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.