  By using DFT+U, we explore the formation of oxygen vacancies and their impact
on the electronic and magnetic structure in strained bulk LaNiO3 and
(LaNiO3)$_1$/(LaAlO3)$_1$(001) superlattices. For bulk LaNiO3, we find that
epitaxial strain induces a substantial anisotropy in the oxygen vacancy
formation energy. In particular, tensile strain promotes the selective
reduction of apical oxygen, which may explain why the recently observed
superconductivity of infinite-layer nickelates is limited to strained films.
For (LaNiO3)$_1$/(LaAlO3)$_1$(001) superlattices, the simulations reveal that
the NiO2 layer is most prone to vacancy formation, whereas the AlO2 layer
exhibits generally the highest formation energies. The reduction is
consistently endothermic, and a largely repulsive vacancy-vacancy interaction
is identified as a function of the vacancy concentration. The released
electrons are accommodated exclusively in the NiO2 layer, reducing the vacancy
formation energy in the AlO2 layer by 70% with respect to bulk LaAlO3. By
varying the vacancy concentration from 0% to 8.3% in the NiO2 layer at tensile
strain, we observe an unexpected transition from a localized
site-disproportionated (0.5%) to a delocalized (2.1%) charge accommodation, a
re-entrant site disproportionation leading to a metal-to-insulator transition
despite a half-filled majority-spin Ni $e_g$ manifold (4.2%), and finally a
magnetic phase transition (8.3%). While a band gap of up to 0.5 eV opens at
4.2% for compressive strain, it is smaller for tensile strain or the system is
metallic, which is in sharp contrast to the defect-free superlattice. The
strong interplay of electronic reconstructions and structural modifications
induced by oxygen vacancies in this system highlights the key role of an
explicit supercell treatment and exemplifies the complex response to defects in
artificial transition metal oxides.
