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The Effect of $f$-$d$ Magnetic Coupling in Multiferroic $R$MnO$_3$ Crystals

We have established detailed magnetoelectric phase diagrams of (Eu$_{0.595}$Y$_{0.405}$)$_{1-x}$Tb$_x$MnO$_3$ ($0 \le x \le 1$) and (Eu,Y)$_{1-x}$Gd$_x$MnO$_3$ ($0 \le x \le 0.69$), whose average ionic radii of $R$-site ($R$: rare earth) cations are equal to that of Tb$^{3+}$, in order to reveal the effect of rare earth 4$f$ magnetic moments on the magnetoelectric properties. In spite of the same $R$-site ionic radii, the magnetoelectric properties of the two systems are remarkably different from each other. A small amount of Tb substitution on $R$ sites ($x \sim 0.2$) totally destroys ferroelectric polarization along the a axis ($P_a$), and an increase in Tb concentration stabilizes the $P_c$ phase. On the other hand, Gd substitution ($x \sim 0.2$) extinguishes the $P_c$ phase, and slightly suppresses the $P_a$ phase. These results demonstrate that the magnetoelectric properties of $R$MnO$_3$ strongly depend on the characteristics of the rare earth 4$f$ moments.