## 3 Results
### Dielectric Loss Tangent
In this regard, the designs of high-speed nonvolatile memory devices based on the thin films of ferroelectrics with a rectangular hysteresis loop (RHL) are promising, and they are characterized by anomalously long remanent polarization relaxation times, increasing mechanical performance and thermal stability. In order to obtain such phenomenological relations, we use the expression obtained from \(\varepsilon_{\rm S}(\Gamma)=\varepsilon_{\infty}\frac{\pi}{2}\sqrt{\alpha_{1 }}\text{cth}\big{(}\frac{\pi}{2}\sqrt{\alpha_{1}}\big{)}\)-Equation (131) in the Maxwell relaxation region when \(\alpha_{1}=\frac{T_{\rm D}}{T_{\rm M}}\gg 1\). Moreover, when \(\zeta=\frac{\pi}{2}\sqrt{\alpha_{1}}\gg 1\), by virtue of \(\zeta\text{cth}\zeta\approx\zeta\) we have \(\varepsilon_{\rm s}\approx\varepsilon_{\infty}\frac{\pi}{2}\sqrt{\alpha_{1}}\), where \(\frac{2\varepsilon_{\rm s}}{\varepsilon_{\infty}}=\pi\sqrt{\frac{T_{\rm D}}{ T_{\rm M}}}\). The relative depth of dispersion for a diffusive relaxation mechanism is small and can be calculated via expression (131), taking into account the decomposition of \(\text{cth}\zeta\approx\frac{1}{\zeta}+\frac{\zeta}{3}\) in a \"deep\" diffusive relaxation field (\(T_{\rm D}\ll T_{\rm M}\), \(\alpha_{1}=\frac{T_{\rm D}}{T_{\rm M}}\ll 1\)). Then, based on the expression \(\varepsilon_{\rm S}(\text{T})=\varepsilon_{\infty}\zeta\text{cth}\zeta\) (131), including \(\zeta=\frac{\pi}{2}\sqrt{\alpha_{1}}\), \(\alpha_{1}=\frac{T_{\rm D}(\text{T})}{T_{\rm M}(\text{T})}=\frac{T_{\rm d}}{T} \times\frac{W^{(1)}(\text{T})}{W^{(0)}(\text{T})}\), and \(T_{A}=\frac{\text{d}^{2}q^{2}\,n_{0}}{\varepsilon_{0}\varepsilon_{\infty} \kappa_{\rm s}\kappa_{\rm s}\kappa_{\rm s}\kappa^{2}}\) (according to (132)), at \(\zeta\ll 1\), we approximately have \(\varepsilon_{\rm S}(\text{T})\approx\varepsilon_{\infty}\Big{(}1+\frac{\zeta^ {2}}{3}\Big{)}\), and we receive the approximated expression \(\varepsilon_{\rm S}(\text{T})\approx\varepsilon_{\infty}\Big{(}1+\frac{\pi^ {2}}{12}\frac{T_{\rm D}(\text{T})}{T_{\rm M}(\text{T})}\Big{)}\), which allows the determination of relative static permeability \(\frac{\varepsilon_{\rm S}(\text{T})-\varepsilon_{\infty}}{\varepsilon_{\infty} }\approx\frac{\pi^{2}}{12}\times\frac{T_{\rm D}(\text{T})}{T_{\rm M}(\text{T })}\). From identity \(\frac{T_{\rm D}(\text{T})}{T_{\rm M}(\text{T})}=\Big{(}\frac{\text{d}}{T_{\rm D }}\Big{)}^{2}\), we calculate the Debye screening radius \(\text{r}_{\rm D}(\text{T})=\text{d}\sqrt{\frac{T_{\rm M}(\text{T})}{T_{\rm D }(\text{T})}}\) or  
\[\text{r}_{\rm D}(\text{T})=\text{d}\sqrt{\frac{\text{T}}{\text{T}_{A}}\times \frac{W^{(0)}(\text{T})}{W^{(1)}(\text{T})}}. \tag{160}\]  
Relation (160) expresses the size effects that arise during the relaxation of the space charge. From \(\text{r}_{\rm D}(\text{T})=\text{d}\sqrt{\frac{T_{\rm M}(\text{T})}{T_{\rm D}( \text{T})}}\), it is obvious that in the area of \"deep\" Maxwell relaxation (\(T_{\rm M}\ll T_{\rm D}\)), according to \(\text{T}_{\rm M}=\frac{\varepsilon_{0}\varepsilon_{\infty}\kappa_{\rm B}\text{ T}}{q^{2}n_{0}a^{2}W^{(1)}}\ll T_{\rm D}=\frac{\text{d}^{2}}{\pi^{2}a^{2}W^{(0)}}\), the system's immersion effect (of the simulated crystal) into a state with small radii in relation to the shielding volume charge of \(\text{r}_{\rm D}\ll\text{d}\) is provided by macroscopic states with large values of crystal thickness d against the background of a rapid increase in concentrations of relaxers (ions) \(n_{0}\) with increasing crystal temperatures. According to formula (160), this effect is caused by abnormally high values of characteristic temperature \(\text{T}_{A}=\frac{\text{d}^{2}q^{2}\,n_{0}}{\varepsilon_{0}\varepsilon_{0} \varepsilon_{0}\kappa_{\rm s}\text{R}\text{R}\text{R}^{2}}\gg\text{T}\), which is also accompanied by high values of parameters d and \(n_{0}\).