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(Mg$_{1/3}$Nb$_{2/3}$)O$_3$-PbTiO$_3$ (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.