Subcoercive-field dielectric response of 0.5(Ba_0.7Ca_0.3TiO_3)-0.5(BaZr_0.2Ti_0.8O_3) thin film: peculiar third harmonic signature of phase transitions and residual ferroelectricity

Sub-coercive field non-linearities in 0.5(Ba_0.7Ca_0.3TiO_3)-0.5(BaZr_0.2Ti_0.8O_3) (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→-225→+45→0 instead of the -180→-90→0 found for relaxor. This peculiar behavior is observed only on heating, and is tentatively attributed to changes in the correlations between polar nanoregions.