On the ferroelectric and magnetoelectric mechanisms in low Fe$^{3+}$ doped TbMnO$_3$

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.