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

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 d₃₁ nonlinear coefficient in LiTaO₃ as compared with the isomorphic LiNbO₃, as well as the opposite signs of d₃₃ in the isomorphic BaTiO₃ and PbTiO₃. The unusually large deviation of Pb₅{Ge}₃O₁₁ from the Jerphagnon relationship between the vector part of Miller's Δ and the spontaneous polarization is also discussed.