Effect of hysteresis of dipole on remnant polarization in ferroelectrics

Decrease in remnant polarization at lower temperature, or low temperature degradation of polarization, in some ferroelectrics has attracted much attention. To investigate the mechanism of the decrease, phenomenological theory of ferroelectrics and the relevant mechanism of dipole in alternating electric field are used to develop a model of hysteresis-frozen effect of dipole in electric hysteresis loop measurement. Within the frame of Landau-Ginzburg-Devonshire theory, Ising model is used to derive the relationship among remnant polarization, coercive field, and saturated polarization strength. Then, two aspects are investigated: response of a dipole and thermodynamic properties of ferroelectric. Response of a dipole in an electric field is often described by relaxation time, on the assumption that Debye equation is satisfied. Potential barrier in the Debye equation is the Gibbs free energy barrier from one ferroelectric state, +P, to another ferroelectric state, -P. Increase in the Gibbs free energy barrier with temperature decreasing will prolong the relaxation time. As ferroelectrics can be taken as a capacitor, first order response function is used to introduce a hysteresis factor with measuring frequency and relaxation time into the expression of remnant polarization. In the aspect of thermodynamic properties of ferroelectric, the variation of compositions is a significant reason. In numerical simulation based on the derived formula the remnant polarization exhibits a frequency related peak, and shift of the peak depends on some other reasons: the increase of soft-mode coefficient in phase transition shifts the peak towards high temperature; the increases of coercive field, temperature-polarization coefficient (a concept defined in the present paper to indicate increase in polarization with increasing temperature) and saturated electric field shift the peak toward low temperature. Compared with the reported experimental results of BaTiO3/BiScO3 compound ceramics, the results show a good coincidence with numerical simulations. The parameter values of numerical simulation indicate that a large shift toward high temperature in peak of remnant polarization with increasing BiScO3 composition ratio is due to the increase in soft-mode coefficient with only small decrease in the Curie temperature. The soft-mode coefficient and temperature-polarization coefficient are closely related to polarization characteristic, ferroelectric, dielectric and mechanical properties. Therefore, the decrease in remnant polarization at low temperatures, ascribed to the hysteresis of dipole to a constant measuring frequency, may have an influence on changes in various properties, but freezing effect of dipole at low temperature can help ferroelectrics to save data longer.