Effect of rare-earth ions on an electric polarization induced by the phase separation domains in $R$Mn$_{2}$O$_{5}$ ($R$ = Er, Tb)

The effect of rare-earth ions ($R$ = Er$^{3+}$, Tb$^{3+}$) with a strong spin-orbit coupling on the dielectric properties and electric polarization induced by the local polar phase separation domains in $R$Mn$_2$O$_5$ multiferroics is studied. A qualitative difference between these parameters and those studied previously in GdMn$_{2}$O$_{5}$ was discovered, in which the Gd$^{3+}$ ion in the $^8S_{7/2}$ ground state is weakly coupled to the lattice. It has been shown that the properties of the polar phase separation that arise in the subsystem of Mn$^{3+}$ and Mn$^{4+}$ ions due to the finite probability of electron tunneling between these ions of different valencies substantially depend on the magnitudes of the crystal fields in which these domains are located.