“…Often one acoustical mode alone of symmetry H has been considered [117,119,120], but this implies a renounce to reproduce all observed ZPL's in the extended absorption range. It is also possible to try 2 W modes coupling to the electronic orbitals present in Fe 2+ [125,127,129]. Moreover, several authors have considered coupling to more than one phonon mode, in the range of the acoustical and optical phonon modes, and also mixing H and 2 W modes [121,127,129,131].…”
Section: +mentioning
confidence: 99%
“…It is also possible to try 2 W modes coupling to the electronic orbitals present in Fe 2+ [125,127,129]. Moreover, several authors have considered coupling to more than one phonon mode, in the range of the acoustical and optical phonon modes, and also mixing H and 2 W modes [121,127,129,131]. Even more, multimode distributions have also been considered for this problem [217].…”
This chapter is devoted to the study of the dynamic Jahn-Teller effect on the optical spectra of 3d-ions impurities in crystals, with particular attention to the theoretical efforts addressed to the interpretation of the experimental results. The presentation assumes that the reader is familiar with the spectroscopic notation for atomic energy levels. In addition, basic concepts and notation of point-group theory are also used. First, we will present a survey of the main experimental and theoretical results according to the electronic configuration. Then we discuss with a tutorial style the main contributions needed to model the optical spectra of the Jahn-Teller active 3d-ions impurities and asimple example is discussed in details. Next we concentrate on the calculation procedures required to address realistic systems. Some applicative examples of the proposed procedure are described in details.
“…Often one acoustical mode alone of symmetry H has been considered [117,119,120], but this implies a renounce to reproduce all observed ZPL's in the extended absorption range. It is also possible to try 2 W modes coupling to the electronic orbitals present in Fe 2+ [125,127,129]. Moreover, several authors have considered coupling to more than one phonon mode, in the range of the acoustical and optical phonon modes, and also mixing H and 2 W modes [121,127,129,131].…”
Section: +mentioning
confidence: 99%
“…It is also possible to try 2 W modes coupling to the electronic orbitals present in Fe 2+ [125,127,129]. Moreover, several authors have considered coupling to more than one phonon mode, in the range of the acoustical and optical phonon modes, and also mixing H and 2 W modes [121,127,129,131]. Even more, multimode distributions have also been considered for this problem [217].…”
This chapter is devoted to the study of the dynamic Jahn-Teller effect on the optical spectra of 3d-ions impurities in crystals, with particular attention to the theoretical efforts addressed to the interpretation of the experimental results. The presentation assumes that the reader is familiar with the spectroscopic notation for atomic energy levels. In addition, basic concepts and notation of point-group theory are also used. First, we will present a survey of the main experimental and theoretical results according to the electronic configuration. Then we discuss with a tutorial style the main contributions needed to model the optical spectra of the Jahn-Teller active 3d-ions impurities and asimple example is discussed in details. Next we concentrate on the calculation procedures required to address realistic systems. Some applicative examples of the proposed procedure are described in details.
“…The spin-orbit interaction further splits the tenfold-degenerate 5 Γ 3 multiplet into five levels of symmetries Γ 1 , Γ 4 , Γ 3 , Γ 5 , and Γ 2 , listed in order of increasing energy. The excited 5 Γ 5 multiplet separates [25] into levels of increasing energy Γ 5 ', Γ 4 ', Γ 3 ', Γ 5 '', Γ 4 '', and Γ 1 '. The zero-phonon line corresponds to a transition between the Γ 1 ground state and the Γ 5 ' excited state.…”
Section: Theoretical Formalismmentioning
confidence: 99%
“…Work on the effects of isotopic composition includes the discovery of the enhancement of the thermal conductivity of isotopically enriched Ge relative to that of natural Ge [3], the measurement of isotopic effects on the lattice parameter of Ge [4] and diamond [5] and the dependence of the frequency of the zone center F 2g (Γ 25 + ) optical mode on the inverse square-root of the mass observed in the Raman spectrum of monoisotopic Ge [6,7] and diamond [8]. More recently, the effects of the anharmonicity of the lattice vibrations and of the zero-point motion of the atoms have been observed and analyzed in natural and 13 C-enriched diamond [9,10].…”
A theoretical study of the isotopic-mass dependence of the internal transitions of Fe 2+ at a cation site in a cubic zinc-blende semiconductor is presented. The model used is based on crystal-field theory and includes the spinorbit interaction and a weak dynamic Jahn-Teller coupling between the 5 Γ 5 excited manifold of Fe 2+ and a local vibrational mode (LVM) of Γ 5 symmetry. The mass dependence of the LVM frequency is described, in the harmonic approximation, within two different limits: the rigid-cage model and a molecular model. In the rigidcage model, the Fe 2+ ion undergoes a displacement but the rest of the lattice is fixed. In this case, a simple M -1l2 dependence of the frequency is obtained and the Jahn-Teller energy, E JT is independent of the mass. In the molecular model, the four nearest neighbors of the magnetic ion are allowed to move and the LVM then behaves as the Γ 5 mode of a MX 4 tetrahedral molecule leading to a more complicated dependence of the frequency on the isotopic mass and to a mass-dependence of E JT . The theoretical results obtained with these two models are compared with the observed isotopic shifts of the zero-phonon lines in InP:Fe and GaP:Fe corresponding to an optical transition between the vibronic Γ 1 ground state and the lowest Γ 5 state originating from the 5 Γ 5 excited orbital multiplet. A prediction of the isotopic shifts of the zero-phonon line in GaAs:Fe is also presented.
“…20,21 In Refs. 20 and 21, we had found that the near-and far-infrared spectra could be explained well by considering a strong JT interaction between the 5 ⌫ 5 orbital multiplet of Fe 2ϩ and a TA phonon of average energy corresponding to the various TA modes and a weak coupling of the 5 ⌫ 3 orbital ground state with a ⌫ 3 TA͑L͒ phonon.…”
Optical absorption and emission measurements of Cu 2ϩ as a substitutional impurity in cubic ZnS and ZnTe are analyzed by means of an electron-phonon coupling model. The 2 D term of Cu 2ϩ is split by a crystal field of tetrahedral symmetry into a 2 ⌫ 5 orbital triplet and a 2 ⌫ 3 orbital doublet. Optical transitions have been observed between these two multiplets in ZnS:Cu 2ϩ and within the 2 ⌫ 5 ground state in ZnTe:Cu 2ϩ . The theoretical model is based on crystal-field theory and includes the spin-orbit interaction and a dynamic Jahn-Teller interaction between the electronic 2 ⌫ 5 states and a transverse acoustic phonon of ⌫ 5 symmetry. Starting from the ten spin-orbit wave functions appropriate to the orbital triplet and doublet manifolds, the symmetryadapted vibronic basis is constructed and used to diagonalize the Hamiltonian matrix. Phonon overtones up to nϭ14 are included to ensure convergence of the energy eigenvalues. The measured positions and relative intensities of the spectral lines are described with good accuracy by the theoretical model, including covalency effects. In ZnS, comparison between theory and experiment yields the following values of the physical parameters: the crystal-field splitting ⌬ϭ5990.6 cm Ϫ1 , the spin-orbit coupling constants 1 ϭϪ667 cm Ϫ1 and 2 ϭϪ830 cm Ϫ1 , the phonon energy បϭ73.5 cm Ϫ1 , and the Jahn-Teller stabilization energy E JT ϭ474.5 cm Ϫ1 . The corresponding parameters in ZnTe are ⌬ϭ6000 cm Ϫ1 , 1 ϭϪ888 cm Ϫ1 , 2 ϭϪ830 cm Ϫ1 , បϭ38.8 cm Ϫ1 , and E JT ϭ468.5 cm Ϫ1 .
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