Third-order dielectric susceptibility in a model quantum paraelectric.

In the context of perovskite quantum paraelectrics, we study the effects of a quadrupolar interaction Jq, in addition to the standard dipolar one Jd. We concentrate here on the nonlinear dielectric response χ (3) P , as the main response function sensitive to quadrupolar (in our case antiquadrupolar) interactions. We employ a 3D quantum four-state lattice model and mean-field theory. The results show that inclusion of quadrupolar coupling of moderate strength (Jq ∼ 1 4Jd) is clearly accompanied by a double change of sign of χ (3) P from negative to positive, near the quantum temperature TQ where the quantum paraelectric behaviour sets in. We fit our χ (3) P to recent experimental data for SrTiO3, where the sign change is identified close to TQ ∼ 37K.