Optical properties of ferroelectric ${\text{Bi}}_4{\text{Ti}}_3{\text{O}}_{12}$

We report optical properties of ferroelectric ${\text{Bi}}_4{\text{Ti}}_3{\text{O}}_{12}$ based on spectroscopic ellipsometry and calculations with the recently developed density functional of Tran and Blaha. We find a close accord between the experiment and the calculated results with this functional, including the energy onset of optical transitions and the scale of the optical conductivity. The band gap is indirect, with a value of 2.9 eV, and an onset of direct optical transitions at 3.1 eV.

Figure 1

(Color online) Relaxed structure of ${\text{Bi}}_4{\text{Ti}}_3{\text{O}}_{12}$. Bi is denoted by large light gray spheres, O by small dark red spheres, and Ti by dark blue spheres. The cations are numbered as in Table .

Figure 2

(Color online) Electronic DOS in ${\mathrm{eV}}^{-1}$ per f.u. as obtained using the PBE (top) and TB-mBJ (bottom) functionals. The projections are onto the LAPW spheres.

Figure 3

(Color online) Optical conductivity with the TB-mBJ functional and a 0.025 eV broadening. The $xx$ direction is the $Pc$ $a$-axis direction, the $yy$ direction is perpendicular to the $a$ and $c$ axes, i.e., the $c$-axis direction of the doubled cell with the $B1a1$ setting and the $zz$ direction is along $c$.

Figure 4

(Color online) Refractive index with the TB-mBJ functional and a 0.025 eV broadening.

Figure 5

(Color online) Experimental optical conductivity and dielectric function for ${\text{Bi}}_4{\text{Ti}}_3{\text{O}}_{12}$.