the rattling motion of the ions inside the cage have been proposed to contribute an additional relaxation,[33] and possibly have been seen in filled-skutterudites LaOs4Sb12 and LaPt4Ge12.[34,35] In the systems, one might also expect that the Sn(1) atoms rattle inside the cage and contribute additionally to 1/T1T. However, our data show that the Sn(1) and Sn(2) sites exhibit the same behavior, even though the Sn(2) atoms are not involved in the rattling motion. Therefore, the possibility of rattling as a cause for the upturn in 1/T1T may be excluded. Rather, the rise of 1/T1T at low temperatures likely originates from antiferromagnetic spin fluctuations, which cause an increase of at a finite q when the temperature is lowered. Therefore, coming back to Fig. 5(b), we believe that, the reduction of S is more likely due to antiferromagnetic spin fluctuations that develop below T* and become more evident at low temperatures.

Fig. 6. (color online) The temperature dependence of 1/T1T for (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13. The dash arrows indicate T*. The solid arrows indicate Ts. The solid black arrows mark the temperature below which 1/T1T shows an upturn.
3.4. Phase diagram

In Fig. 7, we display the phase diagram of (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13. The lattice constant of (Sr1−xCax)3Ir4Sn13 shrinks linearly upon substituting Sr with Ca. Therefore, increasing calcium content x is equivalent to applying a hydrostatic pressure (P).[18] We note that Hu et al. have also scaled (Sr1−xCax)3Ir4Sn13 and (Sr1−xCax)3RH4Sn13 in one phase diagram.[36] When a pressure of 25.7 kbar is applied to Sr3Ir4Sn13, Ts and Tc become almost the same as those of (Sr0.5Ca0.5)3Ir4Sn13. Such a phenomenon also occurs between (Sr0.5Ca0.5)3Ir4Sn13 and Ca3Ir4Sn13.[18] These results suggest that the change in x (Δx = 1) corresponds to a change in pressure of ΔP = 52 kbar. The Ts extrapolates to zero temperature at P = 18 kbar in Ca3Ir4Sn13.[18] In the (Sr1−xCax)3RH4Sn13 series, Ts extrapolates to zero temperature at x = 0.9, or equivalently, at P = −6.8 kbar relative to Ca3RH4Sn13.[19] Based on these results, we obtain the relative pressure for our samples with respect to Ca3Ir4Sn13, and construct a phase diagram as shown in Fig. 7.

Fig. 7. (color online) The phase diagram of (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13. T* and Ts are obtained from NMR spectral line width, 1/T1T, and the Knight shift. For Sr3Ir4Sn13, the anomaly above Ts can be identified from 1/T1T but less clear in FWHM and K, thus we plot T* = Ts ± 10 K. The yellow region is a crossover rather than a new phase. The correspondence between the pressure and the composition is inferred from Refs. [18] and [19].

As the pressure increases, Ts and T* are suppressed while Tc increases slowly, which means that there exists a competition between the structural phase transition and superconductivity. A similar phase diagram has been seen in other systems such as LaPt2−xGe2+x,[37] where Tc increases from 0.41 K to 1.95 K and Ts decreases from 394 K to 50 K. Note that the Knight shift and thus the electronic DOS remain T-independent at low temperatures, while its absolute value increases from Sr3Ir4Sn13 to Ca3RH4Sn13. Therefore, the increase of DOS may be partly responsible for the increase of Tc.

Ca3RH4Sn13 is located near the end point of the T* curve, and its superconducting transition temperature Tc = 8 K is close to the highest value of this class of materials under chemical or physical pressures. In cuprates and Fe-based superconductors, Tc has a close connection to magnetic fluctuations or structural/orbital fluctuations. Although it is not clear at the moment how the antiferromagnetic spin fluctuations found in this work are related to the structural phase transition, the antiferromagnetic spin fluctuations may also contribute to the increase of Tc. In fact, a systematic change of the Korringa ration S is found as the chemical pressure is increased, as seen in Fig. 5(b). This is a direction to be explored in the future.

3.5. Superconducting properties

In this section, we discuss the properties of Ca3Ir4Sn13 in the superconducting state. In order to minimize the effect of the external field, we have performed NMR measurements for the Sn(2) site under a low field of H0 = 0.4 T that is much smaller than Hc2 ≈ 7 T. The Tc is 6.4 K at H0 = 0.4 T. The 119Sn Knight shift below Tc(H) is shown in Fig. 8(a). At the low temperature of 1.5 K, the Knight shift approaches a value of 0.32%, which is very close to Korb = 0.34 ± 0.01% obtained from Fig. 5(a) for Ca3RH4Sn13. The small excess reduction at T = 1.5 K (by about 0.02%) could be due to the diamagnetism of the vortex lattice.[38] The result indicates that the spin susceptibility vanishes completely at T = 1.5 K, which indicates that the Cooper pairs are in the spin-singlet state.

Fig. 8. (color online) (a) The temperature dependence of the Knight shift for Ca3Ir4Sn13 at H0 = 0.4 T. The arrow indicates Tc. (b) The temperature dependence of 1/T1 below 10 K. (c) The temperature dependence of 1/T1 below Tc in semilogarithmic coordinate. The solid line represents the relation 1/T1 ∝ exp(−Δ/kBT).

Figure 8(b) shows the temperature dependence of 1/T1. There are two noticeable features. One is that 1/T1 decreases exponentially over three decades with decreasing temperature. The other is that 1/T1 shows no Hebel–Slichter coherence peak just below Tc. The lack of a Hebel–Slichter coherence peak was previously reported in filled-skutterudite PrOs4Sb12.[39] To see the decay more intuitively, we replot 1/T1 in a semilogarithmic scale in Fig. 8(c). As can be seen, a straight line of the relation 1/T1 ∝ exp(−Δ/kBT) fits the data well down to 1.5 K, where Δ and kB denote the superconducting energy gap at T = 0 and the Boltzmann constant, respectively. The fitting parameter 2Δ = 4.42kBTc is obtained, which is larger than the BCS gap size 2Δ = 3.53kBTc. Our result is different from an earlier NMR measurement on Ca3Ir4Sn13, where a small Hebel–Slichter peak was claimed.[40] The large superconducting energy gap suggests strong-coupling superconductivity, which is consistent with the muon spin rotation measurements and specific heat experiments.[41–43] Our result is similar to that of the Chevrel phase superconductor TlMo6Se7.5,[44] in which NMR experiments also revealed a large gap, yet with no coherence peak due to the strong phonon damping that suppressed the coherence peak below Tc.[45]

4. Conclusion

We have grown single crystals of (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3RH4Sn13, and performed electrical resistivity and 119Sn NMR measurements. In the normal state, we found an anomaly at T* above the structural phase transition temperature Ts in (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1). The NMR line width increases below T* and 1/T1T and K begin to decrease, followed by more distinct changes at Ts. None of these anomalies was observed in Ca3RH4Sn13 that does not undergo a structural phase transition. Our detailed analysis of (Sr1−xCax)3Ir4Sn13 suggests antiferromagnetic spin fluctuations developing below T* and becoming more visual below T ∼ 20 K as a possible cause. The increase of Tc from Sr3Ir4Sn13 to Ca3RH4Sn13 can be partly ascribed to the increase of the electronic DOS, but the antiferromagnetic spin fluctuations may also make a contribution. Remarkably, the precursory electronic anomaly shares a similarity with a phenomenon under active investigation in the Fe-based high-Tc superconductors where a change in the electronic properties expected at T* occurs already above Ts. Therefore, our work sheds light on other correlated electron systems in a broad context.

In the superconducting state of Ca3Ir4Sn13, the spin susceptibility vanishes at low temperature, indicating a spin-singlet electron pairing. The spin-lattice relaxation rate decays exponentially with decreasing temperature as exp(−Δ/kBT), which indicates a fully opened energy gap. The large superconducting gap 2Δ = 4.42kBTc accompanied by a lack of the coherence peak indicates that Ca3Ir4Sn13 is a strong-coupling superconductor.

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