Far-IR spectra of magnons, crystal field transitions, and phonons in hexagonal \textit{RE}MnO$_{3}$ (\textit{RE}=Er, Tm, Yb, Lu) single crystals*

Far-IR spectra of hexagonal \textit{RE}MnO$_{3}$ (\textit{RE}=Er, Tm, Yb, Lu) single crystals have been studied between $T$=1.6 K and 300 K using transmission in high magnetic field and rotating analyzer ellipsometry. The symmetry of the IR optical phonons and their oscillator strengths were determined for compounds with different \textit{RE} ions. The temperature dependence of the phonon frequencies revealed a strong spin-phonon interaction in the temperature range below $T_{N}\sim $70 K. The effective g-factors have been determined for the AFM resonances and crystal field transitions using external magnetic fields up to 10 T. The frequency of the AFM resonances around 50 cm$^{-1}$ increases systematically with a decrease of the \textit{RE} ion radius. The observed effects are analyzed taking into account main magnetic interactions in the system including exchange of the Mn$^{3+}$ spins with \textit{RE}$^{3+}$ paramagnetic moments. The magnetic ordering of \textit{RE} ions was observed at low temperatures $T<$3.5 K and in strong magnetic fields.