Structure of the singular free energy for triglycine selenate and triglycine sulfate ferroelectrics

A method to determine the dominant powers of the order parameter in the free energy of real physical systems is proposed. A series of equations for the susceptibility scaling functions were obtained from the analytical two-term scaling free energy. The experimental scaling functions for triglycine selenate (TGSe) and triglycine sulfate (TGS) ferroelectrics inserted into these equations show marked deviations from linearity. Relations between these deviations and the nonzero-field critical invariant Q={χ}(τₘ, E=0)/{χ}(τₘ,E) were found, where τₘ is the reduced temperature (τₘ=Tₘ/Tc-1) at which the susceptibility {χ}({τ},E) is maximum for a given value of the electric field E. This nonlinearity proves the existence of a nonzero-field critical invariant describing the competition of the three scaling terms P²,P⁴, and P⁶ in the singular free energy for TGSe and TGS ferroelectrics. The higher-order terms P⁸,P¹⁰,..., are shown to be absent or much less important than the P²,P⁴, and P⁶ powers of the polarization P.