Amplitude dependences of the dielectric losses in the thin-film nanogranular composite $(x)$Ni–$(1-x)$PZT

At the temperatures $T$ lower than ferroelectric Curie point and various intensities of constant ele-ctric field $E_{=}$, the dependences of dielectric loss $\operatorname{tg}\delta$ in the thin-film nanogranular composite $(x)$Ni–$(1-x)$[Pb$_{0.81}$Sr$_{0.04}$(Na$_{0.5}$Bi$_{0.5}$)$_{0.15}$][(Zr$_{0.575}$Ti$_{0.425}$)]O$_{3}$ on intensity of oscillating electric field $E_\sim$ were studied. It has been found that $\operatorname{tg}\delta$ almost does not vary with increase of $E_\sim$ till the strength of some threshold field $E_t$ and increases continuously at $E_\sim>E_t$. The value $E_t$ decreases when the $T$ increases, while $x$ and $E_{=}$ decrease. The found dependences $\operatorname{tg}\delta(E_\sim)$ and $E_t$ on $T$, $x$, and $E_{=}$ are explained within the context of the model of interaction of domain walls with the point defects pinning them, in ferroelectric materials.