Theoretical Calculations of Thermal Shifts of Ground-StateZero-Field-Splitting for Ruby

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 wavefunctions within d³ electronic configuration, the thermal shifts (TS) of the ground-state zero-field-splitting (GSZFS) due to EPI for ruby have microscopic-theoretically been calculated; the contribution to TS of GSZFS from thermal expansion has also been calculated. The results are in very good agreement with experiments. It is found that the contributions from the first-order perturbation of the second-order term in EPI Hamiltonian are dominant in the Raman term and optical-branch term for TS of GSZFS; the different between the TS due to EPI of t₂^{3 4}A₂±(1/2) e₂ (G₂) level and the TS due to EPI of t₂^{3 4}A₂±(3/2) e₂ (G₁) level gives rise to the TS due to EPI of GSZFS, which is very small in comparison with the TS due to EPI of G₂ or G₁ level. Among various terms in TS of GSZFS, Raman term is the largest one and the signs of the Raman term and optical-branch term are opposite to the sign of the thermal-expansion term; the optical-branch term plays an important role in TS of GSZFS and increases rapidly with temperature; all various contributions to TS of GSZFS have to be taken into account, since the subtle balance among them determines the total result. The comparison between the features of TS of GSZFS and those of TS of R₁ and R₂ lines has been made. For TS of GSZFS, the contribution from thermal expansion is especially important; the neighbor-level term is insignificant.     

Energy Spectrum of YAG:Cr3+ and Thermal Shifts of Its R Lines

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 as well as thermal shifts of R₁ line and R₂ 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:Cr³⁺ is compressed along the [111] direction. Thus, for YAG:Cr³⁺ and ruby, the splitting of t₂³⁴A₂ (or t₂³²E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R₁ and R₂ lines of YAG:Cr³⁺, the temperature-dependent contributions due to EPI are dominant.     

Energy Matrix of the d3 Configuration in Trigonal Field and Analysis of the Entire Energy Spectrum of Ruby

By using the strong-field scheme, we have calculated all the reduced matrix elements and the matrix elements of the trigonal crystal field and all the matrix elements of the spinorbit interaction for the d³ electronic configuration: The complete energy matrix of the d³ configuration in trigonal field has been constructed. This matrix has been diagonalized to fit the experimental optical and microwave spectral data of ruby. The calculated results are in good agreement with the experimental data. In particular, the zero-field splitting δ of the ground state and the splitting between R₁ and R₂ lines agree very well with the experimental results. The assignments of all the energy levels and the rates of change of the levels with respect to various parameters are given. The contributions from various parameters to δ and the splitting between R₁ and R₂ lines are also given.     

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.     

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

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 R₁, R₂, B₁, B₂, B₃, and R'₃ lines and the ground-state zero-field-splitting of ruby have been uniformly calculated. The calculation results are in very good agreement with all the experimental data. At normal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of |t₂²(³T₁)e⁴T₂〉and |t³₂²E〉bases in the wavefunction of R₁ level of ruby is small at normal pressure, and it gradually decreases with increasing pressure, which causes the R₁-line PS of ruby to monotonously red shift with approximate linearity. The combined effect of the pure electronic PS of R₁ line and the PS of R₁ line due to EPI gives rise to the total PS of R₁ line. The analyses and comparisons among the features of R₁-line PS's of three laser crystals (ruby, GSGG:Cr³⁺ and GGG:Cr³⁺) have been made, and the origin of their difference has been revealed.     

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

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, R₃', R₂', and R₁' 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 calculated. The 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.     

Theoretical Calculations of Thermal Broadenings and Transition Probabilities of R,R' and B Line-Groups for Ruby

On the basis of the unified calculation of the thermal shifts of R₁ line, R₂ line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R, R'and B line-groups for ruby, by taking into account all the levels and admixtures of wavefunctions within d³ electronic configuration and all the ΓM in electron-phonon interaction,the transition probabilities of direct and Raman processes have theoretically been calculated, The thermal broadenings of R,R' and B line-groups have successfully been interpreted in terms of the direct and Raman processes of acoustic phonons. The theoretically predicted transition probabilities are in good agreement with the experimental ones.     

Microscopic—Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：V^2＋

A great improvement on a previous work (PHYS.Rev.B48 (1993) 14067) has been made.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 d^3 electronic configuration,the values of all the parameters in the expressions of thermal shift(TS) and thermal broadening (TB) from EPI for the ground level,R level and R line of MgO:V^2 have microscopically been evaluated;and then,both the 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 from EPI are red shifts;the term of the contribution to TS from thermal expansion is blue shift.The Raman term is the largest,and the other terms are also important for TS.The R-line TS of MgO:V^2 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:V^2 .For calculations of both the TS and TB,it is very important to take into account all the admixtures of wavefunctions.     

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

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 d^3 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:Cr^3 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:Cr^3 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:Cr^3 .For both TS and TB,it is very important to take into account all the admixtures of basic wavefunctions within d^3 electronic configuration.     

Energy Spectra of the Tunable Laser Crystal Gd3Ga5O12:Cr3+ and Their Pressure-Induced Shifts

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction (EPI), at 300 K, the `pure electronic' contributions and the contributions from EPI to R₁ line, R₂ line, and U band of GGG:Cr³⁺ as well as their PS have been calculated, respectively. The total calculated results are in good agreement with all the experimental data. Their physical origins have been explained. It is found that the mixing-degree of |t₂²(³T₁)e ⁴T₂> and |t₂³²E> base-wavefunctions in the wavefunctions of R₁ level of GGG:Cr³⁺ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role for PS of R₁ line or R₂ line. At 300 K, both the temperature-independent contribution to R₁ line (or R₂ line or U band) from EPI and the temperature-dependent one are important. The remarkable difference between pressure-dependent behaviors of PS of R₁ lines of GGG:Cr³⁺ and GSGG:Cr³⁺ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr³⁺ at various pressures have satisfactorily been explained.     

Energy Spectrum of La3Lu2Ga3O12：Cr^3＋ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced Shifts （PS） of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction （EPI）, the normal-pressure energy spectra of α and β centers of Cr^3＋ ions for LLGG：Cr^3＋ and the PS＇s of R1 lines and U band of these centers have been calculated at 10 K, respectively. The total calculated results are in very good agreement with the experimental data. For LLGG：Cr^3＋, the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Rmix^ei （2E - 4T2） [mixing-degree of （t2^2 （^3T1）e^4T2） and （t2^3 E） base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line. The comparison between R1-line PS＇s of GSGG：Cr^3＋ and LLGG：Cr^3＋ has been made. It is found that a peak of R1-line PS appears at Rmix^ei （^2E - ^4T2） ≈ 0.08.     

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.     

Pressure-Dependent Base-Wavefunction Admixture and Lifetime of R1 State of La3Lu2Ga3O12:Cr3+

As a key factor leading to the pressure-dependent R₁-line-shift reversal and R₁-state lifetime, at 10 K, the pressure-dependent variation of mixing-degree of |t₂²(³T₁)e⁴T₂〉 and |t₂³² E〉base-wavefunctions in the wavefunction of R₁ state of LLGG:Cr³⁺ has been calculated and analyzed. From this, the physical origin of the pressure-dependent R₁-line-shift reversal has been revealed. Furthermore, by using the pressure-dependent values of the sum of all square mixing-coefficients of |t₂²(³T₁)e⁴T₂〉in the wavefunction of R₁ state, the lifetimes of R₁ state of LLGG:Cr³⁺ at various pressures have been calculated, which are in good agreement with observed results. The quantum anticrossing effect between t₂³²E and t₂²(³T₁)e⁴T₂ levels due to both spin-orbital interaction and electron-phonon interaction is remarkable, which is related to the admixture of |t₂²(³T₁)e⁴T₂〉and |t₂³² E〉as well as the low-high crystal-field transition.     

The magnetic properties and magnetocaloric effects in binary R-T(R = Pr,Gd,Tb,Dy,Ho,Er,Tm;T = Ga,Ni,Co,Cu)intermetallic compounds

In this paper, we review the magnetic properties and magnetocaloric effects(MCE) of binary R–T(R = Pr, Gd, Tb,Dy, Ho, Er, Tm; T = Ga, Ni, Co, Cu) intermetallic compounds(including RGa series, RNi series, R_(12)Co_7 series, R_3 Co series and RCu_2series), which have been investigated in detail in the past several years. The R–T compounds are studied by means of magnetic measurements, heat capacity measurements, magnetoresistance measurements and neutron powder diffraction measurements. The R–T compounds show complex magnetic transitions and interesting magnetic properties.The types of magnetic transitions are investigated and confirmed in detail by multiple approaches. Especially, most of the R–T compounds undergo more than one magnetic transition, which has significant impact on the magnetocaloric effect of R–T compounds. The MCE of R–T compounds are calculated by different ways and the special shapes of MCE peaks for different compounds are investigated and discussed in detail. To improve the MCE performance of R–T compounds,atoms with large spin(S) and atoms with large total angular momentum(J) are introduced to substitute the related rare earth atoms. With the atom substitution, the maximum of magnetic entropy change(?SM), refrigerant temperature width(Twidth)or refrigerant capacity(RC) is enlarged for some R–T compounds. In the low temperature range, binary R–T(R = Pr, Gd,Tb, Dy, Ho, Er, Tm; T = Ga, Ni, Co, Cu) intermetallic compounds(including RGa series, RNi series,R_(12)Co_7 series, R_3 Co series and RCu_2series) show excellent performance of MCE, indicating the potential application for gas liquefaction in the future.     

Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations

The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, R_νλ (ν, λ=0, ±1), are obtained on the space of universal enveloping algebra of two-state Heisenberg-Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of R_νλ are given. The expectation values of R_νλ in the angular momentum coherent states are calculated as well as the corresponding classical limits.     

Invar properties in the rare earth-3d transition metal alloys

The RCo₂ and R₂Fe₁₇ compounds (R = rare earth) exhibit Invar-like thermal expansion anomalies below their ordering temperatures. These spontaneous volume magnetostrictions are discussed by considering their magnetic properties. In RCo₂ compounds there is no intrisinc Co-moment is induced by the exchange and applied fields. The volume expansion anomaly is associated with the onset of the 3d magnetic moment. IN R₂Fe₁₇ compounds there is an intrisinc Fe- moment. Magnetic structures give evidence for positive and negative exchange interactions between Fe atoms which are strongly distance dependent. The thermal expansion anomaly is a result of this distance of the magnetic interactions.     

氢化杂质和厚度效应对高斯势量子点中二能级体系量子跃迁的影响

在计及氢化杂质和厚度效应下,分别选取抛物线型限定势阱和高斯函数型限定势阱描写盘型量子点中电子的横向限定势和纵向限定势,采用Lee-Low-Pines-Pekar变分法推导出量子点中电子的基态和第一激发态能量本征值和本征函数,以此为基础,构造了一个二能级结构,并基于二能级体系理论,讨论了电子在磁场作用下的量子跃迁.结果表明,高斯函数型限定势比抛物线型限定势更能精准反映量子点中真实的限定势;量子点的厚度对电子的跃迁概率的影响不凡;电声耦合强度、介电常数比、磁场的回旋频率、高斯函数型限定势阱的阱深和阱宽等对电子基态与第一激发态声子平均数、能量以及量子跃迁的影响显著.     

Magnetic characteristics of R2(Fe, Co)14B systems (R = Y, Nd and Gd)

R₂(Fe, Co)₁₄B compounds (R = Y, Nd and Gd) were prepared in high purity. The magnetic behavior of R₂(Fe, Co)₁₄B compounds is reported over the temperature range 4 to 300 K. The effects of Fe substitution by Co on the saturation magnetization, Curie temperature and anisotropy are presented. The spin-reorientation temperature is lowered as Co replaces Fe. This also results in a reduced cone angle.

The R₂Fe_14−xCo_xB alloys crystallize in the tetragonal structure over the entire concentration range of 0 x 14. When Fe is substituted by Co, the Curie temperature increases significantly, the saturation magnetization increases to a maximum value around x = 2, and the anisotropy becomes planar for R = Y and Gd. The Nd₂(Fe, Co)₁₄B systems all exhibit uniaxial anisotropy at room temperature and Nd₂Co₁₄B is strongly uniaxial at 77 K. The Nd₂(Fe, Co)₁₄B systems are conical at 77 K.     

Photoluminescence of LLGG:Cr crystals under high pressure

We present photoluminescence spectra of La_2.7Lu_2.29Cr_0.01Ga₃O₁₂ and La_2.32Lu_2.59Cr_0.02Ga_3.07O₁₂ doped with Cr³⁺ obtained at high hydrostatic pressure up to 220 kbar, applied in a diamond anvil cell at 20 K and room temperature. In both materials we have obtained a pressure-induced ⁴T₂–²E electronic cross-over. On the basis of the low-temperature R line luminescence at pressures above 100 kbar we have distinguished two dominant Cr³⁺ sites: and β, existing in both materials, and one minor site δ, that exists only in La_2.32Lu_2.59Cr_0.02Ga_3.07O₁₂. The pressure-induced shifts of the R₁, R_1β and R_1δ lines as well as the pressure shift of the broad band related to the ⁴T₂→⁴A₂ transition in both materials have been estimated.     

些V/S,V/Fe/S和Mn/O簇合物溶液化学行为的NMR研究

报道我们对某些V/S,V/Fe/S和Mn/O簇合物溶液化学的核磁研究.(Et₄N)[V₄S₄(C₄H₈NCS₂)₆](1)的¹H NMR谱包含三个宽峰,δ4.77,5.17和7.57,分别归属为端基与桥基配体的α-H.游离配体信号的出现表明了溶液中发生配体与溶剂分子的交换反应.对一系列[VFe₃S₄(R₂ NCS₂)₄]^-簇合物(R₂=OC₄H₈(2),Et₂(3))进行了¹H NMR表征.钒与三个铁中心的配体氢谱被分别归属.对NMR谱的时间跟踪发现位于δ19.6(2)以及δ34.2(3)的信号逐渐增长,这意味着新物种形成.合成反应的动态NMR跟踪指认了新物种为Fe₄S₄(R₂ NCS₂)₄.提出了溶液中簇骼金属原子交换机理.包含H₂O和NO₃配体的单核锰bpy配合物(4)的氢谱指示出这些单齿配体的可交换性.它促使配合物4成为含有两个单核Mn分子的包容化合物.