Modeling of polar clusters in disordered perovskites: The S-K model with tunneling

Abstract

The polar clusters generated by random non-central impurities in quantum paraelectrics determine to a great extent the complex dielectric behaviour observed in systems like SCT, KTN or KTL. The competition between a quantum paraelectric phase and an impurity-driven ferroelectric or glass phase depends on the concentration and on the nature of the interaction between clusters. This work presents a simple model in which each cluster is represented by a quantum two level system involving an effective Ising dipolar moment η and a tunneling energy A. The interactions between clusters are taken into account by following the guide-lines of the Sherrington-Kirkpatrick model for spin glasses. General expressions for the polarization (P) and the Edwards-Anderson order parameter (q) are given and the phase diagram involving temperature, the normalized mean interaction energy Jo/J and tunneling energy A/Jo is built.