A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical bran...A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical brancheshave been derived. It is found that the temperature-independent contributions are very important, especially at lowtemperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PSwithout EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theoryfor PS of energy spectra, the total PS of R1 line of tunable laser crystal GSGG:Cr3+ at 70 K as well as the ones of itsR1 line, R2 line and U band at 300 K will be successfully calculated and explained in this series of papers.展开更多
With the strong-field scheme and cubic bases, the complete d3 energy matrix in a tctragonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectra of Sr TiO3 :Cr3+ and Sr TiO3 :...With the strong-field scheme and cubic bases, the complete d3 energy matrix in a tctragonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectra of Sr TiO3 :Cr3+ and Sr TiO3 :Mn4+ at normal pressure and various temperatures have been calculated. Correspondingly, the FORTRAN program calculating the g factor of the ground state has been worked out. By using the program and the wavefunction obtained from diagonalizing the complete energy matrix, the g factors of the ground state of SrTiO3 :Cr3+ and SrTiO3 :Mn4+ at normal pressure and room temperature have been evaluated. The calculated results are in good agreement with the optical spectral and EPR experimental data. The comparison and analysis of the results of two crystals have been made. It is demonstrated that the covalency of the bonding between Mn4+ and ligands (O2 ) in SrTiO3:Mn4+ is stronger than the one of the bonding between Cr3+ and ligands (O2 ) in SrTiO3:Cr3+. It is shown that the obtained wavefunctions and values of parameters are reasonable.展开更多
With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunct...With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperatureindependent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of g||(R1) and g⊥(R1). It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions, |t32 2E) and |t22(3T1)e4T2 ), the average energy separation △＝ E[t22 (3T1)e4T2]-E[t32 2E] and their variations with temperature have been calculated and discussed.展开更多
By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of...By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R1 line ofGSGG:Cr3+ at 70 K have been calculated, respectively. Their physical origins have been revealed. It is found that theremarkable under the normal pressure, and the degree of the admixture rapidly decreases with increasing pressure. Thechange of the degree of the admixture with the pressure plays a key role for not only the pure electronic PS of R1 line butalso the PS ofR1 line due to EPL The detailed calculations and analyses show that the pressure-dependent behaviors ofthe pure electronic PS of R1 line and the PS of R1 line due to EPI are quite different. It is the combined effect of themthat gives rise to the total PS of R1 line, which has satisfactorily explained the experimental data (including a reversal ofPS of R1 line). In contributions to PS of R1 line due to EPI at 70 K, the temperature-independent contribution is muchlarger than the temperature-dependent contribution. The former results from the interaction between the zero-pointvibration of the lattice and localized electronic state.展开更多
By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal and various pressures,the g factor of the ground state of SrTiO3:Cr^3+ and its pressure-induced shift have been microscop...By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal and various pressures,the g factor of the ground state of SrTiO3:Cr^3+ and its pressure-induced shift have been microscopically calculated.Only by taking the local strains around Cr^3+ in SrTiO3:Cr^3+(which are about twice the bulk ones)and corresponding P-χ dependence,can we obtain a good agreement etween the calculated result of pressure-induced shift of ground-state g factor and the experimental one.The physical origins of this pressure-induced shift have been explained.It is found that the change of Dq^-1 with pressure makes main contribution to the pressure-induced shift of ground-state g factor of SrTiO3:Cr^3+.By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal pressure,the relevant matrix elements and accordingly strain-induced splittings of t2^32E and t2^34A2 of SrTiO3:Cr^3+ have been calculated.The important results of Yc.Zc,Pc and Qc have also been evaluated.It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and /or Coulomb interaction and /or Kramers degeneracy that make the strain-induced splittings of the levels nonzero.It is found that there are nonvanishing matrix elements of operators T2ξ between wavefuncgtions with positive Ms and those with negative Ms′ and those with negative ms′,which have important effects on the strain-induced splittings of the levels.展开更多
文摘A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical brancheshave been derived. It is found that the temperature-independent contributions are very important, especially at lowtemperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PSwithout EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theoryfor PS of energy spectra, the total PS of R1 line of tunable laser crystal GSGG:Cr3+ at 70 K as well as the ones of itsR1 line, R2 line and U band at 300 K will be successfully calculated and explained in this series of papers.
文摘With the strong-field scheme and cubic bases, the complete d3 energy matrix in a tctragonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectra of Sr TiO3 :Cr3+ and Sr TiO3 :Mn4+ at normal pressure and various temperatures have been calculated. Correspondingly, the FORTRAN program calculating the g factor of the ground state has been worked out. By using the program and the wavefunction obtained from diagonalizing the complete energy matrix, the g factors of the ground state of SrTiO3 :Cr3+ and SrTiO3 :Mn4+ at normal pressure and room temperature have been evaluated. The calculated results are in good agreement with the optical spectral and EPR experimental data. The comparison and analysis of the results of two crystals have been made. It is demonstrated that the covalency of the bonding between Mn4+ and ligands (O2 ) in SrTiO3:Mn4+ is stronger than the one of the bonding between Cr3+ and ligands (O2 ) in SrTiO3:Cr3+. It is shown that the obtained wavefunctions and values of parameters are reasonable.
文摘With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperatureindependent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of g||(R1) and g⊥(R1). It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions, |t32 2E) and |t22(3T1)e4T2 ), the average energy separation △＝ E[t22 (3T1)e4T2]-E[t32 2E] and their variations with temperature have been calculated and discussed.
文摘By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R1 line ofGSGG:Cr3+ at 70 K have been calculated, respectively. Their physical origins have been revealed. It is found that theremarkable under the normal pressure, and the degree of the admixture rapidly decreases with increasing pressure. Thechange of the degree of the admixture with the pressure plays a key role for not only the pure electronic PS of R1 line butalso the PS ofR1 line due to EPL The detailed calculations and analyses show that the pressure-dependent behaviors ofthe pure electronic PS of R1 line and the PS of R1 line due to EPI are quite different. It is the combined effect of themthat gives rise to the total PS of R1 line, which has satisfactorily explained the experimental data (including a reversal ofPS of R1 line). In contributions to PS of R1 line due to EPI at 70 K, the temperature-independent contribution is muchlarger than the temperature-dependent contribution. The former results from the interaction between the zero-pointvibration of the lattice and localized electronic state.
文摘By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal and various pressures,the g factor of the ground state of SrTiO3:Cr^3+ and its pressure-induced shift have been microscopically calculated.Only by taking the local strains around Cr^3+ in SrTiO3:Cr^3+(which are about twice the bulk ones)and corresponding P-χ dependence,can we obtain a good agreement etween the calculated result of pressure-induced shift of ground-state g factor and the experimental one.The physical origins of this pressure-induced shift have been explained.It is found that the change of Dq^-1 with pressure makes main contribution to the pressure-induced shift of ground-state g factor of SrTiO3:Cr^3+.By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal pressure,the relevant matrix elements and accordingly strain-induced splittings of t2^32E and t2^34A2 of SrTiO3:Cr^3+ have been calculated.The important results of Yc.Zc,Pc and Qc have also been evaluated.It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and /or Coulomb interaction and /or Kramers degeneracy that make the strain-induced splittings of the levels nonzero.It is found that there are nonvanishing matrix elements of operators T2ξ between wavefuncgtions with positive Ms and those with negative Ms′ and those with negative ms′,which have important effects on the strain-induced splittings of the levels.
