Origin of terahertz excitations in single-crystalline lead substituted M-type barium hexaferrite doped with Al

Single-crystalline lead substituted M-type barium hexaferrites doped with different concentrations of Al³⁺, synthesized by flux technique are investigated at terahertz and infrared frequencies (8-8000 cm⁻¹). The spectra of reflection coefficient (R), transmission coefficient (T), complex dielectric permittivity (ε` and ε``) were obtained using terahertz time-domain, and infrared Fourier transform spectrometers over a broadband frequency range 0.24-240 THz and at temperatures 5 K-300 K. The observed absorption lines are assigned to the electronic transitions within the fine-structured ground state of Fe²⁺ ions at terahertz frequencies and to optical phonon mode at far-infrared frequencies. To analyze the origin of terahertz excitations in the compounds, we provided a model that accounts for the second-order spin-orbit interactions, the triagonal distortion of the crystal field, and the selection rules of the (C_3v) point group symmetry of tetrahedral site-position of Fe²⁺.