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First-Principles Calculation of Born Effective Charges and Spontaneous Polarization of Ferroelectric Bismuth Titanate

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 $μ$C/cm2 in comparison to the reported experimental value of (50+/-10 $μ$C/cm2) for single crystals. The origin of ferroelectricity is attributed to the relatively large displacements of those oxygen ions in the TiO6 octahedra that lie along the a-axis of the bismuth titanate crystal.