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Sub-coercive field non-linearities in$0.5(\text{Ba}_{0.7}\text{Ca}_{0.3}\text{TiO}_{3})-0.5(\text{BaZr}_{0.2}\text{Ti}_{0.8}\text{O}_{3})$(BCTZ 50/50) thin film elaborated using pulsed laser deposition are studiedusing permittivity and phase angle of the third harmonic measurements asfunction of the AC measuring field $E_{\mathit{AC}}$ and temperature.  The global phase transition temperature $T_{\mathit{max}}$ for which thepermittivity is maximum, decreases from 330 K to 260 K when $E_{\mathit{AC}}$increases.  Rayleigh analysis of the AC field dependence of the relative permittivityshows a regular decrease of the domain wall motion contributions as temperatureincreases up to $T_{\mathit{max}}$ and an even more pronounced decrease above$T_{\mathit{max}}$.  This measurement reveals that the ferroelectric behavior subsists 70 K abovethe global phase transition.  The phase angle of the third harmonic at temperatures below 275 K, ischaracteristic of a conventional ferroelectric and from 275 K to$T_{\mathit{max}}=$ 330 K of a relaxor.  Above $T_{\mathit{max}}$, the thin film exhibits a peculiar phase angle ofthe third harmonic, which consists of ${-180}{\deg}\rightarrow{-225}{\deg}\rightarrow {+45}{\deg} \rightarrow {0}{\deg}$ instead of the${-180}{\deg}\rightarrow {-90}{\deg} \rightarrow {0}{\deg}$ found for relaxor.  This peculiar behavior is observed only on heating, and is tentativelyattributed to changes in the correlations between polar nanoregions.

applied physics letters

Subcoercive-field dielectric response of  $0.5(\text{Ba}_{0.7}\text{Ca}_{0.3}\text{TiO}_{3})-0.5(\text{BaZr}_{0.2}\text{Ti}_{0.8}\text{O}_{3})$  thin film: peculiar third harmonic signature of phase transitions and  residual ferroelectricity