Subcoercive field dielectric response of 0.5(Ba_0.7Ca_0.3TiO₃)-0.5(BaZr_{0.2Ti0.8O3) thin film: Peculiar third harmonic signature of phase transitions and residual ferroelectricity}

Sub-coercive field non-linearities in 0.5 (Ba (0.7) Ca- 0.3 TiO3)-0.5(BaZr0.2Ti0.8O3) (BCTZ 50/50) thin film elaborated using pulsed laser deposition are studied using permittivity and phase angle of the third harmonic measurements as function of the AC measuring field E-AC and temperature. The global phase transition temperature T-max for which the permittivity is maximum, decreases from 330 K to 260 K when E-AC increases. Rayleigh analysis of the AC field dependence of the relative permittivity shows a regular decrease of the domain wall motion contributions as temperature increases up to T-max and an even more pronounced decrease above T-max. This measurement reveals that the ferroelectric behavior subsists 70 K above the global phase transition. The phase angle of the third harmonic at temperatures below 275 K, is characteristic of a conventional ferroelectric and from 275 K to T-max = 330 K of a relaxor. Above T-max , the thin film exhibits a peculiar phase angle of the third harmonic, which consists of-180(degrees) ->-225 (degrees) -> +45(degrees) -> 0 (degrees)instead of the-180 (degrees) ->-90 (degrees)-> 0(degrees)found for relaxor. This peculiar behavior is observed only on heating, and is tentatively attributed to changes in the correlations between polar nanoregions.