Electron-phonon interaction in fluoride crystals doped with isoelectronic 3d³ ions (V²⁺, Cr³⁺, Mn⁴⁺)

The aim of this paper is to investigate the electron-phonon coupling between optical electrons of the V²⁺, Cr³⁺ and Mn⁴⁺ ions doped in fluoride crystals CsCaF₃:V²⁺, KMgF₃:Cr³⁺, LicaAlF₆:Cr³⁺, and Cs₂GeF₆:Mn⁴⁺. The ⁴T_2g spinor splitting of these ions, due to spin-orbit interaction has been modeled by the second order spin-orbit Hamiltonian. Effect of the dynamical Jahn-Teller interaction on die spin - orbit splitting of ⁴T_2g term is taken into account and the Jahn-Teller stabilization energy, zero-phonon line splitting and Huang-Rhys parameter are evaluated. The position of the potential surfaces of the ⁴T_2g excited state is considered using an analysis of the displacements of ligands due to the combined effect of the a_1g, and e_g normal modes of the octahedral complex forming by the considered impurities and nearest environment. The net result of these vibrations, both axial and equatorial was obtained. The comparison with experimental data is discussed.