Energy Spectrum and Its Pressure-Induced Shift and J-T Effect of ZnTe:Mn2+

By using strong-field scheme, the complete d⁵ energy matrix with symmetry has been constructed. Then, by diagonalization of this matrix at normal and various pressures,the whole energy spectrum [including the ground-state zero-field splitting (GSZFS)] and its pressure-induced shift (PS) of Znlb:Mn²⁺ have uniformly been calculated. The results are in very good agreement with experimental data. According to the eigenfimctions and PS, the assignments of four absorption bands have been given. By taking into account the dect of different deformations of t₂ and e radial wavefunctions on t₂³(⁴A₂)e²(³A₂)⁴ A₁ and t₂³(²E)e²(³A₂)⁴E, the position of the third absorption band at normal pressure has been estimated.The tetragonal field is important for GSZFS of ZnTe:Mn²⁺ and its PS, which supports the existence of tetragonal Jahn-Teller distortion in ZnTe:Mn²⁺ The physical essentials of typical levels, GSZFS and their PS have been revealed.     

Energy Spectrum and g Factor of MgO:Cr3+ and Their Pressure-Induced Shifts

The unified calculation of the whole energy spectrum and g factor of the ground state for MgO:Cr³⁺ at normal pressure and their pressure-induced shifts has been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d³ energy matrix in a regular octahedral field. All the calculated results are in very good agreement with a lot of experimental data. For the first time, by using the wavefunctions obtained by diagonalization of the complete energy matrix, the pressure-induced shifts of g factor have satisfactorily been calculated and explained by microscopic theory. The rates of change of levels with respect to various parameters and the contributions to levels from various parameters have been calculated. The distinct differences in magnitude and/or sign of pressure-induced shifts of various levels are immediately determined by their characteristic dependencies on the parameters of interactions. The pressure-induced shifts of levels and g factor have provided important criteria for the correctness of the calculations and assignments of the energy spectrum and wavefunctions, and it is quite necessary and important to carry out the unified calculation of the whole energy spectrum and g factor at normal pressure and their pressure-induced shifts.     

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

With the strong-field scheme and cubic bases,the complete d^3 energy matrix in a tetragonally distorted cubic-field has been constructed.By diagonalizing this matrix,the energy spectra of SrTiO3:Cr^3 and SrTiO3:Mn^4 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:Cr^3 and SrTiO3:Mn^4 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 Mn^4 and ligands(O^2-) in SrTiO3:Mn^4 is stronger than the one of the bonding between Cr^3 and ligands(O^2-)in SrTiO3:Cr^3 .It is shown that the obtained wavefunctions and values of parameters are reasonable.     

Pressure—Induced Shifts of Energy Spectra of α—Al2O3：Mn^4＋

By making use of the diagonalization of the complete d^3 energy matriz in a trigonally distorted cubic-field and the theory of pressure-induced shifts (PS) of energy spectra,the whole energy spectrum of α-Al2O3:Mn^4 and PS of levels have been calculated.All the calculated results are in excdellent agreement with the experimental data.The comparison between the results of α-Al2O3:Mn^4 and ruby has been made.It is found that on one hand,R1-line and R2-line PS of α-Al2O3:Mn^4 and ruby are linear in pressure over 0-100 kbar,and their values of the principal parameter for PS are very close to each other.On the other hand,the sensitivities of R1-line and R2-line PS of α-Al2O3:Mn^4 are higher than those of ruby respectively,which comes mainly from the difference between the values of parameters at normal pressure of two crystals;moreover,the expansion of d-electron wavefunctions of α-Al2O3:Mn^4 with compression is slightly larger than the one of ruby,and the effective charge experienced by d-electrons of α-Al2O3:Mn^4 decreases with compression more rapidly than the one of ruby.In the final analysis,all these can be explained in terms of the facts that the two crystals are doped α-Al2O3 with two isoelectronic ions;the strengths of the crystal field and covalency of α-Al2O3:Mn^4 are larger than those of ruby respectively,due to the charge of Mn^4 to be larger than that of Cr^3 .     

Complete Ligand-Field Calculations of Energy Spectrum and g Factor of CaO:Ni2+ and Their Pressure-Induced Shifts

The calculations of the whole energy spectrum and the g factor of the ground state for CaO:Ni²⁺ at ,normal pressure and their pressure-induced shifts have been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d⁸ energy matrix in a regular octahedral field. The calculated results are in very good agreement with experimental data. The physical essentials of the pressure-induced shifts of typical levels and g factor for the ground state have been revealed by using the wavefunctions and energy spectra at various pressures.     

Energy Spectrum and g Factors of α-A12O3:Ni2+ and Their Pressure-Induced Shifts

A unified calculation of the whole energy spectrum and g factors of the ground stateat normal pressure and their pressure-induced shifts for α-A1₂O₃:Ni²⁺ has been carried outon the basis of the theory of pressure-induced shifts and the diagonalization of the completed⁸ energy matrix adopting C_3υ symmetry. The calculated results are in very good agreementwith all the experimental data. The rates of change of all the levels with respect to variousparameters and the contributions to typical levels or splittings from various parameters havebeen calculated. The distinct differences of pressure-induced shifts of various levels are immediatelydetermined by their characteristic dependencies on -the parameters of interactions,and the pressure-induced shifts (especially those of t₂⁶e^{2 1}EÊ) have provided important or,crucial criteria for the correctness of the calculation and assignment of the energy spectrum of α-A1₂O₃:Ni²⁺.     

The Pressure-Induced Shifts of Energy Spectra of ZnS:Ni2+

The calculations of the whole energy spectrum of Zns:Ni²⁺ at normal pressure and pressure-induced shifts of its levels have been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d⁸ energy matrix in a regular tetrahedral field. The calculated results are in very good agreement with experimental data at normal and high pressures. The comparison between the results of ZnS:Ni²⁺ and Mg0:Ni²⁺ indicates that the comlency of ZnS:Ni²⁺ is obviously stronger than the one of MgO:Ni²⁺;the expansion of electron wavefunctions of ZnS:Ni²⁺ under pressure is obviously larger than that of MgO:²⁺; and the pressure-induced shifts of levels of znS:NiZf show strong nonlinearity.     

LiNbO_3:Ni~(2+)的常压能谱和g因子

采用强场方案,通过将d8完全能量矩阵对角化,统一计算了LiNbO3:Ni2+的常压能谱和g因子,计算结果与大量实验数据符合很好.给出了各个能级对不同参量的变化率.研究表明,利用对角化完全能量矩阵获得的波函数对g因子所作的计算为整个理论计算及波函数的归属提供了重要判据,充分体现了将能谱和g因子作统一计算的重要性和必要性. 关键词： 晶场 能谱 g因子     

Energy Spectra and g Factors of α-A1203:Cr3+ and α-A1203:Mn4+

By diagonalizing the complete d³ energy matrix in a trigonally distorted cubicfield and using the wavefunctions from it, unified calculations of the whole energy spectrum as well as the g factors of the ground state and t₂^{3 2} E excited states for α-A1₂0₃:Cr³⁺ and α-A1₂0₃:Mn⁴⁺ have been carried out respectively. A11 the calculated results are in very good agreement with the experimental data. The comparison between the results of the two crystals has been made, which demonstrates that the covalency of α-A1₂0₃:Mn⁴⁺ is stronger than the one of α-A1₂0₃:Cr³⁺. For the zero-field splittings of the ground state and t₂^{3 2} E , their physical origins are revealed; the comparison and analysis of their values of the two crystals have been made.     

Energy Spectra,g Factors and Their Pressure-Induced and/or Thermal Shifts of SrTiO3:Cr3+ and SrTiO3:Mn4+ III: R-Line Thermal Shifts of SrTiO3:Mn4+

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 the parameters in the expressions of thermal shift (TS) from EPI for the ground level, R level and R line of SrTiO₃:Mn⁴⁺ have been evaluated; the R-line TS and various contributions to it have been calculated in the low-temperature region. It is found that all the three terms of R-line TS from EPI relevant to the lattice vibration are red shifts. The Raman term is the largest, the neighbor-level term is the second, and the optical-branch term is very small over the range of T≤80 K. The contribution to R-line TS from thermal expansion has been approximately neglected in this work. The very strong EPI relevant to its lattice vibration for SrTiO₃:Mn⁴⁺ causes its R-line TS to be an unusually large red-shift. Only by taking into account the strong softening of the low-frequency acoustic modes of the lattice vibration at low temperatures, can we successfully explain the variation of R-line TS of SrTiO₃$:Mn⁴⁺ with temperature.     

Energy Spectra,g Factors and Their Pressure—induced and ／or Thermal Shifts of SrTiO3：Cr^3＋ and SrTiO3：Mn^4＋ Ⅱ：Pressure Effects on Ground_State g Factor and Splittings of t2^32E and t2^34A2 of Sr

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.     

Energy Spectrum,g Factors,Strain-Induced Level-Splittingsand R-Line Thermal Shift of MgO:V2+

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, the R line, t₂^{3 2}T₁ and t₂^{3 2}T₂ lines, t₂² (³T₁)e⁴T₂, t₂² (³T₁)e⁴T₁ and t₂ e²(⁴A₂)⁴T₁ bands, g factors of t₂^{3 4}A₂ and t₂^{3 2}E, four strain-induced level-splittings and R-line thermal shift of MgO:V₂₊ have been calculated. The results are in very good agreement with the experimental data. It is found that for MgO:V₂₊, the contributions due to electron-phonon interaction (EPI) come from the first-order term; the contributions from the second-order and higher terms are insignificant. In thermal shift of R line of MgO:V₂₊, the temperature-dependent contribution due to EPI is dominant. The results obtained in this work may be used in theoretical calculations of other effects of EPI.     

BeAl2O4:Cr3+的能谱和R1线压力移位的理论计算

采用强场方案和三角基,通过对角化三角畸变立方场的d3电子组态完全能量矩阵,拟合得到BeAl2O4:Cr3+的能谱和波函数.利用获得的波函数,计算出了基态g因子和R1 、R2线能谱压致移位值,计算值和实验结果相符合.各参数对能级压力移位率的影响也被定量计算,揭示了R1和R2线压力移位的物理起源.     

Complete Ligand-Field Calculation of Energy Spectrum and g Factor of MgO:Ni2+ and Their Pressure Effects

The unified calculation of the whole energy spectrum and g factor of ground state for MgO:Ni²⁺ at normal pressure and their pressure-induced shifts has been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d⁸ energy matrix in a regular octahedral field. A11 the calculated results are in excellent agreement with a lot of experimental data. For the first time, by using the wavefunctions obtained by diagonalization of the complete energy matrix, the pressure-induced shift-of g factor has satisfactorily been calculated and explained by microscopic theory The contributions to typical levels from various parameters have been calculated. The distinct differences of pressure-induced shifts of various levels are immediately determined by their characteristic dependencies on the parameters of interactions. The pressure-induced shifts of levels have provided important criteria for the correctness of the calcutation and assignment of them.     

EPR,optical and superposition model study of Mn2+ doped L+ glutamic acid

Electron paramagnetic resonance (EPR) study of Mn²⁺ doped L+ glutamic acid single crystal is done at room temperature. Four interstitial sites are observed and the spin Hamiltonian parameters are calculated with the help of large number of resonant lines for various angular positions of external magnetic field. The optical absorption study is also done at room temperature. The energy values for different orbital levels are calculated, and observed bands are assigned as transitions from ⁶A_1g(s) ground state to various excited states. With the help of these assigned bands, Racah inter–electronic repulsion parameters B = 869 cm^?1, C = 2080 cm^?1 and cubic crystal field splitting parameter Dq = 730 cm^?1 are calculated. Zero field splitting (ZFS) parameters D and E are calculated by the perturbation formulae and crystal field parameters obtained using superposition model. The calculated values of ZFS parameters are in good agreement with the experimental values obtained by EPR.     

ZnS:Mn2+常压吸收谱与高压移位的理论研究

迄今对ZnS:Mn2+五个吸收谱带归属意见不一.本文采用晶场理论与晶场光谱压力移位理论对ZnS:Mn2+的常压光谱、高压移位作了统一的理论计算和分析;计算结果与实验满意地符合,并对长期以来未能归属的第四,五两带作出了正确的归属.结果表明用一般的晶场理论框架不能解释第三、四带的常压谱值,本文用共价效应对第三、四带作出了令人满意的计算与解释.     

CaF2:Co2+光谱和顺磁g因子的统一解释

基于半自洽场d轨道理论和完全对角化方法,从杂质局部结构统一解释了CaF₂:Co²⁺的光谱和顺磁 g 因子. 杂质局部结构存在塌缩效应,但仍保持八配位立方对称. 在此基础上,用微扰法和完全对角化方法讨论了g因子对晶场参量D_q的依赖关系. Macfarlane的 g 因子三阶微扰公式是好的近似公式,但随着D_q的减小,其有效性变差. 最后,文章讨论了基于完全对角化和自旋哈密顿理论的 g 因子公式的适用性,及其在轨道简并情况下的困难.     

Theoretical Studies of Energy Spectra and g Factors of Cr3+-Doped YAl3(BO3)4

With the strong-field scheme and trigonal bases, by diagonalizing the complete d³ energy matrix in a trigonally distorted cubic-field, the energy spectra and wavefunctions of YAl₃(BO₃)₄:Cr³⁺ have been calculated. The rates of change of levels with respect to various parameters and the contributions to levels from various parameters are calculated, and the physical origins of various levels or splittings have been clearly and quantitatively shown. By using the wavefunctions obtained from diagonalizing the complete energy matrix, the g factors of the ground state of YAl₃(BO₃)₄:Cr³⁺ have been evaluated. The calculated results are in good agreement with the optical-spectral and EPR experimental data. It is demonstrated that the bonding between Cr³⁺ and ligands (O^2-) is ionic.     

Unified Calculations of the Energy and EPR Spectra and Their Pressure-Induced Shifts of Ruby

By taking into account the effect of variation in angular wavefunction, reconsidering the expressions of spin-orbit coupling parameters, diagonalizing the complete d³ energy matrix in a trigonally distorted cubic-field and using the wavefunctions from it, the unified calculations of the energy spectrum and EPR spectrum for ruby and their pressure-induced shifts have been carried out. All the calculated results are in very good agreement with a lot of experimental data. The estimation by making use of superposition model has also demonstrated the high sensitivity of trigonal-field parameters to angular variation. The distinct differences in magnitude and/or sign of pressure-induced shifts of various levels are immediately determined by their characteristic dependencies on the parameters of interactions. The pressure-induced shifts of levels and g factors have provided important criteria for the correctness of calculations and assignments of the energy spectrum and wavefunctions.     

KAl(MoO4)2晶体中掺杂Cr3+的能谱和g因子的理论计算*

采用强场方案和三角基，通过对角化三角畸变的立方晶场下的d3 完全能量矩阵，计算出了KAl(MoO4)2:Cr3+ 的能谱和波函数。使用对角化完全能量矩阵所获得的波函数，进一步计算了KAl(MoO4)2:Cr3+ 的基态g 因子。计算结果与光谱，EPR谱实验数据很好地符合。研究表明,利用对角化完全能量矩阵获得的波函数对 g 因子所作的计算为整个理论计算及波函数的归属提供了重要判据,充分体现了将能谱和g 因子作统一计算的重要性和必要性.