Absorption Edge Splitting inKTaxNb1−xO3

The splitting of the conduction-band edge, deduced from the dichroism of the absorption edge, has been studied for insulating $\mathrm{K}{\mathrm{Ta}}_x{\mathrm{Nb}}_{1-x}{\mathrm{O}}_3$ ($T_c\approx 5°$C) as a function of applied electric field and temperature in the paraelectric and single-domain ferroelectric phases. In the paraelectric phase, without an applied electric field, a small splitting is observed which remains constant if the formation of a multidomain state is avoided. By subtracting this contribution, the polarization-dependent splitting is obtained which can be represented by the expression $\Delta \mathcal{E}=a{P}^2+b{P}^4$. The coefficients $a$ and $b$ are substantially the same in both the paraelectric and ferroelectric phases. The fourth-order term is attributed to higher-order effects of the change in the Ta (Nb) - O spacing on the band edge. The observed deviation from a purely quadratic polarization dependence appears, within the experimental uncertainty, to be independent of temperature and, thus, does not support a polarization-fluctuation model recently proposed to explain a similar deviation observed in ferroelectric BaTi${\mathrm{O}}_3$.