  The fundamental properties of infinite-layer rare-earth nickelates (RNiO2)
are carefully revisited and compared with those of CaCuO2 and RNiO3
perovskites. Combining first-principles and finite-temperature
second-principles calculations, we highlight that bulk NdNiO2 compound are far
from equivalent to CaCuO2, together at the structural, electronic, and magnetic
levels. Structurally, it is shown to be prone to spin-phonon coupling induced
oxygen square rotation motion, which might be responsible for the intriguing
upturn of the resistivity. At the electronic and magnetic levels, we point out
orbital-selective Mott localization with strong out-of-plane band dispersion,
which should result in the isotropic upper critical fields and weakly
three-dimensional magnetic interactions with in-plane local moment and
out-of-plane itinerant moment. We further demonstrate that as in RNiO3
perovskites, oxygen rotation motion and rare-earth ion controlled electronic
and magnetic properties can give rise in RNiO2 compounds to a rich phase
diagram and high tunability of various appealing properties. In line with that,
we reveal that key ingredients of high-Tc superconductor such as orbital
polarization, Fermi surface, and antiferromagnetic interactions can be
deliberately controlled in NdNiO2 through epitaxial strain. Exploiting
strain-orbital engineering, a crossover from three- to two-dimensional magnetic
transition can be established, making then NdNiO2 thin film a true analog of
high-Tc cuprates.
