Dielectric susceptibility in quantum ferroelectrics

Abstract

Dielectric susceptibilities are reported for KTa1-xNbxO3 and K1-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: =A+B[12T1×coth(12T1T)-T0] for T>12T1 and=A+BT-2 for T, TC<~12T1. 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. © 1980 The American Physical Society.