Synthesis and characterization of the La–Ce alloys

We have chosen to synthesize ternary La–Ce–H hydride by a reaction of a La–Ce alloy with hydrogen, which is a relatively simple approach to synthesize multinary polyhydrides. Under pressure, the concentration of ~75% La is predicted to be the phase boundary in the La–Ce phase diagram that may be in favor of the lattice reconstruction35. Hence, we used the La ~0.75 Ce ~0.25 alloy (the ratio of La–Ce is 3:1) prepared by multitarget magnetron sputtering as the initial reactant for typical experimental runs (Supplementary Table S1 and Fig. S1). Before loading into the diamond anvil cell, we have characterized this solid solution with different methods. We got the exact concentration by scanning electron microscopy equipped with energy-dispersive X-ray spectroscopy (SEM + EDX), which also proved the homogeneous distribution of the elements (Supplementary Figs. S14–S16 and S21). The X-ray diffraction (XRD) measurement revealed that the La–Ce alloy belonged to Fm\(\bar{3}\)m symmetry without any other impurity phase (Supplementary Fig. S2). We also discovered that the introduction of Ce atoms obviously suppressed the T c of pure La. The single superconducting transition judging from the R–T curve partly indicated the homogeneity (Supplementary Figs. S19 and S20). It is noteworthy that La and Ce atoms retain random distribution over metal sites even after the formation of the polyhydride at high pressure.

Superconductivity in the La–Ce–H and La–H systems

To synthesize La–Ce–H or La–H compounds, we compressed the La–Ce alloy or pure La in the ammonia borane (NH 3 BH 3 ) sample, which acted both as the pressure-transmitting medium and source of hydrogen. After that, the samples were laser-heated at the target pressure for a few seconds. In this process, hydrogen was released and reacted with La-Ce alloy or pure La at a temperature up to 1500 K, following which reaction products were quenched to room temperature. After synthesizing La–Ce–H compounds by laser heating at specific pressures, we conducted the electrical measurements and plotted the typical data in Fig. 1. To explore the possible high-temperature superconductivity at pressures lower than those of the known LaH 10 , we laser-heated the samples in DACs #2 and #9 at 113 GPa and 120 GPa, respectively. Strikingly, the T c reaches 175 K (113 GPa, Fig. 1b) and 190 K (123 GPa, Fig. 1d), which is about 100 K higher than our previously discovered cerium polyhydrides15. The obtained products are expected to remain metastable below the synthetic pressure. To explore this, we measured the pressure dependence of T c upon decompression and found T c of 155 K at 95 GPa (DAC #2) and 180 K at 104 GPa (DAC #9). To compare with LaH 10 , we heated DAC #6 at 152 GPa and observed the main resistance drop starting from 188 K (Supplementary Fig. S17). We also noticed another slight drop at 206 K. This is because of the formation of two superconducting phases (see Supplementary Fig. S18). T c slightly decreases with further compression to 156 GPa and 162 GPa, which is different from the behavior of C2/m-LaH 10 29. Noteworthy, the pressure scale (diamond Raman edge) used in this study, as well as from Somayazulu et al.8, gives a higher value than using the hydrogen vibron by ~18 GPa29. The same diamond Raman edge scale has been used in both compression and decompression processes. DACs #3 and #5 were both laser-heated at about 130 GPa. Similar to sample #6, we also observed a slight resistance drop at 186 K for sample #3 (Supplementary Fig. S8). Sample #5 showed an obvious step-like transition which indicated the superconductivity of other phases at lower temperatures. The highest T c , decreasing gradually along with the pressure, dropped to 132 K at 104 GPa. In contrast, the lower T c phase (~37 K, at the resistance close to zero) was robust during decompression from 127 GPa (Fig. 1c) to at least 80 GPa (Fig. 1d). Further decompression of sample #9 from 123 to 101 GPa showed the tendency similar to that of the high-T c phase in DACs #2 and #5 (Fig. 1b, c). The resistance of the La–Ce–H samples increased significantly when pressure decreased, and the width of the superconducting transition increased about 2.5 times from 104 GPa to 101 GPa (Fig. 1d), possibly due to disordering of the structure in the vicinity of a phase transition. Compared with the binary fcc-CeH 10 and hcp-CeH 9 15, we obtained higher T c in the ternary La–Ce–H system. However, there was no report on the superconductivity of binary La–H system at pressures lower than 120 GPa for our comparison. To fill this gap, we also explored the La–H system in the same pressure range (Fig. 1e). In DAC #L1, the La–H system showed the T c of 84 K after the first laser heating at 123 GPa. Further increasing the pressure and laser heating the sample led to another superconducting transition with a higher T c of 112 K at 129 GPa (Supplementary Fig. S30). During the decompression of DAC #L1 (Supplementary Fig. S31), superconductivity was preserved down to 78 GPa with a T c = 103 K (Fig. 1e and Supplementary Fig. S28). These data indicate that La–Ce–H system has a greatly enhanced T c compared with La–H and Ce–H systems below 130 GPa.

Fig. 1: Characterization of the superconducting transitions using electrical resistance measurements at selected pressures for typical runs. a Photographs of the sample after laser heating together with four electrodes. b–e The temperature dependence of the electrical resistance for the La–Ce–H sample in DACs #2, 5, 9 and La–H sample in DAC #L1. Full size image

The structural analysis of the La–Ce–H and La–H systems

To reveal the crystal structures of the superconducting polyhydrides, we performed synchrotron X-ray diffraction (XRD) measurements on the electrically characterized La–Ce–H samples in DACs #2 and #3 (Fig. 2a and Supplementary Figs. S4, S5, and S9), and newly prepared La–H samples in DAC #S (Fig. 2a and Supplementary Fig. S35). The data were collected from three individual La–Ce–H electrical DACs at their pressures and from La–H DAC #S during decompression. XRD reflections in phase mixtures were separated according to the phase distribution and the state of Debye rings. The P6 3 /mmc and Fm\(\bar{3}\)m structures were discovered in DAC #3 at 131 GPa simultaneously, which can explain the high-T c phases. The Debye rings of the P6 3 /mmc structure were spot-like in DAC #2 while uniform in DAC #3. The lower pressure of synthesis and sufficient laser heating probably caused a better crystallization of sample #2. Noteworthy, the temperature (<1500 K) is not high enough to melt the La–Ce alloy at megabar pressures. Laser-heating may decompose the synthesized hydrides but cannot change the disordered distribution of La/Ce atoms. During the revision of our manuscript, we noticed another two La–Ce–H works with La/Ce of 1:1 that reported the P6 3 /mmc36 and Fm\(\bar{3}\)m37 phases, respectively. The main differences between our and their data lie in the different La–Ce ratios and synthesized conditions, which contribute to the various results. By comparing with T c –P trend (Fig. 4c and Fig. S36), we propose that the Fm\(\bar{3}\)m phase can possibly only be synthesized at pressures above 130 GPa (DACs #3 and #6) with lower T c than the P6 3 /mmc phase (Supplementary Figs. S8 and S18). Besides, the impurity phases with lower hydrogen content can explain the other lower T c s that we also observed. Current experimental techniques allow one just to determine the metal sublattice and estimate the hydrogen content in metal polyhydrides. Hydrogen atoms cannot be directly determined due to their very low scattering factor. Neutron diffraction38 and nuclear magnetic resonance39,40,41,42 could be employed in the future to give more information on the structure of H-sublattice.

Fig. 2: Synchrotron X-ray diffraction (0.6199 Å) analysis of the synthesized hydrides. a Peaks indexing for the La–Ce–H samples in DACs #2, 3 and the La–H sample in DAC #S. Insets show the integrated diffraction patterns. The wide diffraction band of an impurity located on the seat surface in DAC #3 is masked by gridlines (Supplementary Fig. S10). b Pressure dependence of the unit cell volume of different polyhydrides. The experimental results for the La–Ce–H and La–H systems are shown in color and black, respectively. Gray symbols show literature data for the synthesized La–H phases7,9,29. Solid and dashed lines indicate the P–V relation of La–H and Ce–H phases, respectively. “VASP” marks the equation of state (EoS) calculated using the VASP code (PBE GGA), and “QE” marks the EoS calculated using the Quantum ESPRESSO code (PAW PBE). Full size image

We plotted our P–V data together with the calculated or experimentally reported equations of state (EoS) of binary Ce–H and La–H hydrides for comparison (Fig. 2b). The hydrogen content was determined by comparing the unit cell volume. We concluded that the main superconducting phase in La–Ce–H system below 130 GPa was deemed as P6 3 /mmc-(La,Ce)H 9-10 . Considering that the electrical resistance and XRD measurements are not performed on the same DAC for the binary La–H system, T c values observed in DAC #L1 cannot be directly distinguished from those of the mixed phases P6 3 /mmc-LaH x , and C2/m-LaH x and I4/mmm-LaH x in DAC #S. However, this does not affect the conclusion that ternary hexagonal La–Ce–H system exhibits higher T c than the binary La–H system, both of which are synthesized at the same pressure-temperature conditions.

The upper critical magnetic field

To further confirm the superconductivity and study the upper critical field H c2 (0) of the synthesized superconducting phases, we have applied an external magnetic field to different DACs from 150 GPa to 88 GPa (Fig. 3). We used the T c-mid that can be easily recognized to fit with the Werthamer-Helfand-Hohenberg (WHH) model43, simplified by Baumgartner44. For all the DACs, the T c decreases with increasing magnetic field, as in all superconductors. The acceptable difference between the cooling and warming cycle is because of the temperature gradient between the temperature sensor and the target sample (Fig. 3c). We tried to apply the field parallel and perpendicular to the culet of DAC #9 and observed the trace of anisotropy effect (Fig. 3b). During the decompression of the La–Ce–H system, the upper critical field at 0 K (obtained by extrapolation using the simplified WHH model) increased from 135 T (150 GPa) to striking 235 T (100 GPa), accompanied by a broadening of the transition width. After the decomposition of (La,Ce)H 9-10 , the H c2 (0) for the residual phases dropped to ~25 T at 88–102 GPa and became steady in this pressure range. The La–H system shows a similar H c2 (0) of 24.5 T at 123 GPa (Fig. S29). The strong enhancement of the upper critical magnetic field in the La–Ce–H system is probably related to the random distribution of La/Ce atoms and local distortion of the H-sublattice induced by it. This situation dramatically shortens the electronic mean free path and pushes the system into the dirty limit (Fig. S38). The H-sublattice then becomes extremely unstable and distorted near the decomposition pressure of the polyhydride.