Emergence of the multiferroic state in $R$MnO$_{3}$ ($R$ = Sm and Nd) crystals

In order to understand the emergence of multiferroic behaviour in the $R$MnO$_{3}$ compounds, it is educational to study the relationship between ferroelectricity and magnetoelastically induced lattice modulations. Lattice modulations in $R$MnO$_{3}$ are strongly dependent on the Mn-O-Mn bond angle ($\Phi )$, which in turn is determined by the ionic radii ($r_{R})$ of the $R$ atoms. Multiferroic properties have been observed in the orthorhombic RMnO$_{3}$ (R = Tb,Dy) compounds, in which $\Phi $ is close to 145\r{ }. In order to induce multiferroic behaviour in other magnetic members of the orthorhombic $R$MnO$_{3}$, and to tune the structure to be in the same region of the phase diagram as Tb/DyMnO$_{3}$, it is necessary to substitute at the $R$ site with a suitable (smaller) atom. We have achieved this in SmMnO$_{3}$ and NdMnO$_{3}$ by substitutions at the Sm and Nd sites with smaller $R$ ions. In the optimally substituted compounds (40 to 50{\%}), we observe an additional magnetic transition. Investigations of the dielectric properties of the crystals reveal anomalies in the dielectric properties coincident with this magnetic transition, analogous to those exhibited by Tb/DyMnO$_{3}$, indicative of multiferroic behaviour. We present detailed investigations of the magnetic, dielectric and structural properties in single crystals of selected compositions.