First-principles study of hydrogen ordering in lanthanum hydride and its effect on the metal-insulator transition

We discuss the structural details and the ordering of hydrogen in LaH${}_{x}$ for $2\ensuremath{\leqslant}x\ensuremath{\leqslant}3$. To this end, we combine first-principles calculations with the cluster-expansion method. This approach allows us to follow the H occupation of the interstitial sites within the face-centered cubic matrix of La atoms. We find that LaH${}_{x}$ clearly favors the fluorite structure at $x=2$ and adds excess H atoms at the octahedral interstitial sites. The ground-state behavior of the system is discussed and is found in agreement with experimentally observed structures at compositions LaH${}_{2.25}$ and LaH${}_{2.50}$; an additional ground state at composition LaH${}_{2.71}$ is predicted. The cluster expansion also permits an extensive scan of LaH${}_{x}$ structures with two octahedral vacancies per unit cell. For energetically favorable configurations, this scan yields a vacancy percolation threshold at LaH${}_{2.75}$ that possibly drives the concentration-dependent metal-insulator transition: The band gap calculated for isolated vacancy pairs disappears for percolating vacancy chains. This transition from metallic to insulating state is also experimentally observed near to the composition LaH${}_{2.8}$ and gives rise to the ``switchable mirror'' phenomenon.