Collective Phase Mode and the Role of lattice distortions at T$_{N}\sim $T$_{C}$ in XMn$_{2}$O$_{5}$ (X= Bi, Pr, Sm, Gd, Tb)

We report on detailed temperature dependent infrared reflectivity, Raman, local structure, and X-ray diffraction measurements of multiferroic XMn$_{2}$O$_{5}$ (X= Bi, Pr, Sm, Gd, Tb). While for BiMn$_2$O$_5$ there are weak but distinct spectroscopic changes that together with high resolution diffraction patterns suggest a lattice role at T$_{N}\sim $T$_{C}$, for the rare earth (R) replaced infrared spectra have as a main feature a broad band at meV energies in addition to progressive rotation of Mn-O polyhedra. That band, independent of the R$^{3+}$ ion size and common to all, suggests hopping of carriers through fluctuations at a local scale. It partially condenses below 40 K, i.e., the collective electronic behavior changes from delocalized to one partially localized. We assimilate that condensate to a CDW-like phase mode. It might indicate induced orbital correlation of charge transfers between Mn sites.Frequency Raman phonon shifts are observed at T$\sim $60 K, due to spin-phonon coupling, and at T$_{N}\sim $T$_{C}$. Below T$_{N}\sim $T$_{C}$ there is no a Raman soft mode that might be associated to a CDW amplitude mode.