Microscopic analysis of the crystal field strength and electron-vibrational interaction in cubic SrTiO₃ doped with Cr³⁺, Mn ⁴⁺ and Fe⁵⁺ ions

A detailed microscopic study of the crystal field strength 10Dq for different interionic distances in cubic SrTiO₃ doped with three isoelectronic ions (Cr³⁺, Mn⁴⁺ and Fe⁵⁺) was performed. The exchange charge model of the crystal field was used to calculate the 10Dq values at different distances between impurity ions and ligands. The obtained results were represented by the power laws 1/Rⁿ, with n = 4.9050, 5.7990 and 6.5497 for Cr³⁺, Mn⁴⁺ and Fe ⁵⁺, respectively. For the first time the role of two different contributions (the point charge and exchange charge) into the total crystal field strength was studied separately. With the obtained 10Dq(R) dependences, a number of important physical quantities describing the optical and dynamical properties of impurity centers (such as the constants of the electron-vibrational interaction, Huang-Rhys parameters, Stokes' shifts, Jahn-Teller stabilization energies, changes of the chemical bond lengths due to the combined effect of the local vibrational normal modes, bulk modulus and Grüneisen constants for the a_1g normal mode) were calculated. The obtained results are in good agreement with available experimental data and can be readily applied for analysis of the optical spectra, electron-vibrational interaction and pressure effects for these and other similar systems.