Far-infrared optical transmission spectra of the antiferromagnetic resonances, or magnons, and crystal-field (CF) transitions have been studied in hexagonal $R$MnO${}_3$ ($R$ $=$ Er, Tm, Yb, Lu) single crystals. The magnon and CF frequencies, their oscillator strengths, and effective $g$ factors have been measured using external magnetic fields up to 9 T in the temperature range between 1.5 and 100 K. The magnon frequency increases systematically with a decrease of the $R$ ion radius. The magnetic ordering of $R$ ions ($R$ $=$ Er, Tm, Yb) was observed at low temperatures $T<3.5$ K and in strong external magnetic fields. The observed effects are analyzed taking into account the main magnetic interactions in the system including exchange of the Mn${}^{3+}$ spins with $R^{3+}$ paramagnetic moments.

• Received 26 February 2012

DOI:https://doi.org/10.1103/PhysRevB.85.144422