Origin of the unusual dependence of the nonlinear optical susceptibility on bond length for ionic ferroelectrics

Abstract

The bond nonlinear polarizability is shown to increase with increasing bond length for covalent compounds but to decrease with bond length for sufficiently ionic compounds. This behavior is shown to explain, for example, the anomalously small value of the $d_{31}$ nonlinear coefficient in LiTa${\mathrm{O}}_3$ as compared with the isomorphic LiNb${\mathrm{O}}_3$, as well as the opposite signs of $d_{33}$ in the isomorphic BaTi${\mathrm{O}}_3$ and PbTi${\mathrm{O}}_3$. The unusually large deviation of ${\mathrm{Pb}}_5$ ${\mathrm{Ge}}_3$ ${\mathrm{O}}_{11}$ from the Jerphagnon relationship between the vector part of Miller's $\Delta$ and the spontaneous polarization is also discussed.