Nonlinear dielectric susceptibility of dipole impurities dissolved in the lattice of quantum paraelectrics

A general relation is derived for calculating the nonlinear dielectric susceptibility of a system placed in an external ac magnetic field, which consists of tunneling and interacting dipole impurities described by the Hamiltonian of the transverse Ising model and a lattice of ions whose dynamics is specified in the soft-mode model with the possible ferroelectric phase transition suppressed by zero-point quantum oscillations. It is shown that the relaxation peaks in the dielectric response can be enhanced several times through relaxator interaction with the soft mode. A general expression is obtained to describe the deviation from the Arrhenius law in this case. The results of this work can be employed for interpretation of recent experiments that revealed a strong effect of isovalent impurities at extremely low concentrations on the macroscopic properties of incipient ferroelectrics.