Modifying the magnetoelectric coupling in TbMnO$_3$ by low-level Fe$^{3+}$ substitution

We report a comprehensive study of the low-level substitution of Mn$^{3+}$ by Fe$^{3+}$ effect on the static and dynamic magnetoelectric coupling in TbMn$_{1-x}$Fe$_x$O$_3$ ($x=0$, 0.02 and 0.04). The cationic substitution has a large impact on the balance between competitive magnetic interactions and, as a result, on the stabilization of the magnetic structures and ferroelectric phase at low temperatures. Low-lying electromagnon excitation is activated in the cycloidal modulated antiferromagnetic and ferroelectric phase in TbMnO$_3$, while it is observed up to TN in the Fe-substituted compounds, pointing for different mechanisms for static and dynamic magnetoelectric coupling. A second electrically active excitation near 40 cm$^{-1}$ is explained by means of Tb3+ crystal-field effects. This excitation is observed up to room temperature, and exhibits a remarkable 15 cm$^{-1}$ downshift on cooling in Fe-substituted compounds. Both electromagnon and crystal-field excitations are found to be coupled to the polar phonons with frequencies up to 250 cm$^{-1}$. Raman spectroscopy reveals a spin-phonon coupling below TN in pure TbMnO$_3$, but the temperature where the coupling start to be relevant increases with Fe concentration and reaches 100 K in TbMn$_{0.96}$Fe$_{0.04}$O$_3$. The anomalies in the T-dependence of magnetic susceptibility above TN are well accounted by spin-phonon coupling and crystal-field excitation, coupled to oxygen motions.