Crystal field theory and excitation spectra in Fe$_2$Mo$_3$O$_8$

The parameters of even and odd crystal fields acting on iron ions in tetrahedral and octahedral positions of the Fe$_2$Mo$_3$O$_8$ crystal are calculated. The obtained energy level schemes of the lowest multiplets are discussed in the context of the available experimental data. By comparing the calculated intensities of magnetic and electric dipole transitions with experimental data, the parameters of the effective Hamiltonian of the interaction of $3d$ electrons with an electric field are refined. It is found that the main absorption lines at $T<T_N$ in the region of terahertz frequencies are due to excitations of iron ions and are not associated with collective oscillations of magnetic moments. The splitting of absorption lines upon application of an external magnetic field is a consequence of the difference in the orientations of the magnetic sublattices relative to the crystallographic axes.