| There are two aspects of researches in this thesis. Firstly, the optical and EPR spectra and its pressure effects, especially the unusual /Mine thermal shifts (TS) of incipient ferroelectric crystals SrTiOsiCr3* and SrTiO3:Mn4+ have been systematacially studied respectively. The physical origins, which cause the pressure effects and especially very unusual /?-line TS of two crystals, have been explained. Secondly, by means of both the theory of pressure-induced shifts of energy spectra (PS) and the theory of shifts of energy spectra caused by electron-phonon interaction (EPI), the optical spectra of tunable laser crystal GSGG:Cr3+ at low and room temperatures and their PS as well as dramatic change in overall emission band shape have also been comprehensively investigated, respectively.By using the strong-field scheme of ligand-field theory and trigonal or cubic bases, taking into account the cubic crystal-field, coulomb interaction, spin-orbital interaction and (or) low-symmetry crystal-field, we have constructed and checked the complete d3 energy matrix. Further, on the basis of the whole energy spectrum and wave functions obtained from diagonalizing the complete d3 energy matrix,taking into account all the levels and the admixtures of basic wave functions within d3 electronic configuration, as well as all the irreducible representations of point group of the site occupied by Cr + or Mn4+ and their components, the microscopic-theoretical calculations have been carried out for the three crystals, respectively.In the first aspect, for the first time, the g factor of the ground state and its PS of SrTiO^Cr3"1" or SrTiO3:Mn4+, the uniaxial-pressure-induced splittings of t\2E and t324A2 levels of SrTiO3:Cr3+, the R-\ine TS of SrTiO3:Mn4+ and SrTiO3:Cr3+ have been uniformly calculated by using microscopic theory, and all above-mentioned experimental data, including the very unusual R-lms TS of the two crystals, have been satisfactorily explained. In terms of the obtained values of parameters, it is demonstrated that the covalency of the bonding between Mn4+ and ligands (O2~) in SrTiO3:Mn4H" is stronger than the one of the bonding between Cr3+ and ligands (O2~) in SrTiO3:Cr3*. From theoretical analyses and calculations, it has been confirmed that the local strains around Cr3"1" in SrTiCV.Cr3"1" are about twice the bulk ones. It is found that the change of Dq-1 with pressure makes main contribution to PS of ground-state g factor of SrTiO3:Cr3+. It is the admixtures of basic wave functions that cause the strain-induced splittings of t\2E and t\*A2 levels of SrTiO3:Cr3+. It is found that there are non-vanishing matrix elements of operators C( T2^ ),C( T2rj) and C(T2?) between wave functions with positive Ms and those with negative M'S , and the shortcomings in previous literature have been overcome.Further, the different physical origins of the unusual .K-line TS of SrTiO3:Mn4+ and the one of SrTiO3:Cr3+ have been explained. For SrTiO3:Mn4+, it is the very strong EPI between the local electronic states of impurity Mn4+-ion and the phonons of the lattice vibration that causes the unusually large red-shift of its R-line. However, for SrTiO3:Cr +, the very strong EPI between the local electronic states of impurity Cr3+-ion and the low-frequency local Cr3+-impurity vibration modes makes main contribution to its very large J?-line blue-shift, the EPI between the local electronic states of Cr3+-impurity and the phonons of the lattice vibration causes only small red shift, and their algebraic sum gives rise to the observedunusual and large /Mine TS of SrTiO3:Cr3+. The calculated results show that, in low-temperature region, the strong softening of the low-frequency acoustic lattice-vibration modes of SrTiOa with decreasing T gives rise to important effect on /Mine TS of both SrTiOsMn4* and SrTiO3:Cr3+, and only by taking into account this effect, can we successfully explain the variation of /Mine TS of two crystals with temperature. For SrTiOsrCr3*, in low-temperature range, the harde...
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