  This work addresses the effect of substituting Mn$^{3+}$ by Fe$^{3+}$ at the
octahedral site of TbMnO$_3$ on the magnetic phase sequence, ferroelectric and
magnetoelectric properties, keeping the Fe$^{3+}$ concentration below 5%. The
temperature dependence of the specific heat, dielectric permittivity and
electric polarization was studied as a function of Fe$^{3+}$ concentration and
applied magnetic field. From the experimental results a strong decrease of the
electric polarization with increasing Fe$^{3+}$ substitution is observed,
vanishing above a concentration of 4%. However, within this range, a
significant increase of the magnetic sensitivity of the electric polarization
is obtained by increasing Fe$^{3+}$ concentration. Above that value, a
non-polar, weak ferromagnetic phase emerges, in good agreement with the
predictions of the Dzyalowshinskii-Moriya model. This behavior reveals the
crucial effect of Fe$^{3+}$ substitution in octahedral sites on the magnetic
phase sequence, polar and magnetoelectric behavior of the
TbMn$_{1-x}$Fe$_x$O$_3$ system. From the results obtained in this work, it is
understood that this behavior is not associated with the eg electronic
configuration, but instead to the competition between ferromagnetic and
antiferromagnetic interactions, which is very sensitive to both local fields
and distortions.
