Jahn-Teller Coupling Research Articles

Nd, Ce(fπ)-O(pπ) HYBRIDIZATION IN Nd2−xCexCuO4 AND DYNAMIC JAHN-TELLER PAIRING IN HIGH-Tc SUPERCONDUCTORS

Hybridization of Nd (fπ) and Ce (fπ) orbitals with composite O (pπ)- O (pπ) bonding/ Cu(dπ*)-O(pπ) antibonding orbitals at the Fermi energy (EF) is shown to promote high-Tc superconductivity in Nd 2−x Ce x CuO 4. Dynamic Jahn-Teller coupling of these hybrid molecular orbitals to the lattice leads to Cooper pairing as it does in other high-Tc superconductors, such as La 2−x Sr x CuO 4, where O(pπ) character at E F is dominant.

The role of the Jahn-Teller effect and of the intermediate ligand field in the optical spectra of Cr3+-doped GaP and GaAs

The Jahn-Teller coupling constants for the ground state (4T1) and first excited state (4T2) of Cr3+-doped GaP and GaAs were evaluated by the angular overlap model. The calculation could provide quantitative justification for the recent proposal of Dunn and Bates (1987) according to which the Jahn-Teller effect is responsible for the differences observed in the optical spectra of these systems. The importance of configuration mixing in the ground state is discussed.

State mixing and the preferred jahn-teller coupling in cubic fx systems

The effect of the inclusion of state mixing is examined for the calculation of the Jahn-Teller coupling constants of the two Γ 8 states of f 1 systems in O h symmetry, both ML 6 and ML 8 species being considered. For the values of the spin-orbit coupling constants and ligand-field splitting parameters usually encountered, the results differ significantly from the strong-field limit values, but only slightly from those of the weak-field limit. For ML 6 systems the available estimates for the e λ and ∂ e λ ∂R parameters of the angular overlap model, together with the appropriate force-constant ratios, predict dominant coupling to the ϵ g mode for the Γ 8( 2 F 5 2 : 2 T 2u) level, whilst coupling to the τ 2g mode should prevail for the Γ 8( 2 F 7 2 : 2 T 1u) state. For ML 8 species the calculations similarly lead to the expectation of predominant τ 2g(δ) coupling for Γ 8( 2 F 5 2 : 2 T 1u), with prevailing ϵ g coupling for Γ 8 ( 2 F 7 2 : 2 T 2u). The results suggest the general adequacy of the weak-field limit results for cubic f x systems and, as an example, the T 1 and T 2 states for 3 H 4 of f 2, O h ML 6, systems are thus briefly treated.

The preferred jahn-teller coupling for T states of cubic dx systems

The angular overlap model is used to make predictions of the preferred vibrational coupling for Jahn-Teller active T states of cubic ( O h ML 6 and T d ML 4) d x systems. For the 2,5 T 2(g) states of d 1, d 4, d 6 and d 9and for the 3,4 T 2(g) states of d 2, d 3, d 7 and d 8, where only a single state of the given spin, S, and irreducible representation, Γ, occurs, clear predictions emerge, and ϵ g (or ϵ) coupling should be dominant for all cases except 2,5 T 2g O h(for which E JT for ϵ g and τ 2gcoupling are likely to be of comparable magnitude). For the 3,4 T 1(g) states of d 2, d 3, d 7 and d 8, two admixed states always arise, but for the d 2 and d 7 O h systems and for the d 3 and d 8 T d systems, coupling to ϵ g or ϵ, respectively, ought to be predominant, irrespective of the strength of the ligand field. For the d 2 and d 7 T d systems and for the d 3 and d 8 O h systems, however, a more complex situation results and the preferred coupling is markedly dependent upon the ligand field strength.

The Symmetry of the EL2 Defect in GaAs

AbstractLinear dichroism has been measured in the broad absorption band of the EL2 defect in GaAs under uniaxial stress. In addition, the splittings of the EL2 zero phonon line (ZPL) at 8378 cm-1 under uniaxial stress applied along [100], [111], and [110] directions have been measured. Splitting of the ZPL under [100] stress is over one order of magnitude smaller than under [111] stress, on the other hand, the linear dichroism in the broad absorption band is roughly equal for these two directions of stress. This is an evidence for the quenching of the coupling to tetragonal strains due to interaction with trigonal modes of the lattice (the Ham effect). Therefore, it is established, that the excited T2 state of EL2 is a localized state subject to dynamical Jahn-Teller coupling to trigonal modes of the lattice. The possibility that the excited T2 state has hydrogenic nature associated with the L minima is ruled out by the present results. The observed splittings of the ZPL together with polarization selection rules clearly indicate the tetrahedral Td symmetry of the EL2 defect ruling out any other point group in particular trigonal C3v In view of the presented experimental results, their interpretation, and recent theoretical investigations, the isolated arsenic antisite AsGa most successfully accounts for the properties of the neutral charge state of the EL2 defect.

Detecting the Dynamic Aspect of the Jahn-Teller Coupling for the V<sup>3</sup> Defect in GaAs

Detecting the Dynamic Aspect of the Jahn-Teller Coupling for the V<sup>3</sup> Defect in GaAs

Jahn-Teller reduction factors and the spin-Hamiltonian parameters of4A2(Γ)8ground-state ions

The influence of linear Jahn-Teller coupling on the spin-Hamiltonian parameters of 4A2( Gamma )8 ground-state ions is studied. In particular, it is shown that the Jahn-Teller coupling can change the sign of the Bleaney-Koster-Statz parameters from that predicted by crystal-field theory. Vibronic states are constructed using symmetry-adapted vibrational states with up to three quanta excited. The Hamiltonian matrix using these states as bases is determined and the spin-Hamiltonian parameters and reduction factors found by numerical diagonalisation. Perturbation formulae are also presented for the reduction factors correct to fourth order in the vibronic coupling constants. As an example, it is shown that the theory can provide an explanation of the electron spin resonance spectrum of Re4+ in (NH4)2PtCl6 and an estimate of the vibronic coupling constants for this material is obtained.

Photophysics of atomic magnesium isolated in solid methane and perdeuteromethane. II. Temperature dependence of steady state and time-resolved luminescence

The visible emission resulting from photoexcitation of the first allowed singlet resonance transition of atomic magnesium isolated in the solid methanes is analyzed with spectral and time resolution. Two emission bands are observed in both solid methane (CH4) and solid perdeuteromethane (CD4) at 516 and 560 nm. The measured radiative lifetimes of the two bands are 12 and 19 ms, respectively, and independent of isotopic variation of the host. On the basis of their spectral position and radiative lifetimes, the emission features are assigned to the spin-forbidden 3P–1S intercombination band of atomic magnesium. Emission spectra recorded at various temperatures in the range 12–33 K were found to show reversible temperature dependence whereby the intensity of the higher energy 516 nm band decreased monotonically with a concomitant increase in that of the lower energy 560 nm band. Time-resolved measurements of the two bands in Mg/CH4 and Mg/CD4 show that the radiative lifetime of the 516 nm band decreases with increasing temperature while that of the 560 nm band remains constant but showing a rise time component. The magnitude of this rise time is correlated with that of the decreasing lifetime of the 516 nm band. With a combination of the temperature dependence observed in the radiative lifetimes and spectral intensities of the 516 and 560 nm emission bands in the Mg/CH4 and Mg/CD4 systems, dynamical information is extracted which allows for the creation of a simple kinetic model and an identification of the mechanism giving rise to this temperature dependent phenomenon. The experimental data is found to exhibit linear behavior on an Arrhenius plot indicating an activated process of population interconversion between the emitting levels. In solid methane the barrier in this activated process is 177 and 125 cm−1 in solid perdeuteromethane. The origin of this process is discussed in terms of (a) structural phase transitions of the solid methanes and (b) the effect of strong Jahn–Teller coupling between phonon modes of the solid methane host and the spin triplet electronic state of the atomic magnesium guest yielding symmetry-distinct minima on this surface. The lengthened values of the measured radiative lifetimes in the solid methanes, indicate population equilibration amongst the total degeneracy of the triplet state J sublevels of atomic magnesium in these solids. Because of the extremely low temperatures at which the experiment is conducted, extensive orbital reduction factors are implied to achieve such equilibration conditions. This is a manifestation of very strong Jahn–Teller coupling, a necessary condition for the stabilization of symmetry-distinct minima on the triplet spin state surface and the mechanism proposed to explain the presence of the temperature dependent emission features.

Interplay of Jahn–Teller and pseudo-Jahn–Teller vibronic dynamics in the benzene cation

The static and dynamic aspects of the vibronic interaction of the B̃ 2E2g and C̃ 2A2u electronic states of C6H+6 are analyzed. In the approximation of linear vibrational and vibronic coupling, the model Hamiltonian for this system comprises eight nonseparable vibrational modes, six of which are degenerate (two of A1g symmetry, four of E2g symmetry, and two of E2u symmetry). The coupling constants are estimated from existing ab initio SCF and semiempirical (CNDO/S) calculations. The topology of the adiabatic potential-energy surfaces of this class of model Hamiltonians is investigated. It is shown that the model exhibits a variety of conical intersections which dominate the vibronic dynamics. The dynamical problem is solved with simultanteous inclusion of six vibrational modes, four of which are degenerate (the Jahn–Teller coupling of two of the E2g modes is negligible). Hamiltonian matrices with dimensions up to 6×106 are diagonalized using the Lanczos algorithm. After some adjustments of coupling constants, the calculation reproduces well the complex structure of the overlapping B̃ 2E2g–C̃ 2A2u bands in the photoelectron spectrum of benzene. The vibronic structure of the lower-energy E2g band is dominated by a two-mode Jahn–Teller effect in the B̃ state. At higher energy, the marked diffuseness of the ‘‘C̃ 2A2u band’’ is shown to be a consequence of complete vibronic mixing with the lower-lying B̃ state. Based on the numerical solution of the full problem, the reliability of approximations (neglect of nonseparability of modes, introduction of a single effective pseudo-Jahn–Teller mode) is assessed. A time-dependent analysis reveals an ultrafast decay of the population of the C̃ state on a time scale of about 20 fs, followed by quasiperiodic recurrences which are damped on a time scale of a few hundred femtoseconds. These findings underline the importance of conical intersections and strong nonadiabatic effects also for larger molecules such as aromatic hydrocarbons. They demonstrate that nowadays a full quantum treatment is feasible also for these larger systems.

Jahn–Teller stabilization energies for ZnS:Mn and ZnSe:Mn excited states obtained by the angular overlap model

Linear Jahn–Teller coupling constants are obtained by the angular overlap model. A comparison with the data published recently [Parrot et al., J. Chem. Phys. 87, 1463 (1987)] is made in order to demonstrate the considerable improvement in the calculated Jahn–Teller coefficients when the parameters of the angular overlap model are extracted from a spectral analysis of the systems under consideration.

4f-electron-phonon interaction and collective 4f-excitations in PrF3

The results of Ramanspectroscopic and Fourier transform FIR spectroscopic investigations of PrF3 are presented. Some doubly degenerate optical phonons show magnetic-field dependent splitting and anomalous temperature dependent energy renormalisation. The excitations of the 4f-system can not be treated in the single-ion approximation because Davydow splittings and collective magnetic moments are observed. It is proved that all these effects result from a simple Jahn-Teller type coupling of the 4f- and the phonon system. The excitation energies of the coupled system are determined by a Greensfunction treatment of the problem.

Jahn-Teller effects in the near-infrared absorption spectrum of MgO:Fe2+

Near-infrared optical-absorption measurements on iron-doped MgO make possible a detailed study of the Jahn-Teller (JT) effect in the excited $^{5}\mathrm{E}_{\mathrm{g}}$ state of ${\mathrm{Fe}}^{2+}$. From a moment analysis of the broad doubly peaked absorption band corresponding to the $^{5}\mathrm{T}_{2\mathrm{g}}$\ensuremath{\rightarrow}${\mathrm{}}^{5}$${\mathrm{E}}_{\mathrm{g}}$ transition, and from the strength of the zero-phonon line (ZPL) at 1.5 K, we determine that the JT energy is ${E}_{\mathrm{JT}=1290}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, that the frequency of the effective JT mode is given by \ensuremath{\Elzxh}${\ensuremath{\omega}}_{E}$=280 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, and that totally symmetric (${A}_{1g}$) modes contribute very little to broadening the band. Uniaxial-stress measurements on the ZPL establish that the $^{5}\mathrm{E}_{\mathrm{g}}$ state exhibits a dynamic JT effect with a tunneling splitting 3\ensuremath{\Gamma}=12\ifmmode\pm\else\textpm\fi{}1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, a reduction-factor ratio \ensuremath{\Vert}r/q\ensuremath{\Vert}=1.15\ifmmode\pm\else\textpm\fi{}0.05, and strain-coupling coefficients ${\mathrm{qV}}_{2}$=+(22\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and ${V}_{1}$=-(23\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Polarized spectra taken under stress show that the ZPL is a magnetic dipole transition, that the tunneling state has symmetry $^{5}\mathrm{A}_{1\mathrm{g}}$, and that a second sharp peak in the low-temperature spectrum is due to a vibrationally induced electric dipole transition in which one quantum of an odd-parity mode is emitted. A comparison of these results is made with the predictions of single-mode and many-mode models of the JT coupling and also with interpretations of similar JT effects in the $^{1}\mathrm{E}$ ground state of the neutral vacancy (GR1 center) in diamond.

Electron spin echo spectroscopy of the photo-excited triplet state of pyridine

Magnetic resonance experiments on the elusive triplet state of pyridine as a guest in a single crystal of benzene have been performed with the help of pulsed laser excitation and Electron Spin Echo techniques. From a study of the 14N and 2D hyperfine interactions it is concluded that the molecule is non-planar owing to pseudo Jahn-Teller coupling between the 3B 1 (nπ*) and the close lying 3A 1(ππ*) states.

Dynamical Jahn-Teller coupling of Fe2+ in the cluster approach applied to the Mössbauer quadrupole data of 57Fe doped K2ZnF4 and Ba2ZnF6

We have analysed the Mossbauer quadrupole data of high-spin Fe 2+ located in the tetragonally distorted octahedra of K 2 ZnF 4 and Ba 2 ZnF 6 . The dynamical linear Jahn-Teller coupling between the orbital excited states E g , in D 4h symmetry, involves the vibrational modes A 1g , B 1g , B 2g of the cluster FeF 6 ; spin-orbit coupling is introduced, and a full mathematical treatment is performed in a basis of dimension 5 (orbit)×5 (spin)×10 (vibrations). This leads to a spectacular improvement of the calculated thermal variations of the quadrupole splitting in both systems, when compared to the results of the static crystal field model Analyse des donnees quadripolaires Mossbauer de Fe 2+ a haut spin dans les octaedres a distorsion quadratique de K 2 ZnF 4 et Ba 2 ZnF 6 , en introduisant le couplage Jahn-Teller dynamique lineaire entre les etats orbitaux excites E g , en symetrie D 4h , par les modes de vibration A 1g , B 1g , B 2g de l'agregat FeF 6 . Traitement mathematique rigoureux dans une base de dimension 5 (orbite)×5 (spin)×10 (vibrations), en tenant compte du couplage spin-orbite. Forte amelioration des courbes de variation thermique de la decomposition quadripolaire par rapport aux resultats anterieurs en champ cristallin statique

Energy transfer by exciton-polarons in RbMnF 3

Energy transfer in RbMnF 3 was studied by time-resolved spectroscopy of the 4T 1g-exciton luminescence. The threefold orbital degeneracy of the 4T 1g-state is lifted by a Jahn-Teller coupling to e g-modes. The JT-effect leaves an orientational degeneracy of distorted MnF 6-octahedra, which is lifted by application of uniaxial stress. The dynamics of exciton and trap luminescence after pulse excitation was investigated with and without stress. It was found that stress reduces the excitonic transfer rate considerably. The most striking effect was obtained with [110]-stress which produced a very slow nonexponential decay of the exciton luminescence. This behavior was interpreted as evidence for [110]-stress induced 2-dimensional energy transfer.

High-energy resonant structure in Jahn-Teller spectra

A study is made of the high-energy sharp features (Slonczewski resonances) found in Jahn-Teller optical absorption spectra. By solving Schrodinger's equation in the potential surface generated by diagonalising the static problem the author calculates the positions and the widths of the resonances. The resulting spectra are free from the limitations that constrain numerical calculations. He is able to investigate the limit of very strong Jahn-Teller coupling and to assess the effects of coupling to a continuum of modes. Factors that enhance resonance structure are identified. The investigation is confined to E(X) epsilon but the theory is applicable elsewhere. The application to experimental results is mentioned.

Angular overlap model for the Jahn–Teller coupling constants in the orbital triplet states of d5 ions: Case of Mn2+ in ZnS and ZnSe

A theoretical determination of the Jahn–Teller coupling constants of d5 ions in tetrahedral clusters is performed in the framework of the angular overlap model and the quasimolecular approximation. It is shown that the angular model correctly predicts the trend of the preponderant coupling of the 4T1(G) and 4T2(G) levels of Mn2+ in MnS4 and MnSe4 to the E-vibrational effective mode. Finally, the limitations of this model are discussed. In particular, it is shown that more elaborated covalent models are needed to interpret the Jahn–Teller coupling coefficients of the 4E and 4A1 levels of d5 configurations and to determine the influence of the crystal on the clusters.

Spin-orbit interactions and dynamical Jahn–Teller effect in the 4E states of Mn2+ in cubic and nearly cubic symmetry

A very detailed analysis of the fine structure of the 4E(G) state of Mn2+ in cubic and nearly cubic clusters is presented to account for the unusual fine structure observed in ZnSe:Mn. First, experimental results are reported which show that the spin-orbit interaction in the 4E(G) state of Mn2+ in ZnSe is about one half of that previously observed in cubic or nearly cubic clusters as MnS4, MnBr4, and MnCl4 and that the state Γ8 is neatly shifted with respect to the Kramers doublets Γ6 and Γ7. Second, a model is elaborated which shows that second-order spin-orbit interactions reduced by a Jahn–Teller coupling to E vibrational modes accounts well for the observed overall splitting of the 4E(G) state in the studied clusters and that fourth-order spin-orbit interactions correctly describe the shifts of the Γ8 state. The validity of the perturbation schemes is discussed and the results are compared to those obtained from a complete diagonalization in the d5 configuration.

The first excited states of platinum phthalocyanine in magnetic fields

A Zeeman study of platinum phthalocyanine in Shpol'skii matrices was performed in the temperature range of 25–77 K with magnetic fields up to ∼6·3 Tesla (T). The general phosphorescence region (950–945 nm) exhibited only one principal peak whose position is not affected by the field. An extremely weak structure that is energetically about 26 cm-1 lower than the principal peak and which originally was attributed to a different crystal site turned out to be a genuine field dependent collective response of weakly radiating spin-levels. The weakness of the radiation from these levels and the size of the subsequently confirmed zero field splitting D parameter are a unique case among all porphyrins and phthalocyanines studied to date in magnetic fields. For the first time the coefficients of the 5d (zx and yz) AO of PtPc in the egx LCAO MO were experimentally determined to be about 0·18. The Zeeman effect of the first π-π* absorption, in terms of phosphorescence excitation, was also investigated in approximately the same temperature and field range. An apparent angular momentum of Λ′ ≈ 3.6ħ was deduced from the Zeeman energy in the components of the 1 Eu state lifted by the crystal field. Λ′, in turn, gives rise to an orbital reduction factor q ≳ 0·9 which implies a fairly weak Jahn-Teller coupling, similar to but weaker than that found earlier in PdPc.

Calculation of reduction factors for the Γ8-(e+t) Jahn-Teller case with applications to acceptor defects in semiconductors

The reduction factors of the general one-mode Gamma 8-(e+t) Jahn-Teller (JT) case are calculated throughout the whole coupling range. For small JT coupling parameters the authors use standard matrix diagonalisation procedures combined with a group theoretical projection technique. The application of a unitary transformation method diagonalises the Hamiltonian exactly for infinite couplings. The resulting vibronic Glauber ground states are used for the reduction factor calculation at high coupling values. A combination with perturbational methods extends the validity of the approach to the whole range of coupling strengths. They apply the method to the case of acceptor defects in semiconductors within a one-mode approximation of the defect Hamiltonian. Results for the reduction of the acceptor deformation potential constants are given for the systems Si(In), Si(B) and GaAs(Mn).