First-principles study of oxygen-deficient ${\mathrm{LaNiO}}_3$ structures

We describe the results of first-principles calculations of the properties of oxygen vacancies in ${\mathrm{LaNiO}}_3$. We consider isolated oxygen vacancies, pairs of vacancies, and vacancies at finite concentrations that form oxygen-deficient phases of ${\mathrm{LaNiO}}_3$. The key electronic structure question we address is whether and to what extent an oxygen vacancy acts as an electron donor to the Fermi level (mobile and conducting electronic states). More generally, we describe how one can quantify, based on electronic structure calculations, the extent to which a localized point defect in a metallic system donates electrons to the Fermi level compared to trapping electrons in localized defect states. For ${\mathrm{LaNiO}}_3$, we find that an oxygen vacancy does not create mobile carriers but instead makes the two Ni sites adjacent to it turn into ${\mathrm{Ni}}^{2+}$ cations. Energetically, we compute the formation energy and diffusion barrier for oxygen vacancies. Structurally, we show that pairs of vacancies prefer to form on opposite sides of a Ni cation, aligning along a pseudocubic axis. For finite concentrations of vacancies, we compute the dependence of the ${\mathrm{LaNiO}}_3$ lattice parameters on the vacancy concentration to provide reliable data for experimental determination of the oxygen content in ${\mathrm{LaNiO}}_3$ and ${\mathrm{LaNiO}}_3$ thin films.

Figure 1

Primitive cell of ${\mathrm{LaNiO}}_3$.

Figure 2

Calculated electronic band structure of bulk ${\mathrm{LaNiO}}_3$ in a 10-atom unit cell projected on the Ni $3d$ (red lines) and O $2p$ (blue lines) Wannier functions. High-symmetry points of the Brillouin zone are labeled using the convention for a corresponding simple perovskite cubic five-atom unit cell; i.e., the axial directions connect neighboring Ni cations.

Figure 3

A $2\times 2\times 2$ pseudocubic supercell of ${\mathrm{LaNiO}}_3$ with a single oxygen vacancy showing ${\mathrm{NiO}}_6$ octahedra. The position of the vacancy is indicated by the open black circle. Red balls are O atoms, gold balls are La, blue balls are Ni, and ${\mathrm{NiO}}_6$ octahedra are shown in red.

Figure 4

Theoretically calculated three-dimen-sional (3D) electron redistribution function $\rho \left(V_{\mathrm{O}}\right)+\rho \left(\mathrm{O}\right)-\rho \left(\mathrm{bulk}\right)$ in ${\mathrm{LaNiO}}_3$ upon neutral oxygen vacancy formation. Red (blue) 3D isosurfaces show the increase (decrease) in the electron density in space. Arrows indicate the primary direction of electron redistribution from the vacancy site to the $d_{3z^2-r^2}$ orbitals of the two Ni atoms neighboring the vacancy. The isosurfaces are drawn at $\sim 20\%$ of the maximum value of the electron density. Smaller open (red) circles denote O atoms; larger open (blue) circles, Ni atoms. Dashed black lines indicate Ni-O bonds. The electron redistribution is highly localized.

Figure 5

Bulk band structure of a $2\times 2\times 2$ supercell (thin black curves). Projections of the bands onto Wannier functions with a Ni $e_g$ character are indicated by red overlays where the thickness is proportional to the projection. The Fermi level is at 0 eV.

Figure 6

Band structure of a $2\times 2\times 2$ supercell with a single vacancy. Same nomenclature as in Fig. 5.

Figure 7

Classification of Ni atoms in a $2\times 2\times 2$ supercell based on the proximity to the oxygen vacancy. The vacancy is indicated by the white circle in the (blue) square, and the three types of inequivalent Ni sites are indicated as well.

Figure 8

Projected density of states (PDOS) onto the Ni $3d$ Wannier functions for a $2\times 2\times 2$ supercell. Naming of Ni sites is shown in Fig. 7. The Fermi level is at 0 eV. We also show the Ni PDOS for bulk ${\mathrm{LaNiO}}_3$, which is aligned in energy to match that of ${\mathrm{Ni}}_3$ as closely as possible. The resulting position of the Fermi level of the bulk PDOS is indicated by the dashed vertical line.

Figure 9

Formation energies calculated using supercells of various sizes in the oxygen-rich limit with LDA and PBE exchange-correlation functionals. The extrapolation to infinite cell size is made using similar supercells within the LDA [filled (red) squares] and is shown by the solid line.

Figure 10

Schematic of the seven distinct configurations for two oxygen vacancies in a $2\times 2\times 2 {\mathrm{LaNiO}}_3$ supercell. Solid (blue) lines indicate the volume of the supercell. Dashed black lines indicate the eight interior pseudocubic $1\times 1\times 1$ cells (each has one formula unit). The positions of the two vacancies are indicated by the filled (blue) squares. As the caption at the lower right shows, the vacancy position is in the center of a square (the white circle) and A-site cations (La) are at the corners of the square. The orientation of the square shows the plane bisecting the line between the two Ni atoms neighboring a vacancy. The approximate distance between two vacancies for each case is indicated in units of the $1\times 1\times 1$ pseudocubic lattice constant $a$.

Figure 11

Band structure of a $2\times 2\times 2$ supercell with an apical divacancy, projected on the $d_{3z^2-r^2}$ Wannier functions of the Ni atoms nearest to vacancies.

Figure 12

$c/a$ as a function of O vacancy concentration in tetragonal ${\mathrm{LaNiO}}_{3-\delta }$.

Figure 13

$V/V_0$ as a function of O vacancy concentration in tetragonal ${\mathrm{LaNiO}}_{3-\delta }$. Exp 1 and Exp 2 denote results from Refs. [68] and [69], respectively.

Figure 14

$c/a$ as a function of O vacancy concentration in tetragonal ${\mathrm{LaNiO}}_{3-\delta }$. In-plane lattice parameters are strained to those of bulk ${\mathrm{LaAlO}}_3$.