First-principles study of the cubic perovskites $\mathrm{Bi}M{\mathrm{O}}_3$ ($M=\mathrm{Al}$, Ga, In, and Sc)

We systematically investigated the structure, electronic properties, zone-center phonon modes, and structure instability of four cubic perovskite $\mathrm{Bi}M{\mathrm{O}}_3$ compounds, with three of the $M$ ions being IIIB metals (Al, Ga, and In) and one IIIA transition-metal Sc, using first-principles density-functional calculations. Optimized lattice parameters, bulk moduli, band structures, densities of states, as well as charge density distributions are calculated and compared with the available theoretical data. Our results are in good agreement with those previously reported in the literature. All the $\mathrm{Bi}M{\mathrm{O}}_3$ oxides considered in the present work are semiconductors with an indirect band gap between the occupied $\mathrm{O}2p$ and unoccupied $\mathrm{Bi}6p$ states varying between 0.17 and $1.57\mathrm{eV}$. Their electronic properties are determined mainly by Bi–O bonding, which, in turn, depends on the $M–\mathrm{O}$ bonding. Ferroelectric properties of these oxides come from the $6s^2$ lone pair on the $A$-site Bi ion and is similarly affected by the $M$ ions through their influence on the Bi–O bonding, as suggested by our calculations of density of state, Born effective charge, and soft modes. The existence of soft modes and eight [111] minima suggests that the phase transition in $\mathrm{Bi}\mathrm{Al}{\mathrm{O}}_3$ has a mixed displacive and order-disorder character. There is evidence that ferroelectricity is absent in $\mathrm{Bi}\mathrm{Ga}{\mathrm{O}}_3$. Our investigation suggests that the $\mathrm{Bi}M{\mathrm{O}}_3$ oxides or their modified versions are promising ferroelectric, piezoelectric, multiferroic, and photocatalytic materials.

Figure 1

(Color online) Band structures of four cubic $\mathrm{Bi}M{\mathrm{O}}_3$. The Fermi level corresponds to $0.0\mathrm{eV}$. All the $\mathrm{Bi}M{\mathrm{O}}_3$ are semiconductors with a band gap from $0.17\text{to}1.57\mathrm{eV}$, which is determined by the occupied $\mathrm{O}2p$ and unoccupied $\mathrm{Bi}6p$ states.

Figure 2

(Color online) Total and partial DOSs of four cubic $\mathrm{Bi}M{\mathrm{O}}_3$.

Figure 3

(Color online) Charge density maps for cubic $\mathrm{Bi}M{\mathrm{O}}_3$ in (110) plane.

Figure 4

(Color online) Profiles of PES for the displacement of ions along the tetragonal [001] (lines) and rhombohedral [111] (dot lines) in cubic $\mathrm{Bi}\mathrm{Al}{\mathrm{O}}_3$ (up) and $\mathrm{Bi}\mathrm{Ga}{\mathrm{O}}_3$ (down) at predicted equilibrium lattice constant and 1% volume expansion indicated by solid and vacuity symbols, respectively.