Terahertz spectroscopy of magnetoelectric HoAl$_3$(BO$_3$)$_4$

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl$_3$(BO$_3$)$_4$ were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm$^{-1}$ for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho$^{3+}$ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho$^{3+}$ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.