Dielectric properties of glycine phosphite crystals in the model of a phase transition with inclusion of high-order invariants

Dielectric anomalies in the vicinity of the ferroelectric phase transition in nominally pure glycine phosphite (GPI) crystals and glycine phosphite crystals containing 2 mol % glycine phosphate (GP) are studied. It is revealed that the impurity-induced internal macroscopic polarization observed for GPI-GP crystals brings about smearing of the dielectric anomalies in directions both parallel and perpendicular to the axis of spontaneous polarization. The ferroelectric phase of the GPI and GPI-GP crystals is characterized by an unusual variation in the inverse permittivity in the Z direction perpendicular to the Y axis of spontaneous polarization. The temperature dependence of the inverse permittivity is described by a power expression (T _c ? T) ⁿ with an exponent n larger than unity. The experimental data are analyzed in terms of the proposed thermodynamic model with two order parameters, namely, the displacement parameter η and the order-disorder parameter P, which have different physical natures but the same symmetry and allow for coupling invariants of the ηP and η³ P types, as well as for the built-in polarization in the case of GPI-GP crystals. The experimental and theoretical dependences are in good agreement. The coefficients of bilinear and nonlinear coupling between the order parameters are determined. It is shown that the phase transition in the crystals occurs in the vicinity of the tricritical point and that the unusual behavior of the permittivity with a variation in the temperature is explained by the contribution from high-order invariants of coupling.