Multiferroics in Eu$_{1-x}$Tb$_x$MnO$_3$ system

A low-$T$ phase diagram of the Eu$_{1-x}$Tb$_x$MnO$_3$ (0 $\leq$ x $\leq$ 1) is reported. Systematic substation of Tb into the system changes the perovskite lattice structure which further varies the electronic and magnetic behaviors of the system from a paraelectric-canted-AFM to a ferroelectric-spiral-AFM ground state. The Mn$^{3+}$ spins ordered, presumably, in a collinear incommensurate sinusoidal antiferromagnetic structure below $T_N$ = 52-45 K (x = 0 to 1). Then system enters a canted-AFM (weak- ferromagnetic) state below $T_{cant}$ for the $x \leq$ 0.5 compounds, which decreases from 42 K to 25 K with increasing $x$. For the $x \geq$ 0.5 compounds, ferroelectricity was found below $T_C \sim$ 28 K with a presumably spiral spin arrangement as that in TbMnO$_3$. At the boundary, $x$ = 0.5, the multiferroics coexists with the weak-ferromagnetism. The Rietveld refinement shows an Mn-O2-Mn angle of 145.9$^\circ$ for the Eu$_{0.5}$Tb$_{0.5}$MnO$_3$ suggesting a critical Mn-O2- Mn angle of $\sim$146$^\circ$ that multiferroics appears at the smaller angle side.