High Pressure Properties for Electrical Resistivity and Ce Valence State of Heavy-Fermion Antiferromagnet Ce2NiGa12

A heavy-fermion antiferromagnet Ce2NiGa12 has been studied at a viewpoint of pressure effects. Electrical resistivity measurements show that the antiferromagnetic ordering is suppressed at PC ~ 5.5 GPa, and that Fermi liquid behaviour is observed above PC. To investigate how Ce valence state is associated with the observed critical phenomena, X-ray absorption spectra at Ce L3-edge have been performed. Ce valence state drastically varies at Pv ~ 9 GPa in the initial applying pressure process, whereas anomalous behaviour is not observed in the Ce valence under pressures around PC. Consequently, the quantum critical phenomena in Ce2NiGa12 around PC is not strongly connected with Ce valence state.


Introduction
Quantum criticality phenomena have attracted much attention for exotic physical properties such as spin and orbital ordering, unconventional superconductivity, and magnetic phase transitions. Such phenomena have been observed in many Ce intermetallic compounds [1]. In particular, the unconventional superconductivity often appears near a quantum critical point (QCP), at which the magnetic order disappears. Moreover, the QCP can be controlled by external fields such as pressure and magnetic field since a competition between RKKY interaction and Kondo effect has an influence on the QCP. Recently, several theoretical approaches for the unconventional superconductivity have been proposed [2][3][4]. Among them, importance of valence transition near the QCP is predicted [3], and a number of experimental efforts for valence transition have been performed in Ce intermetallic compounds [5,6]. However, an association of the QCP with the valence transition still remains as an open question.
Pressure as external fields provides large energy to the electron system compared with magnetic field because pressure directly affects band structure through the hybridization of electronic states. In fact, pressure-induced heavy-fermion (HF) superconductors have been reported for the Ce-based intermetallic compounds such as CeCu 2 Si 2 and CeCoIn 5 whose crystallized symmetry is tetragonal [7,8]. Ce 2 MGa 12 (M=Ni, Pd, and Pt) also crystallizes in the tetragonal symmetry (space group P4/nbm), and the Ce atom is aligned in a two-dimensional square lattice site perpendicular to the c-axis [9].
Moreover, these compounds have been reported as HF antiferromagnets with Néel temperature T N = 10, 11, and 7 K the ground state at ambient pressure (AP) for M = Ni, Pd, and Pt, respectively. Therefore, it is important to investigate the properties of isostructural Ce compounds for understanding the quantum criticality behavior from a view point of Ce valence state.
To capture the valence transition, X-ray absorption spectroscopy (XAS) at Ce L 3 -absorption edge is suitable for observation of pressure effect because chemical shift occurs in the spectrum due to valence transition [10]. To study the quantum criticality of Ce 2 NiGa 12 and its Ce valence state, the electrical resistivity and XAS measurements were performed under high pressure and low temperature.

Experimental
Single crystals of Ce 2 NiGa 12 is synthesized by a gallium self-flux method [11]. Crystal structure with tetragonal P4/nbm is confirmed by the X-ray powder diffraction using Cu Kα line. Estimated lattice parameters, a = 0.6108 nm and c = 1.5506 nm, are slightly larger than those of previous report [9]. The electrical resistivity measurements at high pressure were performed by Palm Cubic Anvil Cell. Gasket of MgO and pressure medium of glycerin were used. Pressure is applied up to 8.0 GPa in a temperature range of 0.45 ~ 300 K. The residual resistivity ratio was evaluated to be ~14 at AP.
Diamond-Anvil-Cell (DAC) is often used as a high-pressure cell for XAS measurements. A compact DAC with φ23.5 × 17t mm made of CuBe alloy was used to achieve lower temperature below 10 K. This compact DAC can be easily inserted to the superconducting magnet or cryostat. Pressure variation between 300 K and 4 K depends on the culet size of anvils. The variation of 30~40% and 5~10% was observed by using anvils with culet diameter of 300 and 600 μm, respectively.
Nano-Polycrystalline Diamond (NPD) anvils with culet diameter of 300 μm and with height of 1.0 mm were used to avoid glitches in XAS spectra [12,13]. A tapered hole with depth of 0.7 mm is fabricated to one anvil in pressure direction to increase X-ray intensity. X-ray transmissivity is improved 22 times higher by the fabrication for X-ray energy of 5.72 keV. Within present work, a fabricated NPD anvil withstands pressure of 15 GPa at 3.4 K.
XAS measurements at high pressure were performed at BL39XU of SPring-8 facility [14]. All measurements were carried out in transmission mode using ionization chambers. X-ray beam of 2 (vertical) × 9 (horizontal) μm 2 is focused on the sample position by Kirkpatrick and Baez mirror [15]. The compact DAC was mounted on the pulse-tube type cryostat and temperature cools down to 3.4 K. A small chip of single crystal was put into the sample room of φ100 μm, and mixed liquid of methanol:ethanol = 4:1 was used as a pressure-transmitting medium. Pressure at both low temperature and room temperature inside the DAC was estimated by ruby-fluorescence method [16]. Figure 1 shows a magnetic component of electrical resistivity (ρ mag ) dependent on temperature in Ce 2 NiGa 12 at selected pressures, where ρ mag is obtained by subtracting the resistivity of the isostructural non-magnetic La 2 NiGa 12 compound [9]. ρ mag at AP shows a typical HF feature of Ce compounds, i.e. a cusp peak due to an antiferromagnetic (AFM) ordering at T N = 10 K and a broad maximum due to Kondo scattering at T H max = 60 K are observed in ρ mag curve. As increasing pressure, the overall ρ mag increases in magnitude whereas the peak position at T H max decreases. The T N decreases with increasing pressure, and another anomaly appears at T N2 < T N above 2.7 GPa. With further increasing pressure, both T N and T N2 are suppressed and no longer visible above 5.8 GPa, indicating the disappearance of AFM ordering at P C ~ 5.5 GPa. At low temperatures near P C , there appears an additional broad peak at T L max , which increases with pressure above 5.3 GPa.

Results and Discussion
The behavior of ρ mag at low temperature region is analyzed according to Fermi-liquid (FL) character, ρ mag = ρ 0 + AT 2 , where ρ 0 represents a residual resistance for Ce 2 NiGa 12 . The pressure dependence of ρ 0 and A values are shown in figure 2(a). Both ρ 0 and A are enhanced with approaching P C . In addition, ∝ ( max L ) relation is also satisfied above 5.8 GPa as shown in figure 2(b). The relationship indicates that FL state realizes in Ce 2 NiGa 12 above P C . Therefore, T L max is associate with the Kondo temperature T K , which increases with applying pressure as observed in Ce-based HF compounds [17]. Figure 3 shows the pressure-temperature (P-T) phase diagram of Ce 2 NiGa 12 drawn by the characteristic temperatures. The P-T phase diagram clearly shows that the FL phase appears around P C after disappearance of AFM ordering with applying pressure. In addition, the ρ 0 value is enhanced inside the AFM phase (see figure 2(a)). Similar results have been observed in CeAl 2 and CeCu 5 Au [18,19]. It is suggested that the ρ 0 enhancement is attributed to the energy scale of T K comparable to T N [4]. Another possibility is that quantum criticality of valence fluctuation induces instability of ρ 0 [3]. In particular, the latter possibility can be explored since the estimation of Ce valence state under high pressure is feasible by XAS measurements.    The spectral profile at AP indicates Ce trivalent state, reflecting localized f electron feature. As increasing pressure up to 9 GPa, the profile moderately changes with pressure, i.e. a main-peak (called white-line) intensity at 5726.0 eV decreases and the intensity of a shoulder structure at 5735.7 eV increases. This variation is well known as valence variation [10]. However, no anomaly of Ce valence variation is observed around P C . Therefore, the quantum critical phenomena in Ce 2 NiGa 12 observed by electrical resistivity may not be strongly connected with Ce valence state. On the other hand, a drastic change in XAS profile, in which the shoulder structure at 5735.7 eV becomes clear, is observed above 10 GPa. The phenomenon obviously indicates Ce valence transition.
To elucidate pressure-dependent Ce valence, XAS profiles were analyzed by the profile fitting method as shown in figure 4(b). The averaged Ce valence is obtained by the rate of Ce 4+ content to Ce 3+ one. The result estimated by the fitting is shown in figure 4(c). Ce valence is almost trivalent at AP. The valence moderately increases with pressure up to P v ~ 9 GPa, and is suddenly enhanced above P v . The change rate is comparable to the case in Ce γ-α transition [20]. Here, it is necessary to distinguish the spectral change due to valence variation from the effect of lattice compression according to the Natoli's rule, k·r = constant, where k and r represent X-ray wave number (∝ E -1/2 ) and interatomic distance, respectively [21]. Natoli's rule gives energy shifts for XAS profile so that moderate variation of Ce valence below P v seems to be the effect of Natoli's rule.
Ce valence state was investigated for pressure-decreasing process. As shown in figure 4(c), Ce valence returns to the previous state for pressure-decreasing process. However, Ce valence for reapplying process is different from that for initial applying-pressure process. On the other hand, the result in another sample is the same as the pressure variation for both increasing and decreasing processes. The difference is attributed to the strain of sample for powderization of single crystal. The situation is often observed in intermetallic compounds such as CeCu 6-x Au x [22]. In fact, different pressure dependence is observed in Ce valence state when pressure decreases after applying above P v . The crystal structure of Ce 2 NiGa 12 might change above P v . Note that the sample for electrical resistivity measurements is corresponding to the initial applying process because of no strain for shape forming. Further investigation such as X-ray powder diffraction and/or electrical resistivity measurements are necessary to discuss Ce valence state in higher pressure region above P v .
XAS measurements at low temperature were also performed. We succeeded in measuring at 3.4 K up to 15 GPa. Unfortunately, the measurements were performed for only reapplying process. Within current results, no temperature dependence of Ce valence was observed. In addition, pressure dependence at low temperature is as same as the result at room temperature.
For Ce 2 NiGa 12 , absence of obvious valence transition near P C provides no correlation between the quantum critical phenomena and Ce valence state. The situation might be similar to the case of CeCu 2 Si 2 , in which the different characteristic pressures P C and P v are located on two superconducting domes in P-T phase diagram [23]. Moreover, it seems that P v agrees the pressure which T H max merges into T L max . To ensure the appearance of P v , low temperature measurements are required for the initial applyingpressure process. Additionally, structural information and electrical resistivity at higher pressure are desired since the drastic variation of Ce valence above P v is curious.

Conclusion
The electrical resistivity and XAS measurements at Ce L 3 -edge in Ce 2 NiGa 12 were performed under high pressure. Quantum criticality phenomena were observed at P C ~ 5.5 GPa in the electrical resistivity. To investigate a relationship between Ce valence state and the quantum criticality, XAS spectra up to 15 GPa were analyzed. Ce valence is drastically enhanced above P v ~ 9 GPa only in the initial applying pressure process. The result indicates that Ce valence variation is not directly associated with the quantum criticality in Ce 2 NiGa 12 around P C . Detailed study of electrical resistivity and crystal structure determination above P v is necessary to discuss about the Ce valence variation.