Interplay between spin dynamics and crystal field in multiferroic compound HoMnO$_3$

In the multiferroic hexagonal manganite HoMnO3, inelastic neutron scattering and synchrotron based THz spectroscopy have been used to investigate the spin waves associated to the Mn order together with Ho crystal field excitations. While the Mn order sets in first below 80 K, a spin reorientation occurs below 37 K, a rare feature in the rare earth manganites. We show that severalHo crystal field excitations are present in the same energy range as the magnons, and that they are all affected by the spin reorientation. Moreover, several anomalous features are observed in the excitations at low temperature. Our analysis and calculations for the Mn spin waves and Ho crystal field excitations support Mn-Ho coupling mechanisms as well as coupling to the lattice affecting the dynamics.