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Traditional ligand-field theory has to be improved by taking into account both "pure electronic" contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R-1, R-2, R-3', R-2', and R-1' lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R-1 line and R-2 line of yAG:Cr3+ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr3+ ion in YAG:Cr is compressed along the [111] direction. Thus, for YAG:Cr3+ and ruby, the splitting of t(2)(3) (4)A(2) (or t(2)(3) E-2) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R-1 and R-2 lines of YAG:Cr3+, the temperature-dependent contributions due to EPI are dominant.

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