Anisotropic Oxygen Polarizability in BaTiO3

The optical anisotropy of tetragonal BaTi${\mathrm{O}}_3$ is examined according to the point-dipole description, and it is shown that anisotropic electronic polarizabilities are the dominant source of the birefringence of BaTi${\mathrm{O}}_3$. This anisotropy is attributed to the ${\mathrm{O}}_a$ oxygen ion (Slater's notation) due to the known $\mathrm{T}\mathrm{i}-{\mathrm{O}}_a$ and $\mathrm{B}\mathrm{a}-{\mathrm{O}}_a$ overlap in the tetragonal phase, and the recent refractive-index data for BaTi${\mathrm{O}}_3$ at 5893 Å are analyzed for this anisotropic ${\mathrm{O}}_a$ polarizability according to a generalized Lorentz scheme that accounts for the lattice distortions. It is found that at room temperature the ${\mathrm{O}}_a$ polarizabilities parallel and perpendicular to the polar axis are 85 and 95% of the isotropic oxygen polarizability in the cubic phase. The published dispersion data on the refractive indices of SrTi${\mathrm{O}}_3$ and Ti${\mathrm{O}}_2$ (rutile) are similarly analyzed for the oxygen polarizability, the long-wavelength absorption in both crystals being attributed to electron-transfer excitations of the oxygen ion. Based on these derived dispersion data of the oxygen polarizability in SrTi${\mathrm{O}}_3$ and Ti${\mathrm{O}}_2$, the dispersions of the refractive indices in BaTi${\mathrm{O}}_3$ at 20 and 120°C are computed and compared with experimental data. The anisotropy of the oxygen polarizability at infinite wavelength in BaTi${\mathrm{O}}_3$ is calculated; at room temperature, the static polarizabilities of ${\mathrm{O}}_a$ and ${\mathrm{O}}_b$ parallel to the polar axis are 1.85 and 2.16 ${\mathrm{\AA }}^3$, respectively. The previous isotropic value due to Slater was 2.39 ${\mathrm{\AA }}^3$. The anomalous nature of the birefringence in PbTi${\mathrm{O}}_3$ is discussed.