Ab initio prediction of the high-pressure phase diagram of ${\mathrm{BaBiO}}_3$

${\mathrm{BaBiO}}_3$ is a well-known example of a 3D charge density wave (CDW) compound, in which the CDW behavior is induced by charge disproportionation at the Bi site. At ambient pressure, this compound is a charge-ordered insulator, but little is known about its high-pressure behavior. In this work, we study from first principles the high-pressure phase diagram of ${\mathrm{BaBiO}}_3$ using phonon mode analysis and evolutionary crystal structure prediction. We show that charge disproportionation is very robust in this compound and persists up to 100 GPa. This causes the system to remain insulating up to the highest pressure we studied.

Figure 1

${\mathrm{BaBiO}}_3$ ground-state structures used in this work. (a) $Pm\overline{3}m$: ideal perovskite structure. (b) $C12/\overline{m}1$: experimental ${\mathrm{BaBiO}}_3$ structure for ambient pressure and room temperature. (c) $P\overline{1}$: triclinic structure stable from 20 GPa to 28 GPa pressure. (d) $C12/\overline{m}{1}^C$: clustered monoclinic structure stable between 28 GPa and 87 GPa pressure. (e) Nonsymmetric distorted structure stable from 87 GPa pressure. Structures (c), (d), and (e) where obtained using evolutionary crystal structure prediction (EP). Large green spheres are Ba atoms, large purple spheres are Bi atoms, and small red spheres are O atoms.

Figure 2

Predicted high-pressure phase diagram of ${\mathrm{BaBiO}}_3$. Up to 100 GPa, we predict three structural phase transitions: monoclinic $\left(C12\overline{m}1\right)$ to triclinic $\left(P\overline{1}\right)$ at about 20 GPa, triclinic to clustered $\left(C12\overline{m}{1}^C\right)$ at about 28 GPa, and clustered to distorted $\left(P1\right)$ at about 87 GPa. The values of the enthalpies are referred to a 40 atoms unit cell.

Figure 3

Breathing and tilting distortions applied to an ideal cubic perovskite structure. Breathing is indicated by squares of different size where the white arrows show the direction in which O atoms are displaced. Tilting is shown as a rotation of a square by angle $\phi$ around axis normal to the plane of the paper.

Figure 4

Average number of O neighbors of Bi atoms for a pool of 2 f.u. ${\mathrm{BaBiO}}_3$ structures obtained using the evolutionary algorithms approach. Each dot is associated with a specific structure and its color denotes the average number of neighbors. For the perovskite structure the average number of neighbors is 6 and the deviation from this value shows the amplitude of distortion presented in the system. Details on the neighbor analysis can be found in the Supplemental Material in subsection “D. Neighbors analysis” [68].

Figure 5

DOS/atom and the difference of average PDOS for ${\mathrm{Bi}}^{5+}$ and ${\mathrm{Bi}}^{3+}$ atoms [69] for stable structures at the pressure of its stability. Left panel shows results obtained with PBE functional for structural relations and DOS calculations. Right panel shows results for structures at the left panel but DOS calculations were performed using the HSE functional using the structures from PBE calculations.

Figure 6

Charge difference $\mathrm{\Delta }\rho$ between two different Bi atoms for all stable structures in the phase diagram: the one with the maximal charge (represented by the ${\mathrm{Bi}}^{3+}$ atom) and the one with the minimal (represented by the ${\mathrm{Bi}}^{5+}$ atom); the HSE functional was used. The color scale at the bottom indicates the stability range of the various structures.