Nonlinear Dielectric Susceptibility in Doped Incipient Ferroelectrics

The theory of dc-electric field nonlinear susceptibility in the doped incipient ferroelectrics is developed in a random field approach. The calculations of the susceptibility X(E,T) had shown that the coefficients X (k) nl(T, n) in power serie of susceptibility X(E, T) = Σ X (k) nlE 2k (k = 0 and k = 1, 2, 3... correspond respectively to linear and nonlinear susceptibility of the first, second etc. order) diverge at the same temperature T = T m that depends on the impurity dipoles concentrations. The critical indexes of the divergency for the concentration of the dipoles which correspond to mixed ferroglass phase with coexistence of short- and long-range polar order were shown to be the same as those calculated in mean field approximation. The comparison of the theory with experimental data obtained for KTa 1-x Nb x O 3 (0.0075 ≤ x ≤ 0.05) is performed. The calculations describe the main peculiarities of temperature, electric field and concentrational dependence of observed nonlinear dielectric susceptibility. Since the temperature T m corresponds to the transition from dipole glass to ferroglass phase the transition is proven to be equilibrium one in the disordered ferroelectrics.