Frustration of exchange-striction ferroelectric ordering and growth of electric polarization of phase separation domains in $R_{0.8}$Ce$_{0.2}$Mn$_{2}$O$_{5}$ ($R$ = Er, Tb) solid solutions

The effect of rare-earth ions ($R$ = Er$^{3+}$, Tb$^{3+}$, Ce$^{3.75+}$) on the dielectric properties and the electric polarization induced by local polar phase separation domains in solid solutions of $R_{0.8}$Ce$_{0.2}$Mn$_{2}$O$_{5}$ ($R$ = Er, Tb) multiferroics has been studied. These parameters are found to qualitatively differ from those of initial $R_{0.8}$Ce$_{0.2}$Mn$_{2}$O$_{5}$ ($R$ = Er, Tb) crystals studied before. It is shown that the properties of the polar phase separation domains that form in a subsystem of Mn$^{3+}$ and Mn$^{4+}$ ions due to a finite probability of tunneling electrons between these ions with different valences are substantially dependent on the values of crystal fields in which these domains exist. A combined influence of Er$^{3+}$, Tb$^{3+}$, and Ce$^{3.75+}$ ions is found to substantially change the crystal field in $R_{0.8}$Ce$_{0.2}$Mn$_{2}$O$_{5}$ ($R$ = Er, Tb) as compared to $R$Mn$_{2}$O$_{5}$ ($R$ = Er, Tb).