Far- and mid-infrared emission and reflection of magnetoelectric RMnO$_3$ and RCrO$_3$ (R$=$Rare Earth)

Far- and mid-infrared emission and reflection spectra of ferrielectric hexagonal TmMnO$_{3}$ show that small polarons, a paramagnetic collective electronic mode, and lower than T$_{\mathrm{N}}$ soft hybrid modes are in concomitant relation. CO$_{\mathrm{2}}$ laser heating in dry air triggers oxidation and Mn$^{3+}$- Mn$^{4+}$ double exchange hopping conductivity. A collective excitation in the paramagnetic phase is assigned to e$_{\mathrm{g}}$ electrons in THz low energy d-orbital fluctuations. It locks-in at the E-type antiferromagnetic onset (T$_{\mathrm{N}}$ $\sim$ 80K) into soft bands that harden simultaneously down to 4 K with temperature dependence given by the magnetic long range order coupling of the collective electric dipole. They have T$_{\mathrm{N}}$ as critical temperature and critical exponents suggesting a second order phase transition. They also match zone center spin wave modes measured in isomorphous LuMnO$_{3}$ (Lewtas et al, Phys. Rev. B~\textbf{82}, 184420 (2010)). Both excitations, magnons y electric dipoles, are generated by electrons e$_{\mathrm{g}}$ in deformed d-orbitals. Sharing this behavior with orthorhombic NdMnO$_{3}$ there is no evidence of new phonons in a structural deformation down to 4K Preliminary results in ErCrO$_{3}$ (T$_{\mathrm{N}}$ $\sim$ 130 K) show the emerging soft bands in an order-disorder scenario. Overall, we conclude that magnetoelastic deformations in an orbital fluctuating environment are close related to magnetoelectric couplings.