Antiferromagnetic Resonance in Multiferroic YMnO$_3$ and LuMnO$_3$*

Multiferroic rare-earth manganites have attracted much attention because of the coexistence of ferroelectric and magnetic orders. Combining conventional far-infrared Fourier-transform and THz-range free electron laser electron spin resonance (ESR) spectroscopy techniques, magnetic excitations in hexagonal multiferroic YMnO$_3$ and LuMnO$_3$ in the antiferromagnetically (AFM) ordered phase have been studied. The gap in the excitation spectrum ($\sim 42$ and $\sim 48$ cm$^{-1}$ for YMnO$_3$ and LuMnO$_3$, respectively) was observed directly. Similar slope of the frequency-field dependences of AFM resonance modes, $\sim$ 0.5 cm$^{-1}$/T, was revealed for both compounds. A fine structure of AFM resonance absorption has been revealed by means of high-resolution ESR techniques, which can be explained taking into account a finite interaction between the neighboring Mn$^{3+}$ layers. The work was done in collaboration with M. Ozerov, D. Kamensky, E. \v{C}i\v{z}m\'{a}r, J. Wosnitza, A.K. Kolezhuk, D. Smirnov, H.D. Zhou, and C.R. Wiebe.