dc electric-field dependence of the dielectric constant in polar dielectrics: Multipolarization mechanism model

The dc electric-field dependence of the relative dielectric constant ${\ensuremath{\varepsilon}}_{r}(E)$ in polar dielectrics is studied. The Landau-Ginzburg-Devonshire (LGD) theory and its approximate treatments in dealing with ${\ensuremath{\varepsilon}}_{r}(E)$ are reviewed. It is found that the LGD theory works well in the case of a single polarization mechanism existing in the dielectrics, and the Johnson relation ${\ensuremath{\varepsilon}}_{r}(E)={\ensuremath{\varepsilon}}_{r}(0)/{1+\ensuremath{\lambda}[{\ensuremath{\varepsilon}}_{0}{\ensuremath{\varepsilon}}_{r}(0){]}^{3}{E}^{2}{}}^{1/3}$ is a reasonable approximate expression describing ${\ensuremath{\varepsilon}}_{r}(E).$ Many polar dielectrics, however, exhibit more than one polarization mechanism contributing to the total dielectric constant. The dielectric response of such polar dielectrics under an external dc electric field cannot be purely described by LGD theory. In this work, we introduce a ``reorientational polarization'' to describe the ``extrinsic'' contribution to the dielectric constant, such as might arise from polar clusters, domain-wall motions, fluctuation of microcluster boundaries, defects, etc. A ``multipolarization-mechanism'' model is proposed, and a combined equation ${\ensuremath{\varepsilon}}_{r}(E)={\ensuremath{\varepsilon}}_{r}(0)/{1+\ensuremath{\lambda}[{\ensuremath{\varepsilon}}_{0}{\ensuremath{\varepsilon}}_{r}(0){]}^{3}{E}^{2}{}}^{1/3}+\ensuremath{\Sigma}{(P}_{0}x/{\ensuremath{\varepsilon}}_{0})[\mathrm{cosh}(\mathrm{Ex}){]}^{\ensuremath{-}2}$ is adopted to describe the total ${\ensuremath{\varepsilon}}_{r}(E)$ response of a polar dielectric, where the first term is Johnson's relation which represents the ``intrinsic'' polarization, and the latter represents the ``extrinsic'' polarization. Agreement between the fitting of this equation to the experimental data is obtained for paraelectrics ${\mathrm{KTaO}}_{3}$ and ${\mathrm{B}\mathrm{i}:\mathrm{S}\mathrm{r}\mathrm{T}\mathrm{i}\mathrm{O}}_{3}.$