Among them, $\theta_{1}$ and $\chi_{1}$ have substantial changes over the specified frequency range as shown in Fig \[fig:w1T\](a). Figures \[fig:w1T\] (a) shows that $\theta$ depends on $\log\left(f\right)$ quadratically while $\chi_{1}$ linearly depends on it, and Fig. \[fig:w1T\](b) shows $w_{1}\left(T\right)$. At low frequency ($\lesssim10$ GHz), $w_{1}\left(T\right)$ resembles the Fermi-Dirac function, that is, below$\sim250$ K, its value is close to one but becomes close zero for $T$ above $\sim250$ K. At a higher frequency (e.g., 1000 GHz), however, this function strongly deviates from the Fermi-Dirac function, with a long tail extending to high temperature.

![Experimental susceptibility of Ba(Ti$_{0.675}$Zr$_{0.325}$)O$_{3}$ ceramics versus temperature fitted with Eq. (\[eq:BZT-frequency\]). \[fig:real-bzt\]](Fig4_v2){width="6cm"}

To further verify the suitability of this equation for experimental data, we also fit the result shown in Fig. 1 of Ref. [@Bokov2007BZT], where Ba(Ti$_{0.675}$Zr$_{0.325}$)O$_{3}$ ceramics is measured at $10^{-2}$ and $10^{5}$ Hz. Figure \[fig:real-bzt\] shows that satisfactory fittings are achieved.

Pb-based relaxors \[subsec:Lead-based-relaxors\]
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Unlike the lead-free BZT, which possesses PNRs that separate dipole clusters, lead-based ferroelectrics [@Kirillov1973; @Gridnev2004; @PMNeffHami2015; @PNR-PMN] have the Pb-driven dipoles across the system [@Yk], which cause phase transitions in systems such as PbTiO$_{3}$ and Pb(Zr,Ti)O$_{3}$ [@PZTPhase; @PTOeffHam; @JiangPTOFilm-1]. Due to heterovalent ions inside, typical lead-based relaxors are subject to random 