Microscopic analysis of the crystal field strength and lowest charge transfer energies in the elpasolite crystals Cs2NaYX6 (X=F, Cl, Br) doped with Cr3+

Detailed microscopic study of the crystal field strength 10Dq and lowest charge transfer (CT) energies for different interionic distances in Cs2NaYX6:Cr3+ (X=F, Cl, Br) crystals is performed in the present paper. The method used in the calculations is the first-principles fully relativistic discrete variational multielectron (DVME) method [K. Ogasawara , Phys. Rev. B 64, 115413 (2001)] based on solving Dirac equations with the local density approximation. From the results of performed calculations, the functions describing the dependencies of 10Dq and lowest CT energy on the metal-ligand distance R were obtained without introducing any fitting or semiempirical parameters. It was shown that 10Dq depends on R as 1/R-n, with n=4.4634, 4.3742, and 4.3532 for Cs2NaYF6:Cr3+, Cs2NaYCl6:Cr3+, and Cs2NaYBr6:Cr3+, respectively. The lowest CT energies E(CT) are linear functions of R and decrease with increasing R with dE(CT)/dR=-953 cm(-1)/pm, -621 cm(-1)/pm, and -520 cm(-1)/pm for Cs2NaYF6:Cr3+, Cs2NaYCl6:Cr3+, and Cs2NaYBr6:Cr3+, respectively. Using these results, the constants of the electron-vibronic interaction, Huang-Rhys parameters, Stokes shifts, and Gruneisen constants for the a(1g) normal mode in all considered hosts were calculated. The obtained results are in good agreement with the experimental data and can be readily applied for analysis of the optical spectra and electron-vibronic interaction of the [CrX6](3-) (X=F, Cl, Br) units in other hosts.