Electronic properties and crystal structures of double-perovskites, Ba2BiIIIBiVO6,Ba2PrBiO6, and Ba2PrSbO6: First-principles study

In recent experiments, a significant band gap widening was observed when Sb was substituted for Bi in the double-perovskite Ba2PrBiO6. In this work, we study a series of double-perovskites, Ba2BiIIIBiVO6, Ba2PrBiO6, and Ba2PrSbO6 using the first-principles density functional theory with the Heyd-Scuseria-Ernzerhof hybrid functional to investigate the substitution effect on the structural and electronic properties. We find that the two topmost valence bands are disappeared on the substitution of PrIII for BiIII, and the two bottommost conduction bands are disappeared on the substitution of SbV for BiV, causing the significant band gap widening. Further, our calculation suggests that the Ba2PrPrBiO6 is a possible candidate as a source of the PrIV signal observed in the experiment. We find that the B-site disordering atomic configuration, Ba2B″VB′IIIO6, are restored to those of the original structures. On the other hand, our results also suggest the importance of the partial B-site disorder to explain the experimentally observed band gaps.


Introduction
TiO 2 is well known as an efficient photo catalytic material and has a wide range of application area from airpurifier to antimicrobial coating [1][2][3][4][5][6]. However, TiO 2 uses only the ultraviolet ray which is less than 3% of the whole sunlight pouring on the Earth surface. Therefore extensive studies have been devoted to develop photocatalytic materials sensitive to visible light that makes up 50% of the sunlight. A large number of doubleperovskite oxides, A 2 B′ III B″ V O 6 , have been studied due to their intriguing physical and chemical properties originating in their mixed valence nature [7]. Above all, Ba 2 PrBiO 6 was found to show an efficient photo catalytic activity to dissolve water molecules into oxygen and hydrogen gases under the visible light [8,9]. Recent experiment on the Ba 2 PrSbO 6 suggests the presence of the typical B-site ordering and the band gap modification [10,11]. However, detailed theoretical analysis on the electronic structures and the crystal geometries of the double-perovskites has not been performed. In this work, we study the structural and electronic properties of Ba 2 Bi III Bi V O 6 , Ba 2 PrBiO 6 , and Ba 2 PrSbO 6 double-perovskites using the first-principles density functional theory. The Heyd-Scuseria-Ernzerhof hybrid functional was applied to the calculations to handle the strong electron-correlation. We find that the Bi III 6s states at the top of valence band of Ba 2 Bi III Bi V O 6 vanish on the Pr substitution for Bi at ¢ B III -site. When Sb is substituted for Bi at B″ V -site, the Bi V 6s states at the bottom of the conduction band vanish causing additional widening of the band gap. Further, our calculation suggests that the Ba 2 PrPr Bi O 6 is a possible candidate as a source of the Pr IV signal observed in the experiment. We find that the Bsite disorder atomic configurations, Ba 2 B″ V B′ III O 6 , are easily restored to those of the original structures. This demonstrates the stability of the B-site ordering in the double-perovskite framework. On the other hand, our results also suggest the importance of the partial B-site disorder in the double-perovskites to explain the experimentally observed band gaps.

Calculation method
We use the density functional theory (DFT) as implemented in the Vienna ab-initio Simulation Package (VASP) [12] and the projector augmented wave (PAW) potentials [13] to study the structural and electronic properties of the double perovskite. It has been known that standard exchange-correlation functionals, such as the local density approximation (LDA) and the generalized gradient approximation (GGA), predict the electronic properties of double perovskites as metal or semi-metal with a very narrow band gap [14]. Theoretical study considering the electron correlations through the GGA+U method showed an improvement on the optimized structural and electronic properties of Ba 2 Bi III Bi V O 6 [15]. However, since the method utilizes specially tuned parameter U, application of the method to the other double-perovskites is not straightforward. On the other hand, recently developed Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) [16,17] is known to have an ability to account for the strong correlation effects and has been successfully applied to analyze the structural and electronic properties of the double-perovskites [18]. Therefore we use the HSE06 functional throughout our study. We use an energy cutoff of 500eV for plane wave basis set together with a 6×6×6 k-point grid. The rather high energy cutoff and dense k-point grid are necessary to predict correctly the crystal structures in the HSE06 computations. Equilibrium crystal structures were achieved so that the maximum force component was smaller than 1 meV/Å 3 , and the maximum stress component smaller than 1 meV/Å 3 . Optimized crystal structures were visualized using the VESTA [19].

Results and discussion
First of all, we evaluate the structural and electronic properties of Ba 2 Bi III Bi V O 6 as it gives the basis in analyzing the double perovskite crystals [20,21]. Unit cell contains four BaBiO 3 chemical units where the Bi III octahedra and the Bi V octahedra are arranged alternately forming the B-site ordering. It has the monoclinic I2/m symmetry at room temperature [22], and which is equivalent to the conventional setting of C2/m No.12 [23,24]. The I2/m cell is outlined on the C2/m supercell in the figure 1.
Where the distortions of octahedra caused by the mixed valencies are characterized by breathing distortion δ and tilting angle f as depicted in figure 2.
Structural optimization has been done for the room temperature phase of C2/m (table 1). Lattice constants optimized within PBE are significantly overestimated thereby causing the overestimation of v 0 . On the other hand, HSE06 correctly predicts not only the lattice constants but also the internal distortion parameters, δ and f. The difference is even clear when we calculate the electronic property of the system: Ba 2 Bi III Bi V O 6 is semimetallic in the PBE functional while it opens band gap significantly when we use the HSE06 functional consisting with the experiment. It has been argued that this shortcoming of the PBE comes from lesser ability in describing the exchange correlation effect of strongly-correlated electron system [18,25].
Next, we calculate the electronic band structure. In a monoclinic system, the shape of the Brillouin zone depends non-trivially on the lattice vectors [27]. In fact, there are five possible shapes of Brillouin zones for the monoclinic crystal structure depending on the choice of lattice vectors [28,29]. We choose the C2/m which corresponds to the MCLC 1 lattice as defined in [29]. To generate the set of k-points along the edges of the Brillouin zone, we use the code pymatgen [30].
High resolution band structures and electronic density of states curves were obtained thorough the WANNIER90 package by constructing maximally localized Wannier functions (MLWFs) [31][32][33][34] using the VASP2WANNIER90 interface [35] (figure 3). The band gap is indirect and We substituted Pr for the Bi III to form Ba 2 PrBiO 6 . The optimized structural parameters show an excellent agreement with the experiments (table 2). Electronic band structure is given in the figure 5. The band gap is indirect It is visible that the two isolated valence bands near the fermi level are now vanished. The breathing distortion δ as well as the tilting angle f retain the values before the substitution reflecting the preservation of their valence states (Ba 2 Pr III Bi V O 6 ).
It has been reported that experimentally prepared Ba 2 PrBiO 6 sample exhibits the valence mixing between Pr III and Pr IV [10,11]. In the experiment, the valence state Pr IV was gradually suppressed as the amount of substitution of Sb for Bi was increased, and was completely resolved in the Ba 2 Pr III Sb V O 6 sample. However, the valence state Pr IV must be compensated locally to keep the charge neutrality. One of the potential candidates for the compensation is the locally generated B-site disorder. We construct the structure by exchanging the atomic positions of Pr and Bi (Ba 2 Pr III Bi V O 6 →Ba 2 Bi III Pr V O 6 ) while fixing the framework made by Ba and O atoms.
After the optimization, the structure recovered to that of the Ba 2 Pr III Bi V O 6 by adjusting the distances from Pr and Bi to the nearest oxygen atoms and the valence state Pr IV was not be realized. Next, we investigated the   parameters (a, b, and c) and the angle β in the monoclinic I2/m cell extrapolated from those of the C2/m cell are presented. Cell volume per chemical formula unit is v 0 . δ and f are the breathing distortion and the tilting angle, respectively.     We now focus on the substitution of the smaller ion Sb V for Bi V . The stable crystal structure is R3. Again, the optimized crystal structure shows excellent agreement with the experimental one (table 3).
The distances from Pr and Sb to the nearest neighbor oxygen atoms are almost identical to those of the Ba 2 PrBiO 6 , reflecting the formation of the valence state of Ba 2 Pr III Sb V O 6 . We also tried to create the B-site disordered structure by interchanging the atomic positions of Pr and Sb in Ba 2 PrSbO 6 . Structural optimizations were performed only for the atomic positions while fixing the cell shape and the cell volume. The system again restores its crystal symmetry demonstrating the stability of the B-site ordering of the Ba 2 Pr III Sb V O 6 framework.
The electronic band structure is shown in the figure 6. The Bi V bands located at the bottom of the conduction bands of Ba 2 Pr III Bi V O 6 are vanished and the band gap is widened. The calculated indirect band gap is  = E Z L 5.90 eV i ( ) and the direct band gap is = E 5.97 eV d . Experimentally estimated band gap E ex also show the similar widening tendency on the substitution of Sb for Bi V (E ex (Ba 2 PrBiO 6 )= 0.977 eV→E ex (Ba 2 PrSbO 6 )= 2.395 eV [11]). However, the experimental values are about half of the theoretical values obtained in this work.
The hybrid functional HSE06 incorporates the short-range Hartree-Fock type exchange at the fraction of α ( a < < 0 1). It has been reported that the parameter α is somewhat material-specific and the best value often deviates from the standard value of α=0.25 [18,27,35]. Therefore we calculated the band gaps for α=0.25, 0.1, and 0.05 to see if it is the case for the double-perovskites (table 4).
The band gaps of Ba 2 Bi III Bi V O 6 calculated with the small α significantly deviate from the experimental ones while those of the Ba 2 Pr III Bi V O 6 and Ba 2 Pr III Sb V O 6 show decreasing tendency with decreasing the α but are still lager than the experimental values. We can conclude that the adoption of the smaller α does not improve the   disparity of the band gaps. On the other hand, we focus on the partial disorder of the B-sites as it has been experimentally found in the Ba 2 Pr III Bi V O 6 sample [23]. Although our calculation indicates that the B-site disordered double-perovskites are energetically unfavorable, it dose not exclude the possibility of the presence of partial disordered B-sites in the ordered double-perovskite matrices. It is well known that the electronic properties of semiconductors are easily modified significantly by incorporation of small amounts of impurities or other kind of defects [39]. We evaluated the band gaps of the B-site disordered double-peroveskites using the standard value for the α (