Magnetic and dielectric phase diagrams of Tb$_{1-x}$Eu$_{x}$MnO$_{3}$ ${(0 \leq x \leq 1)}$

The dependence of dielectric and magnetic properties with structural parameters have been investigated for the mixed- crystal system Tb$_{1-x}$Eu$_{x}$MnO$_{3}$ ${(0 \leq x \leq 1)} $. Since the ferroelectricity observed is originated from the incommensurate antiferromagnetism of Mn$^{3+}$ ions, the magnetic interaction strength should pronouncedly affect these properties. The interaction strength is dominated by the Mn-O bond length and Mn-O-Mn bond angle thus makes the structural discussion substantial. The Reitveld refinement showed an $ab$- plain Mn-O-Mn bond angle increases smoothily, as $x$ increased, with a slight jump around $x$ = 0.4-0.5, which is close to the disappearance of ferroelectricity, while the magnetic ordering temperature $T_N$ almost not changed. The phase diagrams observed in magnetism and dielectricity with $x$ indicate enriched magnetic and electric structures in this system and will be discussed in details.