Nonlinear dielectric properties and tunability of 0.9Pb(Mg1∕3,Nb2∕3)O3–0.1PbTiO3 and Ba(Ti0.85,Sn0.15)O3 paraelectrics

We investigate the nonlinear dielectric properties of 0.9Pb(Mg1∕3,Nb2∕3)O3∙0.1PbTiO3 (PMN-PT) and Ba[Ti0.85,Sn0.15]O3 (BTS) paraelectrics experimentally and theoretically. We measure the nonlinear dielectric response in the parallel plate capacitor configuration, whereby we obtain the low frequency linear permittivity (ε33), and the higher order permittivities (ε3333,ε333333) at 298K as ε33PMN-PT=2.1×10−7 and ε33BTS=4.1×10−8F∕m, ε3333PMN-PT=−4.9×10−20 and ε3333BTS=−7.3×10−21F3m∕C2, and ε333333PMN-PT=7.6×10−33 and ε333333BTS=9.85×10−34F5m3∕C4. By using a self-consistent thermodynamic theory in conjunction with the experimental data, we compute the E3 dependence of electrostatic free energy ΔG, the field-induced polarization P3, and the thermodynamic tunability ∂2P3∕∂E32, and prove that electrostatic free energy has to be expanded at least up to the sixth order in the electric field to define the critical field ∣E3*∣ at which maximum tunability is attained. We also show that ∣E3*∣ is a function on ∣ε3333∣∕ε333333 only. Consequently, we find ∣E3*∣PMN-PT=8.0×105V∕m and ∣E3*∣BTS=8.6×105V∕m. We compute the engineering tunabilities as ΓPMN-PT=65% and ΓBTS=55%, and then define a normalized tunability ξ to take into account the ∣E3*∣ parameter. Thereof, we determine ∣ξ∣PMT-PT=8.1×10−5%∕Vm−1 and ∣ξ∣BTS=6.4×10−5%∕Vm−1. Our results reveal that ∣E3*∣BTS>∣E3*∣PMN-PT although ΓBTS<ΓPMN-PT, unequivocally showing the need for defining a critical field parameter in evaluating the nonlinear dielectric response and tunability, in particular, and in nonlinear dielectrics in general. The results also indicate that the nonlinear dielectric properties of PMN-PT are an order of magnitude higher than that of BTS, which we discuss in the context of structure-property relations of relaxors.