Bond disproportionation and dynamical charge fluctuations in the perovskite rare-earth nickelates

We present a theory describing the local electronic properties of the perovskite rare-earth nickelates—materials which have negative charge transfer energies, strong O $2p$ – Ni $3d$ covalence, and breathing-mode lattice distortions at the origin of highly studied metal-insulator and antiferromagnetic ordering transitions. Utilizing a full-orbital, full-correlation double-cluster approach, we find strong charge fluctuations, in agreement with a bond disproportionation interpretation. The double-cluster formulation permits the inclusion of necessary orbital degeneracies and Coulomb interactions to calculate resonant x-ray spectral responses, with which we find excellent agreement with well-established experimental results. This previously absent, crucial link between theory and experiment provides validation of the recently proposed bond disproportionation theory, and provides an analysis methodology for spectroscopic studies of engineered phases of nickelates and other high-valence transition-metal compounds.

Figure 1

(a) Perovskite nickelate structure with alternating octahedra shaded to distinguish the long (green) and short (gray) bond sites in the low-temperature distorted phase. (b) A cutout of the structure demonstrating the $O_h$ arrangement of the two octahedra types. (c) Diagrammatic depictions of the hopping arrangements for the double-cluster model. (d) Visualization of calculated hole density matrices on compressed (left) and expanded (right) octahedra in the distorted phase (ligand hole densities are scaled by a factor of 2 for clarity). (e)–(h) Ground-state characteristics from the double-cluster model: (e) Distribution of Ni $3d$ electrons. (f) Distribution of ligand holes. (g) Spins for the two octahedra. (h) Weights of configurations with hole distributions $\left(n_A,n_B\right)$ on the compressed and expanded octahedra, respectively.

Figure 2

Resonant x-ray responses of the double-cluster model. (a) XAS and MCD spectra are shown in the single-cluster limit (top, intercluster hopping $V_I$ set to zero), and for increasing intercluster hopping values. (b) XAS spectra for different magnitudes of the breathing distortion (with $V_I=0.35$). The spectra of the two inequivalent sites are shown, along with their sum. (c) Resonant magnetic diffraction and site-decomposed MCD spectra are shown for the same breathing distortions as (b), along with the total XAS for comparison. MCD spectra are offset for clarity.

Figure 3

(a) Configuration weights $c_i^2$ are compared for the present double-cluster model (left, green) and conventional ligand field theory (right, green), demonstrating the additional determinants which arise in negative charge transfer situations not captured by single-cluster theory. In both cases, the weights for the noninteracting approximation are shown in red for comparison. Divisions on the bars have values of 0.05 for the double cluster and 0.10 for the single cluster. (b) The compressed octahedron exhibits a wave function with dominant ligand hole-rich $d^8$ determinants, while the expanded octahedron has a much more ionic wave function.