Nonlinear dc electric-field dependence of the dielectric permittivity and cluster polarization of Sr1−xMnxTiO3 ceramics

The dc electric-field dependence of the dielectric constant ε′(E) in Sr1−xMnxTiO3 (x=0.005−0.02) ceramics is studied in the temperature range from 10 to 125 K, i.e., around the ε′(T) peak temperature Tmax. Results are analyzed using equations derived analytically from the implicit equations of the Landau-Ginzburg-Devonshire (LGD) theory. Corrections due to cluster contribution attributed to the reorientation of random-field-induced polar nanometer-scale regions turn out to be important, if not decisive, for a reliable description of ε′(E). So, it is found that a combined equation including the Langevin-type cluster term, i.e., εL′(E)=P02L3∕(2kBTε0[cosh(P0L3E∕2kBT)]2) is the most suited to describe the dc electric-field dependence of the dielectric constant around Tmax. Based on the fitting of the ε′(E) data, the cluster polarization P0 reaches values as high as ∼0.4 μC∕cm2 with the cluster size L of 11±4.5 nm. Thus, the existence in the Sr1−xMnxTiO3 system of polar clusters with nanometer-scale size is consistent with ε′(E) data and their contribution to the permittivity at E=0 and temperatures close to Tm is estimated to be up to 30%. In addition, besides inducing the peak in ε(T), the formation of polar nanoregions is beneficial to the high relative electric-field tunability of the dielectric constant nr=[ε′(0)−ε′(E)]∕ε′(0)∼70% as well as high communication quality factor K=[ε′(0)∕ε′(E)−1]2∕[ε′(0)∕ε′(E)tan δ(0)tan δ(E)]∼10 000 under 20 kV∕cm at 10 kHz.