Electronic and Structural Properties of ABO3: Role of the B-O Coulomb Repulsions for Ferroelectricity

Abstract

We have investigated the role of the Ti-O Coulomb repulsions in the appearance of the ferroelectric state in BaTiO3 as well as the role of the Zn-O Coulomb repulsions in BiZn0.5Ti0.5O3, using a first-principles calculation with optimized structures. In tetragonal BaTiO3, it is found that the Coulomb repulsions between Ti 3s and 3p states and O 2s and 2p states have an important role for the appearance of Ti ion displacement. In BiZn0.5Ti0.5O3, on the other hand, the stronger Zn-O Coulomb repulsions, which are due to the 3s, 3p, and 3d (d10) states of the Zn ion, have more important role than the Ti-O Coulomb repulsions for the appearance of the tetragonal structure. Our suggestion is consistent with the other ferroelectric perovskite oxides ABO3 in the appearance of tetragonal structures as well as rhombohedral structures.

Keywords: coulomb repulsion; electronic band structure; ferroelectrics; phase transitions.

Figure 1

(a) 2 × 2 × 2 super cell of BZT (or BMT). Green, yellow, red, and blue balls denote Bi, O, Zn (or Mg), and Ti atoms, respectively. The lattice with red lines denotes that of Zn (or Mg) and Ti atoms in a tetragonal structure, whose configuration is illustrated in (c); (b) Unit cells of (C-type) tetragonal, monoclinic, and rhombohedral structures; (c) Configurations of Zn (or Mg) and Ti atoms in A-, C-, and G-type tetragonal structures [18].

Figure 2

Optimized calculated results as a function of a lattice constants in tetragonal BaTiO${}_3$: (a) $c/a$ ratio and (b) ${\delta }_{\mathrm{Ti}}$ to the [001] axis. Red lines correspond to the results with the Ti3spd4s PP, and blue lines correspond to those with the Ti3d4s PP. Results with arrows are the fully optimized results, and the other results are those with c and all the inner coordinations optimized for fixed a [17].

Figure 3

Total density of states (DOS) of fully optimized tetragonal BaTiO${}_3$ with the Ti3spd4s PP (solid line) and cubic BaTiO${}_3$ with the Ti3d4s PP (red dashed line) [17].

Figure 4

Two-dimensional electron-density contour map on the $xz$-plane for tetragonal BaTiO${}_3$: (a) with the Ti3spd4s PP; and (b) with the Ti3d4s PP. The optimized calculated results with a fixed to be 3.8Å are shown in both figures. The electron density increases as color changes from blue to red via white. Contour curves are drawn from 0.4 to 2.0 e/${\mathrm{\AA }}^3$ with increments of 0.2 e/${\mathrm{\AA }}^3$ [17].

Figure 5

Illustrations of the proposed mechanisms for the Coulomb repulsions between Ti 3s and 3p states and O 2s and 2p states in BaTiO${}_3$: (a) anisotropic Coulomb repulsions between Ti 3s and 3p${}_{x(y)}$ states and O${}_{x(y)}$ 2s and 2p${}_{x(y)}$ states, and between Ti 3s and 3p${}_z$ states and O${}_z$ 2s and 2p${}_z$ states, in the tetragonal structure; (b) isotropic Coulomb repulsions between Ti 3s and 3p${}_{x(y)(z)}$ states and O${}_{x(y)(z)}$ 2s and 2p${}_{x(y)(z)}$ states, in the rhombohedral structure [17].

Figure 6

Optimized calculated results as a function of the fixed volumes of the unit cells in rhombohedral BaTiO${}_3$: (a) 90$-\alpha$ degree and (b) ${\delta }_{\mathrm{Ti}}$ to the [111] axis. Red lines correspond to the results with the Ti3spd4s PP, and blue lines correspond to those with the Ti3d4s PP. $V_{\mathrm{rhombo}}$ denote the volume of the fully optimized unit cell with the Ti 3spd4s PP. Results with arrows are the fully optimized results, and the other results are those with all the inner coordinations optimized for fixed volumes of the unit cells. Note that the Ti ion with the Ti3spd4s PP is oppositely displaced at $V_{\mathrm{rhombo}}/V$ = 1.2 [17].

Figure 7

(a) $R_{\mathrm{Bi}-\mathrm{Zn}}$, $R_{\mathrm{Bi}-\mathrm{Ti}}$, and $R_{\mathrm{Bi}-\mathrm{Mg}}$ of the A-, C-, and G-type tetragonal, monoclinic, and rhombohedral structures; (b) $R_{\mathrm{Zn}-{\mathrm{O}}_z}$, $R_{\mathrm{Ti}-{\mathrm{O}}_z}$, and $R_{\mathrm{Mg}-{\mathrm{O}}_z}$ of the same structures [18].

Figure 8

Two-dimensional electron density contour maps of monoclinic (a) BZT in Case I; (b) BZT in Case II; (c) BMT in Case I, and (d) BMT in Case II. The electron density increases as color changes from blue to red via white. Contour curves are drawn from 0.2 to 2.0 e/${\mathrm{\AA }}^3$ with increments of 0.2 e/${\mathrm{\AA }}^3$ [18].

Figure 9

Two-dimensional electron density contour maps of BZT in Case II (a) C-type tetragonal and (b) monoclinic. The electron density increases as color changes from blue to red via white. Contour curves are drawn from 0.2 to 2.0 e/${\mathrm{\AA }}^3$ with increments of 0.2 e/${\mathrm{\AA }}^3$ [18].