Stability and superconductivity of lanthanum and yttrium decahydrides

Rare-earth hydrides can exhibit high-temperature superconductivity under high pressure. Here, we apply a crystal structure prediction method to the current record-holding $T_c$ material, ${\mathrm{LaH}}_{10}$. We find a pressure-induced phase transition from the experimentally observed cubic phase to a hexagonal phase at around 420 GPa. This phase is metastable down to low pressures and could explain experimental observations of hcp impurities in fcc samples. We go on to find that ${\mathrm{YH}}_{10}$ adopts similar structures and discuss the sensitivity of superconductivity calculations to certain computational parameters.

Figure 1

The dependence of $T_c$ on the double-$\delta$ smearing width, $\sigma$, for $Fm\overline{3}m-{\mathrm{YH}}_{10}$ at 350 GPa. The region of insufficient smearing is shown, along with our choice of $\sigma$ for this structure and pressure. The smallest value used in an electron-phonon calculation with default quantum espresso settings is shown.

Figure 2

The dependence of $T_c$ on the double-$\delta$ smearing width, $\sigma$, for $Im\overline{3}m-{\mathrm{YH}}_6$ at 160 GPa. A recent experimental measurement at 166 GPa, falling just within our calculated $T_c$ range, is also shown [43]. We note that Refs. [43, 44] highlighted that previous calculated $T_c$ values were considerably higher than their experimental observations and that the results of Ref. [19], which used accurate Wannier interpolation techniques, are in agreement with ours.

Figure 3

Structures of ${\mathrm{LaH}}_{10}$. (a) Two formula unit/cell $C2/m$, (b) two formula unit/cell $P{6}_3/mmc$, (c) one formula unit/cell $Fm\overline{3}m$. The $R\overline{3}m$ structure is not shown as it is visually indistinguishable from the $Fm\overline{3}m$ structure at the pressures of interest.

Figure 4

The Gibbs free energy as a function of pressure for energetically competitive phases of ${\mathrm{LaH}}_{10}$, plotted relative to a third-order Birch-Murnaghan fit of the $Fm\overline{3}m$ data. Crosses represent calculations with unstable phonon modes; these points are not included in the Gibbs free energy fit. Solid lines are at 300 K, dashed lines are at 0 K.

Figure 5

Calculated $T_c\left(P\right)$ for dynamically stable phases of ${\mathrm{LaH}}_{10}$ from direct solution of the Eliashberg equations. The width of the lines arises from our treatment of the Morel-Anderson pseudopotential, ${\mu }^{*}$, [49] as an empirical parameter with values between 0.1 and 0.15. The $Fm\overline{3}m$ result has been extended into the region where it is dynamically unstable (shaded according to unstable fraction of the phonon density of states) in order to facilitate comparison with the experimental results of Refs. [25, 26]. This extension was achieved by removing the contribution of unstable phonon modes, in their entirety, to the Eliashberg function while maintaining its normalization.

Figure 6

A convex hull for the La-H system at 150 GPa, accurately calculated using castep, $\mathbf{k}$-point spacing of $2\pi \times 0.03$ Å${}^{-1}$ and a 700 eV plane-wave cutoff. The on-the-fly pseudopotential strings used are provided in the Supplemental Material [42]; the inclusion of a fraction of a 4f electron in the generation of the La pseudopotential was found to be crucial. A pseudopotential without this addition was unable to reproduce the all-electron $Fm\overline{3}m-{\mathrm{LaH}}_{10}$ PV curve and led to a qualitatively different convex hull [42]. In agreement with Ref. [50], we find that ${\mathrm{LaH}}_9$ is not on the hull at this pressure. However, we also find that ${\mathrm{LaH}}_{16}$ does not lie on the hull at 150 GPa, despite finding the $P6/mmm-{\mathrm{LaH}}_{16}$ structure studied in that work.

Figure 7

Structures of ${\mathrm{YH}}_{10}$. (a) Two formula unit/cell $Cmcm$, (b) one formula unit/cell $Fm\overline{3}m$, (c) two formula unit/cell $P{6}_3/mmc$. The $R\overline{3}m$ structure is, again, not shown.

Figure 8

The Gibbs free energy as a function of pressure for energetically competitive phases of ${\mathrm{YH}}_{10}$, plotted and interpolated relative to a third-order Birch-Murnaghan fit of the $Fm\overline{3}m$ data. Solid lines are at 300 K, dashed lines are at 0 K.

Figure 9

Calculated $T_c\left(P\right)$ for dynamically stable phases of ${\mathrm{YH}}_{10}$ from direct solution of the Eliashberg equations. ${\mu }^{*}$ is, again, taken to have a value between 0.1 and 0.15.