G E Stedman

Phonon Raman spectroscopy in systems with electronic degeneracy

The theory of the vibrational or phonon Raman spectrum of molecules or solids in the nonresonant regime is formulated for systems with electronic degeneracy. A selection rule is established, extending that of Child (1963), previous disagreement on this selection rule is reviewed. Symmetric and antisymmetric parts of the scattering amplitude are proved to combine incoherently, as observed by Kiel and co-workers (1969). Tables of Raman scattering contributions in nondegenerate systems for oriented scatterers by Loudon (1964) and for orientationally averaged scatterers by McClain (1971) are generalised to systems with electronic degeneracy. This should greatly facilitate the assignment of spectral lines in systems with Jahn-Teller or Kramers degenerate ground states, and constitutes the first step in determining a strategy for the economical extraction of the information available through Raman spectroscopy. An alternative recoupling is considered following work in quantum beat spectroscopy. This will prove advantageous when only linear polarisation is used, or when particular intermediate state symmetries are important.

Symmetry restrictions for natural and induced circular dichroism and optical activity for all point groups

Group theoretical techniques are used to analyse the geometrical dependence of natural circular dichroism (CD) and circular dichroism induced by a linear interaction with either a magnetic (MCD) or electric field (ECD). For each of these effects the dependence of the spectra on the relative orientations of the crystal, radiation, and the external field, is given for each point group. At arbitrary orientations the spectrum is a linear superposition of a definite number of irreducible spectra. For example, MCD has axial symmetry in the groups Dn, Dnb, Cnv(n not=2), D2d, D3d while ECD is always forbidden in cubic symmetry, and also for non-cyclic groups if the field and radiation are parallel. The results apply equally to the analogous transmission effects, i.e. natural optical activity, electro-optical activity and the magnetic-field-induced Faraday effect.

Irreducible analysis of Raman spectra for all crystal point groups

Techniques for the optimal and maximal extraction of information by Raman scattering experiments are investigated. All optical interactions are assumed to be electric dipole. For each crystal point group symmetry, a minimal set of choices of experimental arrangement (i.e. choice of polarisation vectors for incoming and outgoing light beams, scattering geometry etc.) is given, together with the transformations necessary to determine the irreducible parts of the spectrum in each of several bases. The more detailed tables are presented as a supplementary publication, SUP 70031. While valid for all crystal point groups, they are restricted to the case of time-reversal-invariant scattering interactions, and also to symmetric scatterers. The latter restriction includes systems which may have an antisymmetric part to the scattering amplitude, but in which the scattering intensity is unchanged by interchanging the incoming and outgoing polarisation vectors. Circular polarisation studies are necessary for a complete analysis of any system. However, the conventional 90 degrees and 180 degrees scattering geometries are adequate. Related symmetries of the Mueller matrix of the scatterer are also analysed.

A quantum field theoretic formulation of Raman spectral line shapes

The Raman spectrum of a solid is formulated using quantum field theory. The photons are assumed to couple via localised electronic states, e.g. paramagnetic impurities. The laser is assumed to be of low power and to have a frequency well away from any electronic resonance. It is shown that the phonon-induced shift and width of each of the lines corresponding to an electronic transition, a first-order phonon line, and a vibronic transition is formally the same whether the transition is studied by absorption or by Raman spectroscopy. Width and shift contributions are given to second order in broadening interactions for the second-order phonon Raman spectrum. These results exhibit complications in some attempts to compare broadening parameters in different experiments. Some consequential adjustments to formulations of the spectrum of resonance fluorescence are suggested.

Partial particle-hole conjugation symmetry in thermopower calculations

The authors discuss the role of partial particle-hole symmetry in calculations of thermopower. The authors resolve the apparent conflict between the work of Krempasky and Schmid and Vilenkin and Taylor regarding the potential cancellation of the Hasegawa terms (which arise from phonon renormalisation of the scattering vertex) in terms of whether or not particle-hole symmetry is assumed. For real crystals, diagrams of even order such as those representing the Hasegawa terms cannot be ignored.

A quantum field theoretic approach to the calculation of reduction factors in Jahn-Teller systems. I. General theory

Ham reduction factors are defined in the context of a field theoretic formalism and are thus generalised to cover arbitrary choices of electronic states, linear and nonlinear ion-lattice couplings, anharmonic lattice interactions, the mixing of electronic levels, second- and higher-order reduction factors and notably the effect of temperature in populating a distribution of vibronic states. Symmetry considerations are integrated with the field theoretic formalism in diagram form. Calculational techniques are described in some detail. Comparison is made with a similar generalisation of the standard definition of the reduction factor, which however implies the choice of particular vibronic states and does not include the effects of finite temperature. Symmetry considerations allow the first-order reduction factor to be written as a sum of products of 6j symbols (of the relevant symmetry group) and physical parameters. This in turn prescribes the form of sum rules linking the reduction factors in some approximation. The most important sum rules are exact at second order if the ion-lattice interaction contains only time-even operators. As a concrete illustration of the results, a simple tetragonal example is analysed in some detail.

Superexchange between one-particle states

In a system of sufficiently high symmetry and with one electron or hole per ion, there are strong restrictions on the contributions of any pair-splitting mechanism to the pair Hamiltonian. For example, the dominant interaction between Ir4+ nearest-neighbour pairs in the hexachloroplatinates is isotropic (in effective spin) and is thus attributable to kinetic exchange. For Ce3+ nearest-neighbour pairs in lanthanide halides, the non-dipolar exchange is of Ising type and is tentatively attributed to the effects of non-orthogonality on interionic matrix elements of the one-particle Hamiltonian. For Tm2+ pairs in the alkaline-earth fluorides, the exchange parameters indicate that both kinetic and potential exchange contribute and that potential exchange is poorly described by the Mulliken approximation.

Internal strain effects and the reduction of the number of ion-lattice interaction parameters

The reduction in the number of ion-lattice interaction parameters, considered by several authors in the context of a uniform strain assumption, is generalised to systems under bulk stress or with long-wavelength acoustic phonon coupling, where the distortion is not necessarily one of uniform local strain. Many earlier simplifications are still valid, since the point group irreps appropriate to the symmetry coordinates affected are just those activated by a uniform strain field. The consequences of this for the dynamic crystal field and for the choice of a minimal set of coupling parameters are discussed, with particuLar reference to laCl, LaF3, and Cr2O3. Useful reductions are achieved when the number of ions in the coordination complex is equal to or greater than the number in the unit cell.

Effect of the electron-phonon interaction on vibronic peaks and on phonon lines in the absorption spectrum

Contributions to the shift, width and vibronic splitting of a line in the vibronic sideband of an electronic transition are given to fourth order in electron-phonon coupling, including anharmonic and nonlinear interactions. The leading contributions represent the width and shift of the basic no-phonon line, including the non-additive elastic scattering contribution, together with the anharmonic width and shift of the phonon associated with the transition. Further contributions are found corresponding to interaction between the electronic and lattice states associated with the transition. These contributions essentially have a double effect on the observed width; they are important in the treatment of vibronic splitting. It is shown that the shape of an infrared phonon absorption line depends on whether the coupling with the photon proceeds directly or is mediated by the electronic system; in the latter case the spectrum is broadened by electronic interaction.

Ion-lattice coupling, spectral moments and transition interference in Fe2+:MgO

The authors determine the magnitude of phonon-induced transition interference in the ESR and far-infrared spectra of Fe2+:MgO. The ion-lattice coupling constants are predicted for Fe2+:MgO using the ligand superposition model. An improved formulation of the theory of spectral moments is included. The broadening component associated with phonon-induced transition interference has a sign dependent on the mechanism for the optical coupling (E2 or M1), a temperature dependence identical to that of the conventional contributions, and a magnitude typically of 20% of the corresponding conventional contributions.