Dielectric susceptibility in quantum ferroelectrics

Dielectric susceptibilities are reported for KTa_1-xNbₓO₃ and K_1-yNayTaO₃ mixed-crystal ferroelectrics with a Curie temperature TC close to absolute zero. According to the temperature range, the two following formulas are fitted to the experimental data: ε=A+B[1/2T₁×coth(1/2T₁T)-T₀] for T>1/2T₁ and ε=A+BT^-2 for T, TC<~1/2T₁. This latter condition defines the quantum limit of a ferroelectric. Both formulas are obtained as limiting cases of a renormalized harmonic approximation of a model involving nonlinear polarizability of the oxygen shell. The constants A, B, T₁, and T₀ are explained in terms of model parameters. The leading term of the divergence of the susceptibility at the quantum limit coincides with the one obtained by the renormalization-group approach. Although renormalized harmonic approximation in general is bound to fail close to TC, it gives valid results for the isolated (Gaussian) fixed point TC=0.