Hybridization effects and bond disproportionation in the bismuth perovskites

We propose a microscopic description of the bond-disproportionated insulating state in the bismuth perovskites $X{\mathrm{BiO}}_3$ ($X=\text{Ba},\text{Sr}$) that recognizes the bismuth-oxygen hybridization as a dominant energy scale. It is demonstrated by using electronic structure methods that the breathing distortion is accompanied by spatial condensation of hole pairs into local, molecularlike orbitals of the $A_{1g}$ symmetry composed of O-$2p_{\sigma }$ and Bi-$6s$ atomic orbitals of collapsed ${\mathrm{BiO}}_6$ octahedra. The primary importance of oxygen $p$ states is thus revealed, in contrast to a popular picture of a purely ionic ${\mathrm{Bi}}^{3+}/{\mathrm{Bi}}^{5+}$ charge disproportionation. Octahedra tilting is shown to enhance the breathing instability by means of a nonuniform band narrowing. We argue that the formation of localized states upon breathing distortion is, to a large extent, a property of the oxygen sublattice, and we expect similar hybridization effects in other perovskites involving formally high oxidation state cations.

Figure 1

(a) LDA electronic structure of ${\mathrm{SrBiO}}_3$ projected onto the Bi-$6s$ orbital and combinations of the O-$p_{\sigma }$ orbitals of a collapsed (top) and expanded (bottom) ${\mathrm{BiO}}_6$ octahedron. For the doublet $E_g$ and the triplet $T_{1u}$, only one projection is shown. The Fermi level is set to zero, and PDOS stands for projected density of states and is given in states/eV/cell. (b) An octahedron of O-$p_{\sigma }$ orbitals coupled via nearest-neighbor hopping integrals $-t$ and its eigenstates.

Figure 2

LDA characterization of ${\mathrm{SrBiO}}_3$ model structures with varying degrees of the ${\mathrm{BiO}}_6$ octahedra's tilting $t$ and breathing $b$: (a) total energy per formula unit (f.u.) and (b) charge gap. In (a), solid lines and solid circles (dashed lines and open circles) represent model structures with fixed (relaxed) Sr atoms. The horizontal dashed line marks the energy of the experimental ${\mathrm{SrBiO}}_3$ structure.

Figure 3

LDA electronic structure of ${\mathrm{SrBiO}}_3$ as a function of breathing $b$ and tilting $t$. Projections are made onto the Bi-$6s$ orbital and the $A_{1g}$ combination of the O-$p_{\sigma }$ orbitals of a collapsed ${\mathrm{BiO}}_6$ octahedron, as well as their bonding (“B”) and antibonding (“A”) combinations.

Figure 4

(a) LDA electronic structure of the oxygen sublattice of ${\mathrm{SrBiO}}_3$. Projections are made onto combinations of the O-$p_{\sigma }$ orbitals of a collapsed ${\mathrm{O}}_6$ octahedron. (b) Model density of states as a function of breathing $b$ and hybridization between $s$ and $p$ orbitals $h$. CC (EC) stands for a collapsed (expanded) $p$-site cage. The model states are 90% filled, i.e., there is one hole per $s$ orbital; the Fermi energy is set to zero and marked with black dashed vertical lines.

Figure 5

The effect of tilting on (a) the half-filled band and on (b) the static susceptibility $\chi (\mathbf{q},\omega =0)$, at zero breathing. In (b), solid (dashed) lines represent calculations where nonlinear effects due to tilting are (are not) taken into account.