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Pressure Effects on Spectra of Tunable Laser Crystal GSGG： Cr^3＋ IV： Pressure—Induced Shifts of R1 Line, R2 Line, and U Band at 300 K

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Communications in Theoretical Physics 2003年第4期39卷 621-630页

作者： madong-ping ZHANGJi-ping DepartmentofAppliedPhysics SichuanuniversityChengdu610065China InterationalCentreforMaterialsPhysics theChineseAcademyofSciencesShenyang110015China DepartmentofAppliedPhysics SichuanuniversityChengdu610065China

By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R1 line, R2 line, and U band of GSGG:Cr3+ at 300 K have been calculated, respectively. The calculated results are in good agreement with all the experimental data. Their physical origins have also been explained. It is found that the mixing-degree of and base-wavefunctions in the wavefunctions of R1 level of GSGG:Cr3+ at 300 K is remarkable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role not only for the 'pure electronic' PS of R1 line and R2 line but also the PS of R1 line and R2 line due to EPI. The pressure-dependent behaviors of the 'pure electronic' PS of R1 line (or R2 line) and the PS of R1 line (or R2 line) due to EPI are quite different. It is the combined effect of them that gives rise to the total PS of R1 line (or R2 line). In the range of about 15 kbar ~ 45 kbar, the mergence and/or order-reversal between levels and levels take place, which cause the fluctuation of the rate of PS for with pressure. At 300 K, both the temperature-dependent contribution to R1 line (or R2 line or U band) from EPI and the temperature-independent one are important.

关键词： high-pressure effect spin-orbit interaction electron-phonon interaction d orbital coupling between t(2)(2)(3T(1))e(4)T(2) and t(2)(32)E tunable laser crystal

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Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

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Communications in Theoretical Physics 2005年第3期43卷 529-538页

作者： madong-ping CHENJu-Ron DepartmentofAppliedPhysics SichuanUniversityChengdu610065China／／InternationalCentreforMaterialsPhysicsAcademiaSinicaShenyang110015China DepartmentofAppliedPhysics SichuanUniversityChengdu610065China

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, R1, R2, R'3, R'2, and R'1 lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG: Cr3+ as well as thermal shifts of GSZFS, R1 line and R2 line of ruby have been *** results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R1 line and R2 line of ruby, several conclusions have also been obtained.

关键词： improved ligand-field theory electron-phonon interaction Stokes shift energy spectrum thermal shift g factor

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Thermal Shifts and Electron—Phonon Interactions of ^4T2 and ^4T1 Broad Bands for Ruby

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Communications in Theoretical Physics 2002年第2期37卷 247-252页

作者： madong－ping MANing 等 DepartmentofAppliedPhysics SichuanUniversityChengdu610065China InternationalCentreforMaterialsPhysics ThechineseAcademyofSciencesShenyang110015China

For the first timc, by taking into account all the irreducible representations and their components in theelectron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d3 electronicconfiguration, the values of parameters in expressions of Raman and optical-branch terms of thermal shifts (TS) due toEPI for three levels, 4T2 band and 4T1 band of ruby have been evaluated; the contributions to TS of 4T2 and 4T1 broadbands from thermal expansion have also been calculated; and then, the TS of the peak energies of 4T2 and 4T1 broadbands have been calculated. The results are in satisfactory agreement with observed data. The values of single-electronreduced matrix elements representing the strengths of EPI of 4T2 and 4T1 bands have respectively been determined. ForTS of the peak energies of 4T2 and 4T1 bands, it is found that the contribution to TS from the second-order term in EPIHamiltonian is dominant; TS due to EPI of acoustic branches are over two times as much as those of optical branches,and both of them increase rapidly with temperature; the neighbor-level term is insignificant; the contribution to TS fromthermal expansion is specially important, and all the three terms of TS of 4T2 or 4T1 band are red shifts.

关键词：晶体热位移带加宽电子-声子相互作用

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Pressure-Induced Shifts of R, R＇, and B Line-Groups and Ground-State Zero-Field-Splitting of Ruby

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Communications in Theoretical Physics 2005年第5期43卷 941-947页

作者： madong-ping CHENJu-Rong DepartmentofAppliedPhysics SichuanUniversityChengdu610065China／／InternationalCentreforMaterialsPhysicstheChineseAcademyofSciencesShenyang110015China DepartmentofAppliedPhysics SichuanUniversityChengdu610065China

By means of improved ligand-field theory, the 'pure electronic'presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R_1, R_2,B_1, B_2, B_3, and R′_3 lines and the ground-state zero-Geld-splitting of ruby have been uniformlycalculated. The calculation results are in very good agreement with all the experimental data. Atnormal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of ∣t_2~2(~3T_1)e~4T_2 > and ∣t_2~(32)E＞ bases in the wavefunction of R_1 level of ruby is small at normalpressure, and it gradually decreases with increasing pressure, which causes the R_1-line PS of rubyto monotonously red shift with approximate linearity. The combined effect of the pure electronic PSof R_1 line and the PS of R_1 line due to EPI gives rise to the total PS of R_1 line. The analysesand comparisons among the features of R_1-line PS's of three laser crystals (ruby, GSGG:Cr~(3+) andGGG:Cr~(3+)) have been made, and the origin of their difference has been revealed.

关键词： high-pressure effect electron-phonon interaction R, R′, and B line-groups ground-state zero-field-splitting admixture of | t_2~2(~3T_1)e~4T_2 > and ∣t_2~(32)E > lasercrystal

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Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ II: Energy Spectra at Normal Pressure, Low and Room Temperatures

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Communications in Theoretical Physics 2003年第3期39卷 349-358页

作者： ZHANGJi－ping madong－ping 等 DepartmentofAppliedPhysics SichuanUniversityChengdu610065China InternationalCentreforMaterialsPhysics theChineseAcademyofSciencesShenyang110015China

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 temperature-independent 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 and . 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,and , the average energy separation and their variations with temperature have been calculated and discussed.

关键词： crystal fields optical properties spin-orbital interaction electron-phonon interaction coupling beween t(2)(2)(T-3(1))e(4)T(2) and t(2)(3) E-2 tunable laser crystal

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Energy Spectra,g Factors and Their Pressure—Induced and ／or Thermal Shifts of SrTiO3：Cr^3＋ and SrTiO3：Mn^4＋ I：energy Spectra and g Factors at Normal Pressure

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Communications in Theoretical Physics 2001年第4期35卷 491-496页

作者： ZHANGJi－ping madong－ping DepartmentofAppliedPhysics SichuanUniversityChengdu610065China InternationalCentreforMaterialsphysics TheChineseAcademyofSciencesShenyang110015China DepartmentofAppliedPhysics Si

With the strong-field scheme and cubic bases, the complete d3 energy matrix in a tetragonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectra of SrTiO3:Cr3+ and SrTiO3: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.

关键词： crystal fields energy spectrum optical properties g factors covalency

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Pressure Effects on Spectra of Tunable Laser Crystal GSGG：Cr^3＋ I：Theory

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Communications in Theoretical Physics 2003年第2期39卷 249-256页

作者： madong－ping ZHANGJi－ping InternationalCentreforMaterialsPhysics AcademiaSinicaShenyang110015China DepartmentofAppliedPhysics SichuanUniversityChengdu610065China DepartmentofAppliedPhysics SichuanUniversit

A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both the temperature-independent contributions and the temperature-dependent ones of acoustic branches and optical branches have been derived. It is found that the temperature-independent contributions are very important, especially at low temperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PS without EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theory for 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 its R1 line, R2 line and U band at 300 K will be successfully calculated and explained in this series of papers.

关键词： high-pressure effect line shift spin-orbit interaction electron-phonon interaction d-orbital coupling between t(2)(2)(T-3(1))e(4)T(2) and t(2)(3) E-2 tunable laser crystal

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Microscopic Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：Cr^3＋

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Communications in Theoretical Physics 2002年第5期37卷 373-380页

作者： madong－ping LIUYan－Yun 等 DepartmentofAppliedPhysics SichuanUniversityChengdu610065China

By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d3 electronic configuration, the values of all the parameters in the expressions of thermal shift (TS) and thermal broadening (TB) due to EPI for the ground level, R level and R line of MgO:Cr3+ have microscopically been evaluated; and then, TS and TB of R line and various contributions to them have uniformly been calculated. The results are in very good agreement with the experimental data. It is found that all the three terms of TS due to EPI are red shifts; the Raman term is the largest one, and the optical-branch term and neighbor-level term are important for TS; the contribution to TS from thermal expansion is blue shift, which is also important. The R-line TS of MgO:Cr3+ comes from the first-order term of EPI. The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:Cr3+. For both TS and TB, it is very important to take into account all the admixtures of basic wavefunctions within d3 electronic configuration.

关键词： crystal fields optical properties thermal shift and broadening electron-phonon interaction thermal expansion

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Theoretical Calculations of Strain—Induced Splittings and／or Shifts of t2^32E and t2^34A2 Levels for MgO：Cr^3＋

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Communications in Theoretical Physics 2001年第2期36卷 219-226页

作者： madong－ping MANing 等 DepartmentofAppliedPhysics SichuanUniversityChengdu610065China DepartmentofComputerScience SichuanU

Under various uniaxial stresses,both strains with low symmetry and isotropic strains of crystals take *** former fives the strain-induced low-symmetry crystal fields and accordingly splittings of levels;the latter gives the isotropic parts of strain-induced crystal fields and accordingly shifts of *** using the wavefunctions obtained from the diagonalization of the complete d^3 energy matrix in a regular octahedral field,the relevant matrix elements and accordingly strain-induced splittings and/or shifts of t2^32E and t2^34A2 for MgO:Cr^3+ have been *** physical origins have been thoroughly analyzed and *** is the admixtures of basic wavefunctions resulted from the spinorbit interaction and/ork Coulomb interaction and/or Kramers degeneracy that make strain-induced splittings of levels *** contrast with this,strain-induced shifts come mainly from the zero-order approximate *** is found that there are nonvanishing matrix elements of operators T2ξ,T2η and T2ζ between wavefunctions with positive Ms and those with negative ms',which have important effects on strain-induced splittings of *** shifts of t2^32E under both hydrostatic pressure and uniaxial pressure have been uniformly *** important results of Yc,Zc,Pc,Qc and have been evaluated.

关键词：晶体 MgO:Cr^3+ 能级位移混合波函数

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Energy Spectra of the Tunable Laser Crystal Gd3Ga5O12：Cr^3＋ and TheirPressure-Induced Shifts

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Communications in Theoretical Physics 2004年第1期41卷 141-150页

作者： madong-ping DepartmentofAppliedPhysics SichuanUniversityChengdu610065ChinaInternationalCentreforMaterialsPhysicsAcademiaSinicaShenyang110015China

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shiftsof energy spectra due to electron-phonon interaction (EPI), at 300 K, the 'pure electronic' contributions and the contri-butions from EPI to R1 line, R2 line, and U band of GGG:Cr3+ as well as their PS have been calculated, *** total calculated results are in good agreement with all the experimental data. Their physical origins have beenexplained. It is found that the mixing-degree of [t2/2(^3T1)e^4T2) and [t3/2^2E) base-wavefunctions in the wavefunctions of R1 level of GGG:Cr^3+ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasingpressure. The change of the mixing-degree with pressure plays a key role for PS of R1 line or R2 line. At 300 K, boththe temperature-independent contribution to R1 line (or R2 line or U band) from EPI and the temperature-dependentone are important. The remarkable difference between pressure-dependent behaviors of PS of R1 lines of GGG:Cr^3+ andGSGG:Cr^3+ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr^3+at various pressures have satisfactorily been explained.

关键词：能量谱可调激光器铬离子掺杂镓酸钆晶体电子-光子相互作用

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