Optical anisotropy and charge-transfer transition energies in BiFeO${}_3$ from 1.0 to 5.5 eV

We discuss uniaxial optical anisotropy in single-crystal BiFeO${}_3$ determined by spectroscopic ellipsometry from 1.0 to 5.5 eV. The dielectric function ɛ $=$ ɛ${}_1$ $+$ iɛ${}_2$ and refractive index $N$ $=$ $n$ $+$ $\mathit{ik}$ spectra of BiFeO${}_3$ are extracted for the tensor components along its ordinary and extraordinary principal axes. Using the standard line-shape analysis, we also obtain the energies of the major optical structures associated with the charge-transfer transitions in BiFeO${}_3$.

Figure 1

(a) Real and (b) imaginary parts of the pseudodielectric function 〈ɛ〉 spectra measured along four different orientations of a single-domain BiFeO${}_3$ (001) crystal. The dependence of 〈ɛ〉 on crystallographic orientation is clearly seen. (c) A schematic depicting the SE measurement along the [110] direction.

Figure 2

Experimental spectra (symbols) and best-fit curves (solid lines) for g-SE parameters (a) Ψ and (b) Δ. The measurements were done along $[0\overline{1}0]$ direction at the incident angle of 75°.

Figure 3

(a) Dielectric function ɛ $=$ ɛ${}_1$ $+$ iɛ${}_2$ and (b) refractive index $N$ $=$ $n$ $+$ $\mathit{ik}$ spectra extracted mathematically for the tensor components along the ordinary (ɛ${}_a$ and $N_a$) and extraordinary (ɛ${}_c$ and $N_c$) principal axes of BiFeO${}_3$.

Figure 4

Best-fit curves for the second-energy-derivative of ɛ${}_a{}_1$ (solid line) and ɛ${}_a{}_2$ (dash-dotted line) of BiFeO${}_3$. The open circles and open squares represent data for $d^2$ɛ${}_a{}_1$/$d$$E^2$ and $d^2$ɛ${}_a{}_2$/$\mathit{dE}$${}^2$, respectively. Energies of each CT transition are indicated by the arrows and labeled using a notation established in a recent theoretical study.[19] The physical origin of the structure at ∼2.5 eV labeled by “?” is not clear, but has been suggested as a defect-related one.