  We report the temperature dependent THz to mid-infrared response of
hexagonal-ErMnO3 using absorption, reflectivity, and emissivity techniques from
2 K to 1700 K. At low temperatures, lowest frequency vibrational modes coexist
with paramagnon excitations associated with well-defined crystal field Rare
Earth pure magnetic replicas in an intriguing phonon-magnetic convergence.
Increasing the temperature, a number of vibrational bands close to the space
group predicted undergo profile broadening and softening. In particular, a
distinctive set of bands in the 288-329 cm-1 (300 K) range has a component
whose profile is carrier screened becoming nearly fully blurred in the
intermediate phase between ~830 K and ~1500 K. Below TC ~830 K this asymmetric
band further splits as spin phonon interaction and the tripling of the unit
cell takes place revealing a delicate balance of long- and short-range
interactions. Ambient Raman scattering brings up evidence of a Fr\"ohlich
resonance due to Coulomb interactions between carriers and the macroscopic
field of the longitudinal optical phonon mode. We found it is dynamically
correlated to the hexagonal c-axis negative thermal expansion. Mid-infrared
(MIR) optical conductivity show that also plays a role in small polarons and
mediates in high temperature bipolarones.At higher temperatures a low frequency
Drude contribution is triggered by electron hopping signaling an
insulator-metal phase transition at ~1600 K while the MIR response suggests
coexistence between single small polarons and bipolarons. We draw a parallel
with improper ferroelectrics sustaining a lattice incommensurate intermediate
phase and unit cell tripling. We argue that in the h-RMnO3 (R=Rare Earth, Y)
family of compounds the intermediate phase be considered incommensurate with
onset at TINC ~1500 K and ferroelectric lock-in at TC ~830 K delimiting this
regime in h-ErMnO3.
