Lattice normal modes and electronic properties of the correlated metal LaNiO${}_3$

We use density functional theory calculations to study the lattice vibrations and electronic properties of the correlated metal LaNiO${}_3$. To characterize the rhombohedral-to-cubic structural phase transition of perovskite LaNiO${}_3$, we examine the evolution of the Raman-active phonon modes with temperature. We find that the $A_{1g}$ Raman mode, whose frequency is sensitive to the electronic band structure, is a useful signature to characterize the octahedral rotations in rhombohedral LaNiO${}_3$. We also study the importance of electron-electron correlation effects on the electronic structure with two approaches that go beyond the conventional band theory [local spin density approximation (LSDA)]: the local spin $\mathrm{density}+\mathrm{Hubbard}U$ method ($\mathrm{LSDA}+U$) and hybrid exchange-correlation density functionals that include portions of exact Fock exchange. We find that the conventional LSDA accurately reproduces the delocalized nature of the valence states in LaNiO${}_3$ and gives the best agreement with the available experimental data on the electronic structure of LaNiO${}_3$. Based on our calculations, we show that the electronic screening effect from the delocalized Ni 3$d$ and O-2$p$ states mitigates the electronic correlations of the $d^7$ Ni cations, making LaNiO${}_3$ a weakly correlated metal.

Figure 1

(a) The crystal structure of rhombohedral $R\overline{3}c$ LaNiO${}_3$ possesses antiphase rotations ($a^{-}{a}^{-}{a}^{-}$ tilt system) of adjacent NiO${}_6$ octahedra with angle $\theta$ (b) about the [111] trigonal axis. The relationship between the pseudocubic perovskite cell (solid lines) and the rhombohedral lattice vectors (dashed lines) of length $a$ is also illustrated.

Figure 2

Displacement patterns for the Raman-active lattice normal modes in the $R\overline{3}c$ structure. The corresponding symmetry labels and our calculated LSDA frequencies (in cm${}^{-1}$) are given for reference.

Figure 3

Occupation numbers $n^i$ for the total Ni 3$d$, $e_g$, and $t_{2g}$ orbitals in LaNiO${}_3$, with respect to potential shift $\alpha$ for the initial (0) (filled circles) and self-consistent (open squares) electronic configurations. The slopes of the linear data fits are used to construct the ${\chi }_0$ and $\chi$ response matrices. Occupation numbers are normalized by subtracting the occupation values $n_i\left(0\right)$ with a zero potential shift ($\alpha =0$).

Figure 4

(a) Landau free energy $G$($\theta ,T=0$ K) of LaNiO${}_3$ as a function of the order parameter $\theta$. Solid lines are calculated using Landau theory, and filled symbols correspond to LSDA total energy results. (b) Equilibrium order parameter $\theta$ as a function of temperature; the second-order phase transition occurs at $T=T_C$.

Figure 5

(a) Temperature-dependent Raman frequencies for rhombohedral LaNiO${}_3$ structures. Solid lines indicate experimental results taken from Ref. 63. Results from our LSDA calculations are shown as filled circles. (b) We observe linear scaling behavior between the $A_{1g}$ Raman frequency and the NiO${}_6$ octahedral rotation order parameter $\theta$. The fitted solid line is a guide for the eye. Inset at upper left: Vibrational pattern of the $A_{1g}$ mode (both side and top views). Inset at lower right: A linear change in the squared $A_{1g}$ soft-mode frequency with temperature.

Figure 6

Spin- and atom-resolved densities of states (DOS) for the LaNiO${}_3$ structures reported in Table with the $\mathrm{LSDA}+U$ exchange-correlation functional.

Figure 7

The experimental PES spectrum for a 20-nm crystalline LNO film (filled circles) from Ref. 69 is compared to the density of states calculated with the $\mathrm{LSDA}+U$ ($U=5.74$ eV), gradient-corrected (PBE) and hybrid (PBE0 and HSE) exchange-correlation functionals. Calculated data are smeared with Lorentzian and Gaussian functions and truncated with a Fermi-Dirac distribution to facilitate the comparison. See the text for peak position assignments.

Figure 8

Spin- and orbital-resolved density of states for rhombohedral LaNiO${}_3$, obtained from LSDA, $\mathrm{LSDA}+U$ ($U=5.74$ eV), PBE, PBE0, and HSE calculations. The Fermi energy is the energy 0. In each case the structure is fully relaxed according to the specific functional, with the exception that the DOS for the hybrid XC functionals are calculated with the LSDA ground-state atomic structure.

Figure 9

Orbital-resolved density of states in the core energy region obtained from the LSDA, $\mathrm{LSDA}+U$ ($U=5.74$ eV), PBE, PBE0, and HSE calculations. The Fermi energy level is shifted to the energy 0. Note that the binding energies predicted by the PBE0 and HSE are not obtained by a simple rigid shift of the PBE results.