Investigation of the Atomic Coordinates of CeNiC2 under Pressure: Switching of the Ce-Ce First Nearest Neighbor Direction
Uwatoko Group
CeNiC2 is notable for its unique properties, including heavy fermion behavior and multiple magnetic orderings. As the temperature decreases, CeNiC2 undergoes an incommensurate antiferromagnetic transition (ICAF) at TICAF ~ 20 K, followed by a commensurate antiferromagnetic transition at TCAF ~ 10 K, and ferromagnetic ordering below 2.2 K. TICAF increases with pressure, reaching a maximum around 7 GPa. Beyond 11 GPa, the ICAF order is suppressed, and a SC dome with a maximum Tc ~ 3.5 K appears. This SC state has a large upper critical field, Hc2(0) ~18 T, nearly three times the Pauli paramagnetic limiting field, indicating an unconventional nature of the SC state. CeNiC2 has the highest Tc among Ce-based heavy fermion superconductors [1]. In NCS superconductors, antisymmetric spin-orbit coupling can occur due to the lack of inversion symmetry, favoring spin-triplet Cooper pairing with large Hc2(0). Also, NCS superconductors can host a mix of spin-triplet and singlet pairing. While CeNiC2 has an NCS crystal structure at ambient pressure, it is unclear if this structure is maintained across the pressure range where the SC state appears. Subtle variations in interatomic distances under pressure can significantly affect the magnetic and electronic properties of heavy fermion materials. However, obtaining precise structural information under pressure is essential for understanding CeNiC2’s properties, although challenging. This study investigates the effect of pressure on CeNiC2’s atomic coordinates using single crystal X-ray diffraction (XRD) measurements at room temperature up to 18.6 GPa.
High-quality single crystals of CeNiC2 were grown using the Czochralski pulling method in an Argon gas environment, with high-purity Ce, Ni, and C atomes. Single crystal X-ray diffraction at 293(2) K was conducted using a Rigaku XtaLab MicroMax007 HFMR with Mo-Kα radiation and a HyPix6000 diffractometer. The crystal structure was solved using Olex2 with SHELXT 2018/2 and refined with SHELXL 2018/3. High-pressure experiments utilized a diamond anvil cell (DAC) with a 300 μm culet size. A CeNiC2 single crystal (~100 μm) was loaded into the DAC with a ruby pressure manometer, and a 4:1 methanol-ethanol mixture served as the pressure transmitting medium.
Figure 1(b) shows the normalized unit-cell parameters and unit-cell volume of CeNiC2 in the pressure range from 0 to 18.6 GPa. The normalized unit-cell parameters show anisotropic compressibility under pressure; the length of the a-axis decreases at a much faster rate compared to the b- and c-axes. The compressibility of the a-axis (ka = d(a/a0)/dP = −3.70 × 10-3) is the highest, whereas the b-axis is the lowest (kb = d(b/b0)/dP = −1.39 × 10-3 GPa-1). The unit-cell parameters decrease linearly with pressure, showing no structural phase transition. Compressibility is anisotropic, with the a-axis compressing fastest. The bulk modulus B0 is ~134 ± 3 GPa with B0’ = 0.75 ± 0.05.

Fig. 1. (a) The positions of C, Ni, and Ce atoms in the unit cell are illustrated with red, blue, and black dashed circles, respectively. (b) The pressure dependence of normalized lattice parameters and unit cell volume. The error bars are smaller than the symbols. The dashed lines are the linear fittings to the pressure dependence of the lattice parameters used for estimating the compressibility. The solid line represents a fit of the Birch-Murnaghan equation of state to the normalized unit cell volume [2].
The anisotropic compressibility of CeNiC2, with higher compressibility along the a-axis than along the b- and c-axes, likely causes this behavior. The stiffness of the NiC2 layer, attributed to strong C-C bonds and Ni-C interactions in the bc plane, hinders compression along these axes. This results in different responses of interatomic distances under pressure. Similar effects on magnetic exchange interactions have been observed in other CeT2X2 compounds, like CeRh2Ge2 and CeCu2Ge2, where interatomic distances govern the c-f interaction strength.
Figures 2(a), (b) and (c) show the interatomic distances between Ce-Ce, Ni-Ni and Ni-Ce atoms. Atomic coordinates of Ce, Ni, and C, and interatomic distances were measured under pressure, revealing changes primarily in the y-coordinate of C and the C-C bond length, especially around 7 GPa. The interatomic distances between Ce-Ce, Ni-Ni, Ni-Ce, and C-C exhibit notable changes with pressure, indicating anisotropic compressibility and bond length variations, particularly highlighting the unique behavior of C-C and C-Ni bonds around 7 GPa.

Fig. 2. The pressure dependence of interatomic distances between the (a) Ce-Ce atom, (b) Ni-Ni atom, and (c) Ni-Ce atom is illustrated. The dashed lines in (c) represent the linear fitting results. The red and black dot-dashed lines in the inset illustrate the direction of interatomic distances 1 and 2 in the unit cell. The solid symbol shows the ambient condition data [2].
Nonmonotonic pressure dependencies in C-C, C-Ni, and C-Ce distances, particularly around 7 GPa, indicate anomalies that may result from increased Ce-Ce interaction along the a-axis penetrating the NiC2 layer. These findings highlight the intricate relationship between pressure, atomic distances, and magnetic properties in CeNiC2, providing critical insights into the behavior of heavy fermion materials. As shown in Fig. 2 the first and second nearest neighbor directions of Ce-Ce and Ni-Ni atoms interchange around 7 GPa, with nonmonotonic pressure dependence observed for interatomic distances between C-Ce, C-Ni, and C-C atoms at this pressure. Increasing pressure causes these distances to decrease and become equal around 7 GPa. Above this pressure, the FNN and SNN directions interchange; the FNN aligns along the a-axis, and the SNN lies in the bc-plane. This interchange correlates with the weakening of incommensurate antiferromagnetic (ICAF) order and the emergence of the Kondo effect above 7 GPa, suggesting increased interplanar Ce-Ce interaction influences the spin structure of CeNiC2 [2].
In summary, we investigated the crystal structure of CeNiC2 from 0 to 18.6 GPa by using single crystal X-ray diffraction with a laboratory X-ray source. Our results reveal a large Bulk modulus ~ 134 GPa and anisotropic linear compressibility following the relationship |ka| > |kc| > |kb|. Although, we do not detect any signature of structural phase transition, the direction of FNN and SNN between the Ce-Ce and Ni-Ni atoms interchanges near the pressure where the antiferromagnetic ordering temperature reaches a maximum in the pressure temperature phase diagram of CeNiC2. Our results suggest that the direction of nearest neighbors interexchange might play a key role in the suppression of magnetic order and the enhancement of the Kondo effect.
References
- [1] S. Katano, H. Nakagawa, K. Matsubayashi, Y. Uwatoko, H. Soeda, T. Tomita, and H. Takahashi, Phys. Rev. B 90, 220508 (2014).
- [2] H. Ma, D. Bhoi, J. Gouchi, H. Sato, T. Shigeoka, J.-G. Cheng, and Y. Uwatoko, Phys. Rev. B 108, 064435 (2023).