The parameters of the free ions Mn5+ and Fe6+

The analysis of the behavior of iron-group ions in crystals, using a free-ion Hamiltonian that involves terms with only three parameters (B, C and ξ), seems to be erroneous since it is incapable of correctly predicting the levels of even a free ion. Such calculations may lead to erroneous conclusions concerning the crystal-field effects and the electron-phonon interaction. In this paper, we present the results of the most exact calculation of the parameters for free ions and the energy levels of Mn5+ and Fe6+ with 3d2 configuration. In the single-configuration approximation, the effective Hamiltonian of the free ions takes into account not only the electrostatic and the spin-orbit interactions, but also the relativistic ones (spin-spin, orbit-orbit and spin-other-orbit) and the linear correlation effect. For both free ions we have calculated the semi-empirical parameters included in the interaction Hamiltonian and the energy level scheme. The values of these parameters are obtained by fitting experimental data with the minimum value of rms errors. The final results are discussed.