Mott gapping in $3dAB{\mathrm{O}}_3$ perovskites without Mott-Hubbard interelectronic repulsion energy U

The existence of band gaps in Mott insulators such as perovskite oxides with partially filled 3d shells has been traditionally explained in terms of strong, dynamic interelectronic repulsion codified by the on-site repulsion energy U in the Hubbard Hamiltonian. The success of the “DFT+U approach” where an empirical on-site potential term U is added to the exchange- and correlation density functional theory (DFT) raised questions on whether U in DFT+U represents interelectronic correlation in the same way as it does in the Hubbard Hamiltonian, and if empiricism in selecting U can be avoided. Here we illustrate that ab initio DFT without any U is able to predict gapping trends and structural symmetry breaking (octahedra rotations, Jahn-Teller modes, bond disproportionation) for all $3dAB{\mathrm{O}}_3$ perovskites from titanates to nickelates in both spin-ordered and spin-disordered paramagnetic phases. Thus, the mechanism of gap formation due to the Hubbard Hamiltonian dynamic interelectronic correlation is not a requirement in these $3d$ electron compounds. We describe the paramagnetic phases as a supercell where individual sites can have different local environments thereby allowing DFT to develop finite moments on different sites as long as the total cell has zero moment. We use the recently developed strongly constrained appropriately normed exchange and correlation functional (SCAN) that is sanctioned by the usual single-determinant, mean-field DFT paradigm with static correlations, but has a more precise rendering of self-interaction cancelation. Our results suggest that strong dynamic electronic correlations are not playing a universal role in gapping of $3dAB{\mathrm{O}}_3$ Mott insulators, and opens the way for future applications of DFT for studying a plethora of complexity effects that depend on the existence of gaps, such as doping, defects, and band alignment in $AB{\mathrm{O}}_3$ oxides.

Figure 1

Sketches of octahedra deformations (a) and (b) and bond disproportionation (c) distortions appearing in some $AB{\mathrm{O}}_3$ materials.

Figure 2

Key properties of oxide perovskites with the SCAN meta-GGA functional without U. We use the SQS supercell for the PM phase. $\mathrm{\Delta }{E}_{\mathrm{NM}}$ (meV/f u) is the energy difference between the current spin polarized and the Naive DFT (N-DFT) solution. $E_g$ is the band gap (in eV), $M_{3d}$ is the local moment (in ${\mu }_{\mathrm{B}}$) associated with the B cation. $Q_2^{-},Q_2^{+}$ and $B_{\mathrm{oc}}$ are the octahedral deformation amplitudes (in Å) (experimental values are provided in parenthesis). Ins. stands for insulating phases. Experimental values are taken from a: Ref. [40], b: Ref. [41], c: Ref. [42], d: Ref. [43], e: Ref. [44], f: Ref. [45]; g: Ref. [46], h: Ref. [47], i: Ref. [48], j: Ref. [49], k: Ref. [50], l: Ref. [51], m: Ref. [52], n: Ref. [53], o: Ref. [54], p: Ref. [5], q: Ref. [55], r: Ref. [56], s: Ref. [57], t: Ref. [58], u: Ref. [4], v: Ref. [59], w: Ref. [60].

Figure 3

Projected density of states (in states/eV/f. u) on B-d levels (filled green) and O-$p$ levels (red line) averaged on all sites in the low temperature phase. Band edges are shown with the vertical lines. The band gap is represented by the light grey area.

Figure 4

Partial charge density maps of levels at the top of the valence band in some selected “correlated oxide perovskites”.

Figure 5

Energy gains $\mathrm{\Delta }E$ (in meV/f.u with respect to the 0-mode amplitude) associated with $Q_2$ distortions (a) and (b) and the bond disproportionation (c) modes (in fractional units) obtained by the naïve nonmagnetic N-DFT (black circles, upper panel), the PM modelled with a SQS supercell (blue triangles, middle panel), and the AFM order (red squares, lower panel). The DMFT potential (orange diamonds) for the PM phase of $\mathrm{LaMn}{\mathrm{O}}_3$ and $\mathrm{LuNi}{\mathrm{O}}_3$ extrapolated from Refs. [15, 61] are also reported. Filled and unfilled symbols correspond to insulating (ins.) and metallic (met.) solutions. The reference structure at 0 amplitude of $Q_2$ or $B_{\mathrm{oc}}$ modes is set to a material displaying octahedra rotations and antipolar motions of ions. A fractional unit equals to 1 corresponds to amplitude appearing in the ground state AFM structure.

Figure 6

Properties of isoelectronic compounds. Energy difference as a function of the bond disproportionation (in fractional units) in $\mathrm{PrNi}{\mathrm{O}}_3$ in the AFM (squares) and PM (triangles) magnetic orders. Filled and unfilled symbols correspond to insulating and metallic solutions, respectively. The reference structure at 0 amplitude of the $B_{\mathrm{oc}}$ mode is set to a material displaying octahedra rotations and antipolar motions of ions. A fractional unit equal to 1 corresponds to the amplitude appearing in the ground state structure.