Effective Hamiltonian approach to doubly degenerate electronic states

Several problems in vibronic spectroscopy are solved within the effective Hamiltonian formalism combined with Lie algebraic methods. We consider mainly vibronic interactions in orbital doublets for molecules with a principal symmetry axis of order n=4k (or n even for Dnd symmetry groups). Effective Hamiltonian models for E ⊗(b1+b2), E ⊗ (bi+aj) and E ⊗(bi+ e) Jahn-Teller dynamical systems are discussed as well as some correlations with previous studies established.     

Effective Hamiltonian approach to doubly degenerate electronic states

Effective vibronic Hamiltonian models are built for E ⊗e Jahn-Teller systems and analytical solutions are obtained through Lie algebraic methods. Although approximate, we show that these models allow in particular to recover the possible ground state crossover when quadratic couplings are present. The equivalence of E ⊗e and G' ⊗e vibronic systems in cubic symmetry is precisely established through a particular realization of the electronic operators for an orbital quadruplet. We show how this equivalence is broken by a rovibronic interaction which, for a G' ⊗e system, still gives an exactly solvable model.     

Magnetic-field dependent phonon states in paramagnetic CeF3

Raman scattering experiments in paramagnetic uniaxial CeF₃ at helium temperature demonstrate a splitting of some degenerate (E_g)-phonon states in an external magnetic field parallel to the crystal axis. A linear splitting is observed in low fields, followed by a field independent (saturation) splitting in high fields. In addition, changes in the Raman scattering efficiencies and a reduction of the line width of phonon transitions are observed with increasing magnetic fields. No such effects are observed for magnetic fields perpendicular to the crystal axis. The splittings of degenerate phonon modes are related to the paramagnetic saturation 〈S_z〉.     

Magnetic transitions in strong coupling expansions for nearly degenerate states

A strong coupling expansion for a two‐band Hubbard model on two sites with nearly degenerate states is considered. A comparative analysis is performed for different schemes of perturbation theory which are applicable to systems with nearly degenerate states. A fourth order approach which builds on a four‐dimensional low‐energy subspace with nearly degenerate states captures accurately the transition from an antiferromagnetic to a ferromagnetic ground state at large on‐site Coulomb interaction.     

Tensile-strain induced phonon splitting in diamond

The first-order Raman spectroscopy of diamond exhibits splitting and redshift after the burst of high-pressure(160–200 GPa) and high-temperature(～2000 K). The observed longitudinal optical(LO) and the transverse optical(TO) splitting of Raman phonon is related to the tensile-strain induced activation of the forbidden or silent Raman modes that arise in the proximity of the Brillouin zone center.     

Universal exchange-driven phonon splitting in antiferromagnets

We report a linear dependence of the phonon splitting Δω on the nondominant exchange coupling constant J(nd) in the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, NiO, and in the frustrated antiferromagnetic oxide spinels CdCr(2)O(4), MgCr(2)O(4), and ZnCr(2)O(4). It directly confirms the theoretical prediction of an exchange-induced splitting of the zone-center optical phonon for the monoxides and explains the magnitude and the change of sign of the phonon splitting on changing the sign of the nondominant exchange also in the frustrated oxide spinels. The experimentally found linear relation [symbol:see text}Δω=βJ(nd)S(2) with slope β=3.7 describes the splitting for both systems and agrees with the observations in the antiferromagnets KCoF(3) and KNiF(3) with perovskite structure and negligible next-nearest neighbor coupling. The common behavior found for very different classes of cubic antiferromagnets suggests a universal dependence of the exchange-induced phonon splitting at the antiferromagnetic transition on the nondominant exchange coupling.     

Magnetic splitting of valence states in ferromagnetic and antiferromagnetic lanthanide metals

The magnetic splitting of Delta(2) valence states in the heavy lanthanide metals Gd, Tb, Dy, and Ho was studied in epitaxial films by angle-resolved photoemission, revealing an essentially Stoner-like temperature dependence in all cases. It scales linearly with the 4f spin moment, even in the case of the helical antiferromagnet Ho. Such a behavior can be explained by a substantial localization of the corresponding wave function in the c direction. The helical magnetic structure was confirmed for the thin Ho films by in situ resonant magnetic x-ray diffraction.     

Phase grating in a doubly degenerate four-level system

In this paper, we suggest a doubly degenerate four-level system, in which the transition takes place between the hyperfine energy 52S1/2 F = 1 and 52P3/2 F = 2 in rubidium 87 D2 line, for studying atomic phase grating based on the cross-Kerr and phase conjugation effects. The phase grating with high efficiency can be obtained by tuning phase shift Ф between the coupling and probe field, when the coupling intensity is much stronger than the strength of probe field. Under different coupling intensities, a high diffraction efficiency can be maintained. A new and simple way of implementing phase grating is presented. However, in such an atomic system, two main limitations must be taken into account. First, the independence between steady state probe susceptibility and the coupling intensity, when the population decay rate is larger than the Rabi frequency of the coupling field, cannot result in diffraction grating; second, the sample to be prepared should not be too long.     

Long-range orders in the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation corrected by Lacroix-Lyon-Caen and Cyrot. The static susceptibility method is used. In the strong scattering limit, a ferromagnetic instability for 1 < N < 2 and 2 < N < 3 is confirmed. It is proved that there is no antiferromagnetic or charge-order instability for any N.     

Temperature dependent splitting of the 59Co hyperfine field in GdCo2

We have studied the temperature dependence of the ⁵⁹Co NMR in the magnetically ordered state in GdCo₂ between 1.3 K and 335 K. A clearly resolved splitting in the ⁵⁹Co spectrum is observed to occur at 200 K. This splitting is interpreted as due to a change in easy axis from [100] to a detection which is not a major symmetry axis. Furthermore, a sharp change in the intensity ratio of the two clearly resolved lines in the spectrum occurs at about 300 K.     

Alloy analogy of the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation. In the strong coupling limit, a ferromagnetic instability occurs when 1 < N < 2 and 2 < N < 3. We compare this approximation with other approximations and with the exact results.     

Studies of the doubly degenerate product Jahn-Teller system

The static product Jahn-Teller (JT) system with two doubly-degenerate electronic open shells coupling to a single e-mode is further studied in the electronic space using the isostationary function method and the energy minimization procedure. These effects are vividly described by the coupling of two electronic vectors that belong to two different E-spaces. The energy levels in the trough positions are also investigated and it is found that the two doubly degenerate electronic levels are generally lifted by the product JT coupling.      

Magnetic field effects on the phonon thermal electromotive force in n-Bi-Sb semiconducting alloys

The phonon thermal electromotive force component α₂₂ (?T ‖ C ₁) prevails in n-Bi_{1 ? x} Sb_x (0.07≤x≤0.16) semiconducting alloys at low temperatures. This component increases by almost an order of magnitude in a classically strong transverse magnetic field H with H ‖ C ₃, which results in an increase in thermoelectric efficiency. The transverse Nernst-Ettingshausen coefficient Q _{12, 3} (?T ‖ C ₁, H ‖ C ₃) changes sign from negative at T > 10 K to positive at T < 10 K. The observed characteristics of the phonon thermal electromotive force and the phonon transverse Nernst-Ettingshausen coefficient are explained in terms of the theory of electron-phonon drag for electrons with a strongly anisotropic spectrum.     

Magnetic field dependent dielectric function for zero-gap semiconductors

Using the random phase approximation and the Yafet wave functions the inter and intraband static dielectric functions of degenerate zero-gap semiconductors placed in a magnetic field are calculated in the long wavelength limit. It is shown that the values of the dielectric function for gapless semiconductors differ considerably from the result obtained previously for the one-band model with parabolic energy dispersion ands-type wave functions. Finally the dielectric function is used to find the static screening of a point impurity charge.     

Density of phonon states in nanostructured copper

Neutron spectroscopy analysis has been used to study the vibrational states in samples of coarse-grained and nanostructured copper. It has been revealed that the phonon spectrum for the nanostructured copper is characterized by a decrease in the local densities of states corresponding to the longitudinal (∼28 meV) and transverse (∼19 meV) vibrational modes. The total contribution to the molar heat capacity of the oscillators having the dispersion laws of coarse-grained copper decreases by about 18%. The experimentally observed increase in the energy (heat capacity) of the crystal in the nanostructured state is attributed to the spectrum transformation in the form of the transfer of the energy from the high-frequency phonons to the long-wavelength region, where the new acoustic branches of oscillations along the grain boundaries (the “second” ion sound effect) are developed. This means that the features of the scattering spectra of the slow neutrons in the samples are determined by the presence of two types of the scatterers.