Anharmonic and quantum effects in Pm3̄ AlM(M = Hf, Zr)H6 under high pressure: A first-principles study

First-principles calculations were employed to investigate the impact of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of Pm3̄ AlM(M = Hf, Zr)H6 at pressures of 0.3-21.2 GPa (AlHfH6) and 4.7-39.5 GPa (AlZrH6) within the stochastic self-consistent harmonic approximation. A correction is predicted for the crystal lattice parameters, phonon spectra, and superconducting critical temperatures, previously estimated without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for lattice dynamics. The findings suggest that quantum ionic fluctuations have a significant impact on the crystal lattice parameters, phonon spectra, and superconducting critical temperatures. Based on our anharmonic phonon spectra, the structures will be dynamically stable at 0.3 GPa for AlHfH6 and 6.2 GPa for AlZrH6, ∼6 and 7 GPa lower than pressures given by the harmonic approximation, respectively. Due to the anharmonic correction of their frequencies, the electron-phonon coupling constants (λ) are suppressed by 28% at 11 GPa for AlHfH6 and 22% at 30 GPa for AlZrH6, respectively. The decrease in λ causes Tc to be overestimated by ∼12 K at 11 GPa for AlHfH6 and 30 GPa for AlZrH6. Even if the anharmonic and quantum effects are not as strong as those of Pm3̄n-AlH3, our results also indicate that metal hydrides with hydrogen atoms in interstitial sites are subject to anharmonic effects. Our results will inevitably stimulate future high-pressure experiments on synthesis, structural, and conductivity measurements.