First-principles calculations of Born effective charges and spontaneous polarization of ferroelectric bismuth titanate

Abstract

In this study, we present the results of our first-principles calculations of the band structure, density of states and the Born effective charge tensors for the ferroelectric (ground state B1a1) and paraelectric (I4/mmm) phases of bismuth titanate. The calculations are done using the generalized gradient approximation (GGA) as well as the local density approximation (LDA) of the density functional theory. In contrast to the literature, our calculations on B1a1 structure using GGA and LDA yield smaller indirect band gaps as compared to the direct band gaps, in agreement with the experimental data. The density of states shows considerable hybridization among Ti 3d, Bi 6p and O 2p states indicating covalent nature of the bonds leading to the ferroelectric instability. The Born effective charge tensors of the constituent ions for the ground state (B1a1) and paraelectric (I4/mmm) structures were calculated using the Berry phase method. This is followed by the calculation of the spontaneous polarization for the ferroelectric B1a1 phase using the Born effective charge tensors of the individual ions. The calculated value for the spontaneous polarization of ferroelectric bismuth titanate using different Born effective charges was found to be in the range of 55±13 µC/cm 2 in comparison to the reported experimental value of (50±10 μC/cm 2 ) for single crystals. The origin of ferroelectricity is attributed to the relatively large displacements of those oxygen ions in the TiO 6 octahedra that lie along the a-axis of the bismuth titanate crystal. 77.22.Ej, 85.50.Gk, 71.15.Mb 3 PACS Number (s):

Optical anisotropy in bismuth titanate: An experimental and theoretical study

“…This substantiates that BiT is an indirect band gap semiconductor, in agreement with our previous work 24 and several other experiments 19,43 and first-principles calculations. 27 Upon fitting our absorption data using Eq.…”

“…All the calculations were performed at 0 K. For electronic structure and optical property calculation, Monkhorst-Pack 42 8 Â 8 Â 8 mesh was used, which proved good in our previous work on the same system. 24 In order to substantiate our results using pseudopotential based approach, we repeated our entire calculations by full potential-linear augmented plane wave (FP-LAPW) method with GGA using WIEN2k. Such a comparison would be first of its kind for a complex system such as bismuth titanate.…”

“…We started our calculations with the optimized lattice parameters and ionic positions of B1a1 and I4/mmm phases of bismuth titanate calculated using GGA and LDA. 24 In the above calculations, we, using the experimental structural parameters, relaxed the cell volume and ionic positions systematically in such a way that the forces on ions are less than the specified limit, and the total pressure on the system is close to zero. In the whole process, we restricted the symmetry of the system to be unaltered.…”

“…In the whole process, we restricted the symmetry of the system to be unaltered. 24 The entire calculation was carried out in the framework of first-principles density functional theory. 32 Vienna ab-initio simulation package (VASP) 33,34 was used with projector augmented wave method (PAW).…”

“…4 At Curie temperature (T c ¼ 948 K), ferroelectric BiT transforms into a paraelectric phase with centrosymmetric tetragonal (I4/mmm) structure having lattice parameters, a ¼ b ¼ 3.8524 Å and c ¼ 33.197 Å . 23 Noncentrosymmetry of the room temperature structure along with its complexity further renders anisotropic physical properties in the material, namely dielectric constant (e a ¼ e b ¼ 153 6 5 and e c ¼ 118 6 5 at 100 kHz), 6 ferroelectric polarization, 15,24 and thermal 25 and electrical 23,26 conductivities. It is interesting to note that anisotropy in different physical properties have different origins.…”