Possible structural quantum criticality tuned by rare-earth ion substitution in infinite-layer nickelates

I show the infinite-layer rare-earth nickelates are near a structural quantum critical point by mapping the energetics of their structural instabilities using first priniciples calculations. I first confirm previous results that show a phonon instability in the $P4/mmm$ phase leading to the $I4/mcm$ structure for $R$NiO$_2$ with $R$ = Sm--Lu. I then study the non-spin-polarized phonon dispersions of the $I4/mcm$ phase and find that they exhibit rare-earth size dependent instabilities at the $X$ and $M$ points for materials with $R$ = Eu--Lu. Group-theoretical analysis was used to enumerate all the isotropy subroups due to these instablities, and the distorted structures corresponding to their order parameters were generated using the eigenvectors of the unstable phonons. These structures were then fully relaxed by minimizing both the atomic forces and lattice stresses. I was able to stabilize only five out of the twelve possible distortions. The $Pbcn$ isotropy subgroup with the $M_5^+(a,a)$ order parameter shows noticeable energy gain relative to other distortions for the compounds with late rare-earth ions. However, the order parameter of the lowest-energy phase switches first to $X_2^- (0,a) + M_5^+ (b,0)$ and then to $X_2^- (0,a)$ as the size of the rare-earth ion is progressively increased. Additionally, several distorted structures lie close in energy for the early members of this series. These features of the structural energetics persist even when antiferromagnetism is allowed. Such a competition between different order parameters that can be tuned by rare-earth ion substitution suggests that any structural transition that could arise from the phonon instabilities present in these materials can be suppressed to 0 K.