Effects of the surface termination and oxygen vacancy positions and on LaNiO$_{3}$ ultra-thin films: First-principles study

While ultra-thin layers of the LaNiO$_3$ film exhibit a remarkable metal-insulator transition as the film thickness becomes smaller than a few unit cell (u.c.), the formation of oxygen vacancies and their effects on the correlated electronic structure have been rarely studied. Here, we investigate the effects of the surface termination and the oxygen vacancy position on the electronic properties and vacancy energetics of LaNiO$_3$ ultra-thin films using density functional theory plus U (DFT+U). We find that oxygen vacancies can be easily formed in the Ni layers with the NiO$_2$ terminated surface (0.5 u.c. and 1.5 u.c. thickness) compared to the structures with the LaO terminated surface and the in-plane vacancy is energetically favored than the out-of-plane vacancy. When two vacancy sites are allowed, the Ni square plane geometry is energetically more stable in most cases as two oxygen vacancies tend to stay near a Ni ion. The in-plane vacancy of the NiO$_2$ terminated structure is favored since the released charge due to the oxygen vacancy can be easily accommodated in the $d_{x^2-y^2}$ orbital, which is less occupied than the $d_{z^2}$ orbital. Remarkably, the oxygen vacancy structure containing the Ni square-plane geometry becomes an insulating state in DFT+U with a sizable band gap of 1.2eV because the large crystal field splitting between $d_{z^2}$ and $d_{x^2-y^2}$ orbitals in the square-plane favors an insulating state and the Mott insulating state is induced in other Ni sites due to strong electronic correlations.