  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 studied
using permittivity and phase angle of the third harmonic measurements as
function of the AC measuring field $E_{\mathit{AC}}$ and temperature.
  The global phase transition temperature $T_{\mathit{max}}$ for which the
permittivity is maximum, decreases from 330 K to 260 K when $E_{\mathit{AC}}$
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 $T_{\mathit{max}}$ and an even more pronounced decrease above
$T_{\mathit{max}}$.
  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
$T_{\mathit{max}}=$ 330 K of a relaxor.
  Above $T_{\mathit{max}}$, the thin film exhibits a peculiar phase angle of
the 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 tentatively
attributed to changes in the correlations between polar nanoregions.
