Proportion of frozen local polarization in relaxor ferroelectrics

A Landau-type phenomenological cluster theory was presented to model the freezing process of local polarization in relaxors. Based on the theory, the proportion of frozen polarization in Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMNT) was calculated from the experiment of dielectric nonlinearity. The local polarization was shown to freeze continuously in a cooling process. The amount of frozen polarization increases with increasing the measuring frequency. PACS: 77.22.Ej, 77.80.-e, 77.22.Ch, 77.84.Lf Typeset using REVTEX Electronic address: [email protected] 1 Relaxor ferroelectrics (relaxors) have been showing great importance both for the fundamental solid state science and the applications to advanced technology.1–3 Relaxors experience no macroscopic phase transition at zero electric field until very low temperatures. However, local polarization exists at much higher temperatures, which is widely believed to be responsible for the special characteristics of relaxors. The concept of “polar micro region” in relaxors was firstly presented by Smolenskii in the chemical inhomogeneity theory. The presence of polar microregions was later confirmed by the experiments on the non-linear variation of the optical refractive index, the thermal strain, and the thermal expansion coefficient.1,5–7 The deviation from the paraelectric Curie-Weiss behavior of the dielectric permittivity also suggested the presence of polar regions. Cross presented in a superparaelectric model that the polar microregions (represented by independent dipoles) are able to switch between the equivalent orientation states and gave an appropriate picture of the nature of the micro polarization at high temperatures. When the temperature decreases, the coupling between the polar microregions controls the kinetics of the fluctuations and the system is frozen into a polar-glassy state. Gui et al. used the Monte Carlo method to simulate the freezing process in relaxors and showed that some dipoles are slowed or frozen due to the interactions. A special phase transition of ergodic space shrinking in succession was also proposed according to the freezing process. Kleemann et al., however, proposed that the polarization is frozen due to the quenched random electric fields. Some works have been done to quantitatively analyze the freezing process of local polarization. Qian and Bursill developed a phenomenological theory to describe the interaction of polar domains and to simulate the dielectric relaxation and phase transition of relaxors. Nambu and Sugimoto proposed a Landau type mean field theory by considering a gradual condensation of local polarization and confirm a picture of diffuse phase transition in relaxors. In this paper, we propose a Landau-type phenomenological cluster theory of relaxors and calculate the proportion of frozen polarization from the experiments of dielectric nonlinearity. A phenomenological free energy is defined as 2 F = 2Nα(T )P 2 + 4−1Nα11P 4 + 2γP 2 ∑