Frozen superparaelectric state of local polar regions in GdMn$_{2}$O$_{5}$ and Gd$_{0.8}$Ce$_{0.2}$Mn$_{2}$O$_{5}$

A comparative study of the dielectric properties and electric polarization of multiferroics GdMn$_{2}$O$_{5}$ and Gd$_{0.8}$Ce$_{0.2}$Mn$_{2}$O$_{5}$ has been carried out in the temperature range 5–330 K. The polarization properties in the ferroelectric state that forms due to a charge ordering and exchange striction have been studied at $T \le T_C$ = 30 K. The properties of the restricted polar phase separation domains formed in the crystals containing ions Mn$^{3+}$ and Mn$^{4+}$ have been studied, too. These domains exhibit the electric polarization in the temperature range from 5 K to some temperatures $T_f\gg T_C$. Such a high-temperature polarization is due to the frozen superparaelectric state of the restricted polar domains.