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.     

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.     

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

For the first time,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 d^3 electronic electron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d^3 electronic configuration,the values of parameters in expressions of Raman and optical-branch terms of thermal shifts (TS) due to EPI for three levels,^4T2 band and ^4T1 band of ruby have been evaluated;the contributions to TS of ^4T2 and ^4T1 broad bands from thermal expansion have also been calculated;and then,the TS of the peak energies of ^4T2 and ^4T1 broad bands have been calculated.The results are in satisfactory agreement with observed data.The values of single-electron reduced matrix elements representing the strengths of EPI of ^4T2 and ^4T1 bands have respectively been determined.For TS of the peak energies of ^4T2 and ^4T1 bands,it is found that the contribution to TS from the second-order term in EPI Hamiltonian 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 from thermal expansion is specially important,and all the three terms of TS of ^4T2 or ^4T1 band are red shifts.     

Improved Ligand-Field Theoretical Calculations of R-Line Thermal Broadenings of NIgO：Cr^3＋ and MgO：V^2＋

With the values of parameters obtained from improved ligand-field theory, by taking into account all the irreducible representations and their components in EPI as well as all the levels and the admixtures of basic wavefunctions within d^3 electronic configuration, the R-line thermal broadenings （TB） of both MgO：Cr^3＋ and MgO：V^2＋ have microscopic-theoretically been calculated, The results are in very good agreement with the experimental data. It is found that the R-line TB of MgO：Cr^3＋ or 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：Cr^3＋ or MgO：V^2＋.     

Improved Ligand-Field Calculation of Energy Spectrum and R-Line Thermal Shift of MgO：Cr^3＋

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, t^3 2^2 T1 lines, t^2 2（^3 T1）e^4 T2, and t^2 2（^3T1）e^4T1 bands, ground-state g factor, four strain-induced level- splittings, and R-line thermal shift of MgO：Cr^3＋ have been calculated. The results are in very good agreement with the experimental data. It is found that for MgO：Cr^3＋, the contributions due to electron-phonon interaction （EPI） come from the first-order term. In thermal shift of R-line of MgO：Cr^3＋, the temperature-dependent contribution due to EPI is dominant.     

Energy Spectrum,g Factors,Strain-Induced Level-Splittings and R-Line Thermal Shift of MgO：V^2＋＋

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, t^322T1 and t^322T2 lines, t^22（^3T1）e^4T2, t^22（^3T1）e^4T1 and t2e^2（^4A2）4T1 bands, g factors of t^32 ^4A2 and t32E, four strain-induced level-splittings and R-line thermal shift of MgO：V^2＋ have been calculated. The results are in very good agreement with the experimental data. It is found that for MgO：V^2＋, the contributions due to electronphonon 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：V^2＋, 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.     

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.     

Theoretical Calculation of Energy Spectrum of YGG：Cr^3＋ and Thermal Shifts of Its R-Lines

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 energy spectrum of YGG：Cr^3＋ at normal pressure and low temperature has been calculated. The g factor of the ground-state has been evaluated in terms of the energy spectrum. At the same time, by using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix and Thermal Shifts theory, we calculate the thermal shifts of the sharp lines of YGG：Cr^3＋ and determine the relevant parameters. The calculated results are all in good agreement with the optical-spectrum and EPR experimental data. It is demonstrated that the obtained wavefunctions and the values of parameters are reasonable.     

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 Shift of R-Line of MgO：Cr^3＋ with Electron-Phonon Interaction Effect

By means of improved ligand-field theory, the ＂pure electronic＂ pressure-induced shift （PS） and the PS due to electron-phonon interaction （EPI） of R-line of MgO：Cr^3＋ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R-line of MgO：Cr^3＋ and the PS of its R-line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R-line, which has satisfactorily explained the experimental results. The comparison between the feature of R-line PS of MgO：Cr^3＋ and that of R1-line PS of ruby has been made.     

First-principles study of lattice dynamics and thermodynamics ofosmium under pressure

We have performed the first-principles linear response calculations of the lattice dynamics, thermal equation of state and thermodynamical properties of hcp Os metal by using the plane-wave pseudopotential method. The thermodynamical properties are deduced from the calculated Helmholtz free energy by taking into account the electronic contribution and lattice vibrational contribution. The phonon frequencies at Gamma point are consistent with experimental values and the dispersion curves at various pressures have been determined. The calculated volume, bulk modulus and their pressure derivatives as a function of temperature are in excellent agreement with the experimental results. The calculated specific heat indicates that the electronic contribution is important not only at very low temperatures but also at high temperatures due to the electronic thermal excitation. The calculated Debye temperature at a very low temperature is in good agreement with experimental values and drops to a constant until 100~K.     

The first-principles study of ferroelectric behaviours of PbTiO3/SrTiO3 and BaTiOn/SrTiO3 superlattices

We have performed the first-principles calculation to investigate the origins of ferroelectricities and different po- larization behaviours of superlattices BaTiO3/SrTiO3 and PbTiO3/SrTiO3. The density of state （DOS） and electronic charge profiles show that there are strong hybridizations between atoms Ti and O and between atoms Pb and O which play very important roles in producing the ferroelectricities of superlattices BaTiO3/SrTiO3 and PbTiO3/SrTiO3. Ow- ing to the decline of internal electric field in SrTiO3 （ST） layer, the tetragonality and polarizations of superlattices decrease with increasing the fraction of SrTiO3 in the superlattices. We find that the polarization of PbTiO3/SrTiO3 is largerthan that of BaTiO3/SrTiO3 at the same ratio of components, because the polarization mismatch between PbTiO3 and SrTiO3 is larger than that between BaTiO3 and SrTiO3. The polarization and tetragonality are en- hanced with respect to those of bulk tetragonal BaTiO3 in the superlattices BaTiO3/SrTiO3, while the polarization and tetragonality are reduced with respect to those of bulk tetragonal PbTiO3 in superlattices PbTiO3/SrTiO3.     

Critical exponents of ferroelectric transitions in modulated SrTiO3：Consequences of quantum fluctuations and quenched disorder

The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations (QFs), quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3(STO) with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1-x(Ca0.6389Ba0.3611)xTiO3(SCBT) with the averaged Sr-site ionic radius identical to the Sr2+ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ε, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO (e.g., Sr1-xCaxTiO3) at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.     

Structural and electronic properties of Fe-doped BaTiO3 and SrTiO3

We have performed first principles calculations of Fe-doped BaTiO3 and SrTiO3. Dopant formation energy, structure distortion, band structure and density of states have been computed. The dopant formation energy is found to be 6.8eV and 6.5eV for Fe-doped BaTiO3 and SrTiO3 respectively. The distances between Fe impurity and its nearest O atoms and between Fe atom and Ba or Sr atoms are smaller than those of the corresponding undoped bulk systems. The Fe defect energy band is obtained, which mainly originates from Fe 3d electrons. The band gap is still an indirect one after Fe doping for both BaTiO3 and SrWiO3, but the gap changes from Γ-R point to Γ-X point.     

Magnetic phase transition and the corresponding magnetostriction of intermetallic compounds RMnsGe2（R=Sm,Gd）

The temperature dependence of lattice constants a and c of intermetallic compounds RMn₂Ge₂ (R=Sm, Gd) is measured in the temperature range 10－800K by using the x-ray diffraction method. The magnetoelastic anomalies of lattice constants are found at the different kinds of spontaneous magnetic transitions. The transversal and longitudinal magnetostrictions of polycrystalline samples are measured in the pulse magnetic field up to 25T. In the external magnetic field there occurs a first-order field-induced antiferromagnetism－ferromagnetism transition in the Mn sublattice, which gives rise to a large magnetostriction. The magnitude of magnetostrictions is as large as 10^-3. The transversal and longitudinal magnetostrictions have the same sign and are almost equal. This indicates that the magnetostriction is isotropic and mainly caused by the interlayer Mn－Mn exchange interaction. The experimental results are explained in the framework of a two-sublattice ferrimagnet with the negative exchange interaction in one of the sublattices by taking into account the lattice constant dependence of interlayer Mn－Mn exchange interaction.     

Characterization of structural transitions and lattice dynamics of hybrid organic–inorganic perovskite CH_3NH_3PbI_3

By combining temperature-dependent x-ray diffraction(XRD) with temperature-dependent Raman scattering, we have characterized the structural transitions and lattice dynamics of the hybrid organic–inorganic perovskite CH_3NH_3PbI_3.The XRD measurements cover distinct phases between 15 K and 370 K and demonstrate a general positive thermal expansion.Clear anomalies are found around the transition temperatures.The temperature evolution of the lattice constants reveals that the transition at 160 K/330 K is of the first-/second-order type.Raman measurements uncover three strong lowfrequency modes, which can be ascribed to the vibration of the Pb/I atoms.The temperature evolution of the modes clearly catches these transitions at 160 K and 330 K, and confirms the transition types, which are exactly consistent with the XRD results.The present study may set an experimental basis to understand the high conversion efficiency in methylammonium lead iodide.     

Reconstruction of Intrinsic Thermal Parameters of Methane Hydrate and Thermal Contact Resistance by Freestanding 3ω Method

It is essential to obtain thermophysical properties of methane hydrate precisely with a freestanding probe for modeling and predicting thermal transport in gas hydrates. A method with a freestanding 3ω probe is presented to reconstruct the intrinsic thermal conductivity, thermal diffusivity, and thermal contact resistance of methane hydrate. Isolated from the thermal contact resistance, the intrinsic thermal conductivity of methane hydrate decreases between 250 K and 280 K and is 41% larger than the effective value at 253 K. More importantly, when the thermal contact resistance is isolated, the temperature dependence of intrinsic thermal conductivity shows a converse trend with the generally accepted glass-like feature at high temperature. Otherwise, thermal contact resistances measured in the experiment between the freestanding 3ω probe and the methane hydrate sample are extraordinary large. The freestanding 3ω method in this work is expected to measure the thermal property of methane hydrate more accurately.     

Improved Ligand-Field Theoretical Calculation of R-Line Pressure-Induced Shift of MgO：V^2＋

By means of an improved ligand-field theory, the ＂pure electronic＂ PS and the PS due to EPI of R line of MgO： V^2＋ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R line of MgO：V^2＋ and the PS of its R line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R line, which has satisfactorily explained the experimental results. The mixing-degree of ｜t2^2（^3T1）e^4T2〉 and ｜t2^3 ^2E〉 in the wavefunetion of R level and its variation with pressure have been calculated and analyzed. The comparison between the feature of R-line PS of MgO：V^2＋ and that of MgO：Cr^3＋ has been made.     

Stability and electronic structure studies of LaAIO3/SrTiO3 （110） heterostructures

The first-principles calculations are employed to investigate the stability, magnetic, and electrical properties of the oxide heterostructure of LaAIO3/SrTiO3 （110）. By comparing their interface energies, it is obtained that the buckled interface is more stable than the abrupt interface. This result is consistent with experimental observation. At the interface of LaAIO3/SrTiO3 （110） heterostructure, the Ti-O octahedron distortions cause the Ti tzg orbitals to split into the two- fold degenerate dxz/dyz and nondegenerate dxy orbitals. The former has higher energy than the latter. The partly filled two-fold degenerate t2g orbitals are the origin of two-dimensional electron gas, which is confined at the interface. Lattice mismatch between LaA103 and SrTiO3 leads to ferroelectric-like lattice distortions at the interface, and this is the origin of spin-splitting of Ti 3d electrons. Hence the magnetism appears at the interface of LaAIO3/SrTiO3 （110）.     

Explicit Proof of Equivalence of Two—Point Functions in the Two Formalisms of Thermal Field Theory

We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal λφ^3 theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories,including the one of the propagators for scalar bound states in an NJL model.