# Synthesis of clathrate cerium superhydride CeH9 at 80-100 GPa with atomic hydrogen sublattice

## Abstract

Hydrogen-rich superhydrides are believed to be very promising high-Tc superconductors. Recent experiments discovered superhydrides at very high pressures, e.g. FeH5 at 130 GPa and LaH10 at 170 GPa. With the motivation of discovering new hydrogen-rich high-Tc superconductors at lowest possible pressure, here we report the prediction and experimental synthesis of cerium superhydride CeH9 at 80–100 GPa in the laser-heated diamond anvil cell coupled with synchrotron X-ray diffraction. Ab initio calculations were carried out to evaluate the detailed chemistry of the Ce-H system and to understand the structure, stability and superconductivity of CeH9. CeH9 crystallizes in a P63/mmc clathrate structure with a very dense 3-dimensional atomic hydrogen sublattice at 100 GPa. These findings shed a significant light on the search for superhydrides in close similarity with atomic hydrogen within a feasible pressure range. Discovery of superhydride CeH9 provides a practical platform to further investigate and understand conventional superconductivity in hydrogen rich superhydrides.

## Introduction

Metallization of hydrogen under high pressure has been a topic of great scientific interest in the past few decades mainly due to expectations of room-temperature superconductivity1,2,3,4,5,6,7. Hydrogen is expected to become metallic under high pressure above 400 GPa7,8,9. But achieving such pressures and verifying superconductivity are very challenging in diamond anvil cell (DAC) experiments, mainly due to diamond failure and lack of a reliable probe on the tiny sample volumes at such high pressures. Alternatively, hydrogen-rich hydrides can also be expected to achieve high-Tc superconductivity perhaps at a much lower pressure than that of required for metallic hydrogen10,11,12. Both hydrides and metallic hydrogen are expected to be conventional superconductors. High phonon frequency, strong electron–phonon coupling, and high density of states at the Fermi level are the essential conditions for superconductivity with Cooper pairs mediated by electron–phonon interaction13. Hydrides may satisfy all these conditions as the low mass of hydrogen results in high phonon frequency; covalent bonding is favourable for strong electron–phonon coupling; metallization under high pressure can result in high electronic density of states at the Fermi level10. Within this view the remarkable prediction and experimental confirmation of superconductivity at a record high Tc of 203 K under pressure of 150 GPa in H3S makes sense14,15. The discovery of superconductivity in H3S gave hopes to achieve room-temperature superconductivity in hydrogen-rich systems under high pressure. Recently superconductivity with Tc of 260 K at 180 GPa and 250 K at 170 GPa were reported for LaH10 by two different research groups by electrical conductivity measurement16,17. Detecting Meissner effect to confirm the superconductivity has been difficult because signal from extremely small sample could be too weak to be picked up by the state-of-the-art techniques. At such pressure the verification of Tc becomes a challenging task. A recent study by Drozdov et al. reported Tc of 250 K in LaH10, which  decreases with the application of magnetic field, and the isotope effect was also observed17. The discovery of superconductivity in LaH10 is a milestone in the search of room temperature superconductivity.

Hydrogen readily reacts with most elements to form binary hydrides18,19. Several hydrogenic motifs such as Hδ, H2δ−, H3, H3+, H4, and H5+, and infinite chains, layers, frameworks were predicted to occur in high-pressure hydrides20,21,22. One-dimensional hydrogen chains and three-dimensional clathrate structures with hydrogen cage were predicted and found to be good candidates for high Tc superconductivity20. Recent theoretical predictions have reported several systems with unusually high hydrogen content, termed as polyhydrides/superhydrides, to become stable under high pressure and to exhibit significantly high Tc under pressure22,23,24,25,26,27,28,29. Notably CaH624, MgH626, YH627, YH923, YH1023,28, LaH1028, ThH1030, AcH10, and AcH1629 were predicted to have Tc above 235 K. Most of the phases with Tc close to room temperature are predicted to have a clathrate structure with hydrogen forming a cage around metal atom (M). In MH6, MH9, and MH10 compounds, metal atoms are located within H24, H29, and H32 cages, respectively23,24,27,28. However, it is essential to know the experimental pressure–temperature condition to stabilize a hydride before carrying out the further electrical or magnetic measurement to verify the superconductivity. Recently, a handful of experiments were reported to synthesize new superhydrides under pressure, particularly FeH5 at 130 GPa31, LaH10 at 170 GPa32, UH7, UH8, and UH9 above 37 GPa33. There were also experimental reports about synthesis of new and unusual hydrides under pressure, such as LiH634, NaH735, Xe(H2)736, and HI(H2)1337 with H2-like molecular units. Hydrides possessing H2-molecular units are not prone to have higher Tc as they tend to have low densities of states at the Fermi level23. Synthesis of FeH5 and LaH10 without any H2-like unit is very intriguing. Interestingly, FeH5 crystallized in layered structure consists two-dimensional atomic hydrogen slabs. LaH10 has three-dimensional clathrate structure in which La atoms surrounded by hydrogen cage. H3S has body-centered cubic structure which can also be visualized as sulfur atom surrounded by three-dimensional hydrogen cage. Nearest H–H distance in FeH5 was reported to be ~1.336 Å at ~100 GPa31, whereas for LaH10 it was ~1.196 Å at ~120 GPa32. LaH10 was claimed as a closest analogue to solid atomic metallic hydrogen based on nearest H–H distance32. However, the pressure required to stabilize FeH5 and LaH10 phases was 130 and 170 GPa, respectively31,32. Synthesis of superhydrides at lower pressures would give an opportunity to further investigate superconductivity in these hydrides with a wide range of probes. Studies on the synthesis path and structure of superhydrides also help to build a deeper understanding of hydride chemistry. Besides superconductivity, hydrides are also very important as hydrogen storage materials for next-generation energy-related applications38. Recently, Peng et al.23 predicted that hydrogen-rich CeH9 with P63/mmc structure becomes stable at a relatively low pressure of 100 GPa, which by itself is very interesting although their estimated superconducting Tc was relatively low, <56 K.

We have carefully studied the Ce–H system in order to understand the crystal chemistry and to seek for superconductivity with, possibly, much higher Tc values. Here we report the successful synthesis of cerium superhydride CeH9 at 80-100 GPa with laser heating up to ~2000 K. Using evolutionary variable-composition searches, the whole compositional space of the Ce–H system explored in a single simulation. We predicted phase stability and superconducting properties of high-pressure cerium superhydrides. Rich chemistry of cerium hydrides manifests itself in numerous stable compounds, including the experimentally synthesized CeH3 and superhydrides CeH9. We have carried out a direct elemental reaction between cerium and hydrogen using a laser-heated DAC coupled with synchrotron X-ray diffraction (XRD). It is found that heating plays an essential role in the formation of Ce–H phases at high pressures. Analysis of XRD results in combination with ab initio calculations shows that CeH9 crystallizes in a clathrate structure with space group P63/mmc at 80-100 GPa after laser heating. Each cerium atom is enclosed within a cage of H29 in which hydrogen atoms are bonded covalently. Besides this, a previously unknown $$Pm\bar 3n$$ structured CeH3 (β-UH3 type39) was synthesized at 36 GPa with laser heating. The detailed first-principles investigation of stability, structural, electronic, and superconducting properties of experimentally synthesized hydrogen-rich phase was carried out. We studied, specifically electron–phonon interaction of P63/mmc-CeH9 and predicted that the CeH9 is a high temperature superconductor with Tc = 105–117 K at 200 GPa.

## Results

### Synthesis of various Ce–H phases

In our experiment, various phases of the Ce–H system such as CeHx (x = 2, 2.5, 3, and 9) were synthesized successfully at high pressures. Initially, the cerium sample and hydrogen gas were loaded into the sample chamber of the DAC and were kept at 9 GPa. A small piece of gold also was loaded along with sample to calibrate pressure. At 9 GPa and ambient temperature, we found that cerium and hydrogen reacted, which resulted in the formation of a cerium hydride compound as shown by the XRD pattern in Fig. 1a. The corresponding XRD image is shown in Supplementary Fig. 1a. All the peaks observed at 9 GPa could be indexed with the $$Fm\bar 3m$$ phase of CeH2 (see Supplementary Note 1). The $$Fm\bar 3m$$ phase of CeH2 persisted up to 33 GPa (Supplementary Fig. 1b). Lebail refinements were carried to extract lattice parameters of the CeH2 phase (Supplementary Fig. 1c). The lattice parameters of CeH2 at 9 and 33 GPa were determined as a = 5.370(1) and a = 5.011(2) Å respectively. Pressure dependence of the unit cell volume of CeH2 was fitted with a third-order Birch–Murnaghan equation of state (EOS) which yielded the fitting parameters such as unit cell volume at zero pressure V0 = 44(1) Å3 per f.u., bulk modulus K0 = 45(6) GPa and first pressure derivative of bulk modulus K0′ = 4 (fixed) (Supplementary Fig. 1d). Pressurization of CeH2 up to 33 GPa did not result in any changes in crystal structure. However, microsecond pulsed laser heating of ~2000 K carried at 33 GPa resulted in obvious structural changes (Supplementary Fig. 2a). The XRD pattern at 36 GPa obtained after laser heating is shown in Fig. 1b, and the corresponding XRD image is shown in Supplementary Fig. 2b. The integrated XRD pattern at 36 GPa was found to be of cubic CeH3 with $$Pm\bar 3n$$ isomorphous to β-UH3 $$(\beta \mbox {-}Pm\bar 3n)$$39. This high-pressure phase of CeH3 with $$\beta \mbox {-}Pm\bar 3n$$ structure has also been predicted in our evolutionary searches to be the energetically favourable phase below 10 GPa and is 32 meV/atom higher in enthalpy than the most favourable CeH3 at the synthesized pressure of 36 GPa (Supplementary Fig. 3). However, inclusion of spin–orbit coupling (SOC) and magnetism changes the enthalpy difference of CeH3 phases by some 0.09 eV per atom. While these calculations affect predicted phase stability range, our experimental results confirm the existence of the predicted phase. To the best of our knowledge, β-UH3 type $$Pm\bar 3n\mbox {-}{\mathrm{CeH}}_{\mathrm{3}}$$ is being reported for the first time here. The experimental lattice parameters of the $$\beta \mbox {-}Pm\bar 3n$$ phase at 36 GPa are a = 6.2788(3) Å. In $$\beta \mbox {-}Pm\bar 3n$$ structure of CeH3, cerium atoms occupy 2a (0, 0, 0) and 6c (1/4, 0, 1/2) Wyckoff positions39. Unfortunately, very low X-ray scattering factor of hydrogen atom did not allow us to determine the exact position of hydrogen atoms in CeH3 unit cell from the experimental XRD data. Theoretical calculations yielded the Wyckoff position for the hydrogen atoms as 24 K (0, 0.1580, 0.6935) at 35 GPa with lattice parameter a = 6.2471 Å, which is highly consistent with the experimental value of $$\beta \mbox {-}Pm\bar 3n\mbox {-}{\mathrm{CeH}}_{\mathrm{3}}$$ observed at 36 GPa. The $$\beta \mbox {-}Pm\bar 3n$$ phase of CeH3 proved stable with further compression up to 80 GPa and also sustained laser heating at an intermediate pressure of 60 GPa (Supplementary Fig. 2a), which agrees with our predictions. A third-order Birch–Murnaghan EOS was used to fit the PV data of CeH3 (see Supplementary Fig. 2d), fitting parameters are V0 = 39.7(4) Å3 per f.u., K0 = 86(4) GPa and K0′ = 4 (fixed).

Several cycles of pulse laser heating with 1 µs pulse width at a repetition rate of 10 kHz for a total heating duration of a few seconds each cycle was used to laser heat the sample assemblage to approximately 1700 K at 80 GPa that resulted in the emergence of new peaks (Supplementary Fig. 4). These new diffraction peaks were indexed to be (101) and (002) of clathrate hexagonal phase of CeH9 (Figs. 1c and 2, also see in Supplementary Fig. 4) as found by our evolutionary search. With further pressurization the relative intensity of the (101) and (002) peaks of CeH9 phase increased (Supplementary Fig. 4). Although most of the peaks of CeH3 phase were present, the intensity of the CeH9 peaks became prominent and increased with pressure (Supplementary Fig. 4). Several further cycles of laser heating at 88 GPa (Supplementary Fig. 4) and 98 GPa improved the intensity of the hexagonal CeH9 phase, as shown in Fig. 1c. A Rietveld refinement plot for the CeH9 phase at 100 GPa is shown in Fig. 2a with the corresponding XRD image as an inset. CeH9 crystallizes in the P63/mmc space group with lattice parameters a = 3.7110(3) and c = 5.5429(7) Å at 100 GPa. Cerium atoms occupy the Wyckoff position 2d (2/3, 1/3, 1/4) in a hexagonal unit cell. Theoretical calculations established positions of hydrogens to be 2b (0, 0, 1/4), 4f (1/3, 2/3, 0.1499), and 12k (0.1565, 0.8435, 0.4404) at 100 GPa. The crystal structure of CeH9 is shown in Fig. 2b. The experimentally observed P63/mmc CeH9 phase and its structural parameters are perfectly consistent with our calculations. Calculated EOS parameters for CeH9 phase are V0 = 53.4(2) Å3 per f.u., K0 = 80.5(13) GPa and K0′ = 4 (fixed). Synthesis of the P63/mmc-CeH9 phase has been confirmed in two independent experimental runs.

During the decompression cycle, the CeH9 phase was observed to start to become unstable at pressures below 93 GPa and ambient temperature (supplementary Fig. 5). Laser heating was also carried out during the decompression cycle at 79 and 54 GPa. Laser heating in decompression cycle did not result in any changes in XRD pattern. Upon further decompression, the $$\beta \mbox {-}Pm\bar 3n\mbox {-}{\mathrm{CeH}}_{\mathrm{3}}$$ phase reappeared below 50 GPa (supplementary Fig. 5). Finally, after complete decompression, the $$\beta \mbox {-}Pm\bar 3n\mbox {-}{\mathrm{CeH}}_{\mathrm{3}}$$ phase was recovered at ambient conditions along with tetragonal Ce2H5 (Supplementary Fig. 5). The P-T path for the formation and stability of various Ce–H phases, observed in our experiments, can be seen in Fig. 3. All these findings are repeatable as demonstrated in a separate run of experiment (see Supplementary Note 2 and Supplementary Fig. 6).

### Theoretical calculations and prediction of cerium hydrides

First-principles calculations were carried out to understand the detailed chemistry of the Ce–H system, dynamical stability, and structural and electronic band structures of experimentally synthesized superhydride phases. We performed variable-composition evolutionary searches at 0, 50, 100, 150, 200, and 250 GPa. The thermodynamic convex hull at different pressures is depicted in Fig. 4. The predicted stable cerium hydrides are shown in the pressure–composition phase diagram in Fig. 5. Several compounds such as I4/mmm-CeH4, P63mc-CeH6, P63mc-CeH8, P63/mmc-CeH9. and $$Fm\bar 3m\mbox {-}{\mathrm{CeH}}_{{\mathrm{10}}}$$, were predicted, in addition to finding three known compounds CeH2, Ce2H5, and CeH3. High-pressure phase of the CeH3 was also predicted with space group $$Pm\bar 3n$$, as shown in Fig. 5. Because of high concentration of hydrogen in hydrogen-rich hydrides, zero-point  energy (ZPE) might be important in determining the relative stability of hydrogen-rich phases; however, in our previous studies22,40, we showed that this quantum effect does not change the topology of the phase diagram, and quantitative effects are just moderate shifts in transition pressures. For example, for GeH4 the inclusion of ZPE shifts the transition pressure Ama2 → C2/m from 300 to 278 GPa40. Among the stable phases predicted, we have synthesized $$Fm\bar 3m\mbox {-}{\mathrm{CeH}}_{\mathrm{2}}$$, $$I4_1md\mbox {-}{\mathrm{Ce}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{5}}$$ $$\beta \mbox {-}Pm\bar 3n\mbox {-}{\mathrm{CeH}}_{\mathrm{3}}$$, and $$P6_3/{mmc}\mbox {-}{\mathrm{CeH}}_{\mathrm{9}}$$. Our pressure–composition phase diagram shows pressure ranges of stability for all the predicted phases along with experimentally known compounds. It clearly shows that higher pressures favour higher hydrogen content compounds, which is consistent with our experiment done at different pressure conditions. Previously known compounds $$Fm\bar 3m\mbox {-}{\mathrm{CeH}}_{\mathrm{2}}$$ and $$I4_1md\mbox {-}{\mathrm{Ce}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{5}}$$ are predicted to be stable only below 8 and 1.5 GPa, respectively. Increase of pressure leads to the formation of I4/mmm-CeH4 above 32 GPa. CeH6 and CeH8 are stable in relatively narrow pressure ranges from 26 to 68 GPa, and 55 to 95 GPa, respectively and that is probably why they are not observed in our experiment. P63/mmc-CeH9 becomes stable at pressures above 78 GPa, which agrees with our high-pressure experiments where it was synthesized at 80-100 GPa after laser heating. Detailed structural information on the predicted phases can be found in Supplementary Table 1. Among the predicted stable cerium hydrides, we focus on modelling of hydrogen-rich CeH9, since a higher hydrogen to metal ratio in hydrides is expected to correlate with higher Tc superconductivity in hydrogen-rich hydrides11.

## Discussion

Addition of hydrogen in metallic sublattice expands the unit cell volume. In most cases, an increase in volume is proportional to hydrogen content in hydride. In hydrides, expansion of the cell volume with respect to pure metal volume was frequently used to establish the hydrogen content and stoichiometry32. In order to ascertain the stoichiometry of high pressure superhydride phase observed at 80-100 GPa after laser heating, we have compared the ideal mixture of Ce–H2 solution with experimental volume per formula unit of CeH3, CeH9, and with theoretical EOS (see Fig. 6a). The curve representing ideal mixture of Ce and (7/2) H2 lies well below the theoretical and experimental EOS of P63/mmc-CeH9 in the pressure range 80–100 GPa, whereas  mixture of Ce and (8/2) H2 partially overlaps with theoretical and experimental EOS of CeH9. This indicates that the hexagonal phase observed at 80-100 GPa after laser heating does not favour energetically CeHX with x < 8 and can decompose into its elemental constituents or hydride with x > 8 and hydrogen. On the other hand, the curve representing an ideal mixture of Ce and (9/2) H2 lies well above the theoretical and experimental EOS of CeH9 in the pressure range 80–100 GPa. This observation clearly indicated that CeH9 can be stabilized in the pressure range mentioned. From our theoretical calculations and energetic considerations, it clearly signifies that the hexagonal phase observed at 80-100 GPa with laser heating has the CeH9 stoichiometry. We can also see that there is a fair agreement between experimental volume and theoretical EOS results (Fig. 6a) for $$P6_3/mmc\mbox {-}{\mathrm{CeH}}_{\mathrm{9}}$$ as well as $$\beta \mbox {-}Pm\bar 3n\mbox {-}{\mathrm{CeH}}_{\mathrm{3}}$$.

In hydrides, hydrogen is pre-compressed by interaction with metal atoms. Hydrogen sublattice in hydrides might be expected to be identical with atomic metallic hydrogen. So, we compared the volume expansion (ΔVH) per hydrogen atom and nearest H–H distance in CeH9 with simulated atomic metallic hydrogen phase extrapolated to lower pressure31 and also with other reported hydrides as shown in Fig. 6b, c, respectively31,32,41,42. The nearest Ce–H distance in $$P6_3/mmc\mbox {-}{\mathrm{CeH}}_{\mathrm{9}}$$ is plotted in Fig. 6d. The inset of Fig. 6d shows the Ce–H29 clathrate cage structure in which the H29 cage is encapsulating a cerium atom. ΔVH per H atom for CeH9 is 2.09 Å3 at 100 GPa, which is lower than that for a hydrogen atom, but larger by ~8% with respect to ΔVH per H atom of layered FeH5. ΔVH per H atom for CeH9 matches with volume of atomic metallic hydrogen around 100 GPa. Formation of CeH9 can also be understood in terms of mixing of Ce and dense atomic metallic hydrogen. This indicates that hydrogen framework surrounding Ce atom is identical to dense atomic metallic hydrogen at a lower pressure. Nearest H–H distance in clathrate CeH9 is 1.116 Å at 100 GPa, which is significantly longer than the H–H bond length (0.74 Å) in H2 gas molecules but is significantly lower than other hydrides such as AlH3, FeH3, FeH5, H3S, and LaH10 as can be seen in Fig. 6c. Surprisingly, the nearest H–H distance in CeH9 almost overlaps with the H–H distance in atomic hydrogen and decreases very slowly with pressure. Among all the superhydrides, the nearest H–H distance observed in CeH9 is among the shortest  at 100 GPa and coincides with H–H distance of atomic metallic hydrogen. Among the reported hydrides, nearest H–H distance of CeH9 is only second to the H–H distance (0.98 Å)23 for atomic metallic hydrogen at 500 GPa at which hydrogen is in a superconducting metallic state43. Judging from the H–H distances, CeH9 is closer to monatomic metallic hydrogen than other hydrides, yet its predicted Tc is not as high as that of hydrogen or of LaH10. The shortest H-H distance is not the only thing that matters for high Tc; the electronic structure of the metal atom plays a crucial role, as shown by Semenok et al.29. In Fig. 6c, we can also see that non-superconducting FeH5 has shorter H–H distance than H3S compound well known for very high Tc. Presence of strongly coupled hydrogen-dominant libration and stretch vibrations are the signatures of high-Tc in hydrogen-rich materials44. Weak H–H interactions with preferred bond distances between 1.2 and 1.3 Å, the stretching and bending vibrations becomes indistinguishable, due to which all H vibrations contribute in the strong electron–phonon coupling process, eventually contributing to enhance the Tc in hydrides44. At 100 GPa the nearest Ce–H distance is ~2.07 Å and it decreases with pressure. It is noteworthy that the clathrate structures predicted in the literature for rare earth (RE) hydrides REH6, REH9, and REH10 have H24, H29, and H30 cages surrounding the RE atom23. Among these cages, The H29 cage has the smallest volume per formula unit for YH9 (ref. 23). Clathrate H29 cage in CeH9 surrounding the Ce atom is almost 1.1 Å thick along the a- and b-axis, while it is 0.9 Å thick along c- axis at 100 GPa45, whereas thickness of clathrate cage in LaH10 is 0.9 Å32. Clathrate CeH9 can be visualized as three-dimensional atomic metallic hydrogen encapsulating Ce atoms (inset of Fig. 6d). Covalently bonded hydrogen sublattice in CeH9 with bond length and ΔVH per H atom similar to atomic metallic hydrogen is likely to have density similar to that for atomic hydrogen slab at 100 GPa. Hence $$P6_3/mmc\mbox {-}{\mathrm{CeH}}_{\mathrm{9}}$$ will be a good platform to investigate H–H properties to understand atomic metallic hydrogen. Recently, Carbotte et al. proposed a new technique to investigate superconductivity in high pressure hydrides and hydrogen based on optical properties, without four probes46. Superconductivity in $$P6_3/mmc\mbox {-}{\mathrm{CeH}}_{\mathrm{9}}$$ can also be evaluated using this optical technique.

Figure 7a shows calculated electronic band structures of CeH9 at 150  GPa. From Fig. 7a, it can be seen that CeH9 is metallic and features numerous flat bands above the Fermi level. Noticeable density of electronic states at the Fermi level 0.73 (0.62) states per eV per f.u., which is 1.4 (1.2) times higher than that of previously found H3S14 and comparable to that of recently synthesized LaH1032 at an optimal pressure of 200 GPa, is a good sign for facilitating high-temperature superconductivity (values in parentheses are the corrected ones using GGA+U with U = 6 eV, see supplementary Table 2). Figure 8a, b represents the electron density of states (DOS) for CeH9 at 150 GPa with and without Hubbard correction respectively. The main contributors to N(Ef) are Ce-4 and H-1s orbitals, however, only those electrons that are coupled strongly to phonons are important. High frequency phonons are mainly related to H vibrations, owing to its light mass, which makes the largest contribution to the electron–phonon coupling constant. Analysis of electron localization function (ELF) shows a moderate ELF value 0.64 between H atoms within the unit, suggesting weak covalent interaction, which forms a three-dimensional hydrogen network i.e., H29 cage consisting of H4, H5 and H6 rings. Very low ELF value between Ce and H indicates that no bonds were present between the Ce and H atoms (Supplementary Fig. 7).

We performed phonon calculations in the thermodynamic stability range of CeH9 i.e., above 80 GPa. Lattice dynamics calculations indicate that the P63/mmc-CeH9 phase is dynamically stable at 150 GPa (Fig. 7b). Selected vibrational mode displacements of the P63/mmc-CeH9 at the H- and K-point from the structure relaxed at 150 GPa are shown in the Supplementary Fig. 8. However, at lower pressures, e.g., 120 GPa and below, DFT calculations show that some phonon modes become imaginary along the H- and K-points ([−1/3, 2/3, 1/2] and [−1/3, 2/3, 0], respectively) (Supplementary Fig. 8). The P63/mmc-CeH9 phase is stabilized anharmonically. To include temperature effect, capturing anharmonicity, we used the approach of Hellman et al.47,48, to obtain temperature-dependent phonon frequencies and the phonon spectra show dynamical stability already at 100 GPa and 500 K (see Supplementary Fig. 9). To resolve the soft modes of the lattice within the harmonic approximation, we used generalized evolutionary metadynamics (GEM)49, in which large displacements along the softest mode eigenvectors are used to equilibrate the system. This hybrid technique is implemented in USPEX and was successfully applied to boron and silicon and found numerous energetically competitive configurations49. We used supercells up to index 4, i.e., 80 atoms per cell. Using GEM, we found a stable structure within harmonic approximation with C2/c symmetry (Supplementary Fig. 10), which is a subgroup of P63/mmc symmetry. Electron–phonon coupling (EPC) calculations revealed that P63/mmc-CeH9 is a high-temperature superconductor. Using the Allen-Dynes modified McMillan equation (Eq. 1), we estimated the superconducting transition temperature (Tc) to be 105–117 K at 200 GPa, when using different Coulomb pseudopotentials (μ), i.e., 0.10 and 0.15 which are widely accepted lower and upper bound values. In P63/mmc, the resulting electron–phonon coupling coefficient λ is 2.30 at 200 GPa, which is higher than that of H3S, λ = 2.19 at 200 GPa14. Since cerium atom is heavy, the logarithmic average phonon frequency (ωlog = 740 K) is lower compared with that of H3S (ωlog = 1335 K), which results in a lower Tc of 105–117 K. The Tc of CeH9 has a lower value of 63–75 K at 100 GPa for C2/c structure. The logarithmic average phonon frequency ωlog of the C2/c phase has a lower value 662 K. However, our results indicate that lower Tc value is mainly related to the lower electron–phonon coupling coefficient λ = 1.48. Earlier report by Peng et al.23 predicted a slightly lower Tc value of 56 K at 100 GPa for the CeH9 phase with P63/mmc structure23. However, our phonon calculations within harmonic approximation indicate instability of P63/mmc phase below 120 GPa (see Supplementary Fig. 8), and it is unclear how Tc of a dynamically unstable phase was computed. So, our systematically carried studies estimate comparatively higher Tc of 63–75 K for the CeH9 at 100 GPa for the dynamically stable C2/c structure. Furthermore, we have tabulated the ωlog, λ, and Tc value of CeH9 along with recently predicted other superhydrides of La-H, Y-H, U-H, Ac-H, and Th-H system for comparison, as shown in Supplementary Table 3. Phonon dispersions curves, phonon density of states, the Eliashberg spectral function α2F(ω), and the EPC parameter λ as a function of frequency are calculated and shown in Supplementary Figs. 11 and 12 for C2/c and P63/mmc-CeH9 at 100 and 200 GPa, respectively. It is known that quantum effects can impact the calculated superconducting transition temperatures; however, in the case of strongly anharmonic H3S (SG $$Im\bar 3m$$), the inclusion of anharmonic correction, lowered the Tc from its harmonic 204 K value14 only to 194 K50 at 200 GPa, and both are close to the reported experiment Tc at 200 GPa15, although the transition pressures shift is considerably large14,51.

In summary, we have successfully synthesized a cerium superhydride phase of CeH9 at 80-100 GPa after laser heating, which crystallized in the hexagonal P63/mmc clathrate structure. In addition to this we have also synthesized a cubic phase of CeH3 with space group $$Pm\bar 3n$$ (β-UH3 type), which was recovered at ambient phase after complete decompression. Our studies give strong evidence for the synthesis of rare earth superhydrides and pave the way for future studies on other rare earth-hydrogen systems under extreme pressure with the aid of laser heating perhaps to make the binary hydrides MHx with x > 9. Apart from this, the estimated Tc of 105–117 K in P63/mmc-CeH9 at 200 GPa is very promising. Electron–phonon coupling in P63/mmc-CeH9 is even higher than in H3S but still could not achieve higher Tc due to lower logarithmic average phonon frequency. Conspicuously, the dense three-dimensional atomic hydrogen sublattice is noted for superhydride P63/mmc-CeH9 as compared with reported super/polyhydrides and similar to atomic metallic hydrogen at 100 GPa. The discovery of CeH9 at a feasible pressure range with prediction of superconductivity will certainly inspire further studies on superconductivity in hydride systems.

## Methods

### Computational  details

Evolutionary variable-composition simulation, implemented in USPEX, is used to explore the high-pressure phase diagram of the Ce–H system from ambient pressure to 250 GPa. The evolutionary algorithm USPEX55,56,57,58,59 is a powerful method for finding thermodynamically stable compounds of a given system and their most stable structures. This method has been shown to be successful in predicting high-pressure structures of variety of systems which were confirmed experimentally, also in a number of in specific superconducting hydrides, e.g., UH833 and H3S14. In this method, the first generation of structures (100 structures) and compositions are created using the random symmetric algorithm. Subsequent generations were obtained using 40% heredity, 20% transmutation, 20% softmutation, and 20% random symmetric generator. We allowed variation operators to automatically evolve in the subsequent generations. The underlying structure relaxations were carried out using the VASP package59 in the framework of DFT and using PBE-GGA (Perdew–Burke–Ernzerhof generalized gradient approximation)60,61. We believe PBE is the most appropriate choice, because PBE best reproduces the experimental data (see Supplementary Fig. 16 and Supplementary Tables 4 and 5). The projector-augmented wave approach (PAW)59,62 was used to describe the core electrons and their effects on valence orbitals. Valence electron configuration of 5s25p64f15d16s2 (i.e., with explicitly included f electrons) and 1s1 was used for the Ce and H atoms, respectively. A plane-wave kinetic-energy cut-off of 1000 eV for hard PAW potentials and dense Monkhorst–Pack k-points grids with reciprocal space resolution of 2π × 0.03 Å−1 were employed63 to sample the Brillouin zone. Phonon frequencies and superconducting critical temperature were calculated using density-functional perturbation theory as implemented in the QUANTUM ESPRESSO package64, also using the PBE-GGA functional. Ultrasoft pseudopotentials for Ce and H were used with a plane-wave basis set cut-off of 70 Ry, which gives a convergence in energy with a precision of 1 meV per atom. Phonon dispersions were also calculated under the quasi-harmonic approximation using the finite displacement method implemented in PHONOPY package65 using forces computed with VASP. The k-space integration (electrons) was approximated by a summation over a 12 × 12 × 6 uniform grid in reciprocal space, with the smearing scheme of Methfessel–Paxton and a fictitious smearing temperature T of kBT = 0.05 Ry for self-consistent cycles and relaxations; a much finer (24 × 24 × 12) grid was used for evaluating DOS and electron–phonon linewidths. Dynamical matrices and electron–phonon linewidths of P63/mmc-CeH9 were calculated on a uniform 6 × 6 × 3 grid in q-space. Electron–phonon matrix elements were calculated based on interpolation method developed by Wierzbowska et al.66. The superconducting transition temperature Tc was estimated using the Allen–Dynes modified McMillan equation67

$$T_{\mathrm{c}} = \frac{{\omega _{{\mathrm{{log}}}}}}{{1.2}}{\mathrm{{exp}}}\left( {\frac{{ - 1.04(1 + \lambda )}}{{\lambda - \mu ^ \ast (1 + 0.62\lambda )}}} \right),$$
(1)

where μ is the Coulomb pseudopotential and ωlog is the logarithmic average phonon frequency. The electron–phonon coupling constant λ and ωlog were calculated as

$$\omega _{\mathrm{{log}}} = {\mathrm{exp}}\left( {\frac{2}{\lambda }{\int} {\frac{{{\mathrm{d}}\omega }}{\omega }\alpha ^2F\left( \omega \right){\mathrm{{ln}}}(\omega )} } \right),$$
(2)
$$\lambda = 2 {\int_0^{\infty}} {\frac{{{\alpha}^2 F\left({\omega} \right)}}{\omega}{\mathrm{d}}{\omega}}.$$
(3)

## Data availability

All data supporting the findings of this study are included in this article and its Supplementary Information, and are also available from the corresponding authors upon request. Data are deposited on https://figshare.com/ and can be found on the link—https://doi.org/10.6084/m9.figshare.9729467.v3

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## Acknowledgements

The authors thank Suyu Fu of UT Austin for his assistance for the XRD data collection, Dr. Neelam Yedukondalu for the calculation of temperature dependent phonon dispersion and Yuyong Xiong for hydrogen loading at Center for High Pressure Science and Technology Advanced Research (HPSTAR). The authors thank Saori Kawaguchi and Naohisa Hirao for the help during experiment at SPring8. J.Z., Y.W., A.O., and J.F.L. acknowledge the support from DOD-ARMY grant (W911NF-16-1-0559). M.M.D.E. acknowledges support from the National Science Foundation (EAR-1723160) for supporting this work. N.P.S. and Y.Z. acknowledge support from HPSTAR. Y.Z. acknowledges support from “the Fundamental Research Funds for the central universities” in China (Grant No. YJ201809) and from the NSFC (Grant No. 41804082). High-pressure XRD experiments were conducted at GeoSoilEnviroCARS of APS, ANL. GeoSoilEnviroCARS operations are supported by the National Science Foundation-Earth Sciences (EAR-1128799) and the Department of Energy, Geosciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Calculations were mainly performed on the cluster (QSH) in our laboratory at Stony Brook University.

## Author information

J.F.L. and N.P.S. conceived the project. J.F.L. supervised the project, and J.F.L. and N.P.S. coordinated the project. N.P.S. planned the experiment and prepared the diamond anvil cell samples. Y.Z., J.F.L., E.G. and V.B.P. carried out the XRD measurements with the laser heating at high pressures. N.P.S. analysed and modelled the data, N.P.S. and J.F.L. interpreted the initial data. M.M.D.E., I.A.K., and A.R.O. carried out the theoretical calculations. All the authors discussed the results. N.P.S. and M.M.D.E. wrote the draft. A.R.O., J.Z., and J.F.L. participated in writing and revising the manuscript, and J.Z. and J.F.L. helped with the draft abstract. Y.W., J.L. and all the authors read and commented on the manuscript.

Correspondence to Artem R. Oganov or Jung-Fu Lin.

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Salke, N.P., Davari Esfahani, M.M., Zhang, Y. et al. Synthesis of clathrate cerium superhydride CeH9 at 80-100 GPa with atomic hydrogen sublattice. Nat Commun 10, 4453 (2019). https://doi.org/10.1038/s41467-019-12326-y

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