Magnetoelectric orthorhombic and multiferroic hexagonal ErMnO$_{3}$: THz hybrid modes in RMnO$_{3}$(R)$=$ Nd, Er, Tm)

We report on far- and mid-infrared emission, reflection, and transmission spectra of metastable orthorhombic perovskite (Pbnm-T$_{\mathrm{N}}$ $\sim$ 42 K) and hexagonal (P6$_{3}$cm- T$_{\mathrm{N}}$ $\sim$ 84 K) ErMnO$_{3}$. The number of phonon modes remains constant from 300 K to 4 K. Magnetically disordered electrons in fluctuating orbitals lead to an ambient THz broad reflectivity band. On cooling toward T$_{\mathrm{N}}$ the electrons exhibit increasing charge and magnetic short-range correlations and condense into soft bands that harden at about T$_{\mathrm{N}}$ as magnetic order sets in. However, at difference of NdMnO$_{\mathrm{3}}$ and TmMnO$_{3}$ that show correlation with a gap opening in transverse acoustical phonon dispersion and spin order, hexagonal ErMnO$_{3}$ develops at 5 K a set of four strong hybridized modes centered $\sim$ 70 cm$^{-1}$ in addition to one peaking at $\sim$ 96 cm$^{-1}$ and another weaker at $\sim$ 44 cm$^{-1}$. Orthorhombic ErMnO$_{3}$ develops a 46 cm$^{-1}$ band and a very strong one at 91cm$^{-1}$ that seems to correlate to a weaker 98 cm$^{-1}$ phonon in the short-range only magnetic order environment. We conclude that Er$^{3+}$ paramagnetic fluctuations increases Mn spins frustration in both compounds being the disruption strongest in orthorhombic ErMnO$_{3}$ where the THz band and short range magnetic onset may be traced even at 150 K, probably, due to the increment in the Jahn-Teller distortion.