Table of contents

Doubts concerning the conventionally assumed centrosymmetry of the cubic crystal structure of spinel ferrites, including magnetite, have existed for many years, chiefly because dielectric constants as high as 10³-10⁴ have been observed at low frequencies. The authors show that evidence neglected in a published X-ray diffraction study of magnetite favors a non-centrosymmetrical structure. They also report new measurements of X-ray diffraction intensity which reveal that, contrary to the behaviour expected of a centrosymmetrical structure. Friedel's law is violated by magnetite when anomalous scattering is present.

The authors study a one-electron tight-binding Hamiltonian with topological disorder using the novel concept of 'quantum connectivity'. The off-diagonal matrix elements are taken to be of the form J_(ij)=-V₀e^-r(ij)a(B)/, and J_(ij)=-V₀(1+^-4(ij)a(B)/) e^-r(ij)a(B)/, where r_ij is the distance between the sites i and j, and the diagonal elements are all zero. In three dimensions the dimensionless parameter R=n¹3/a_B, where n is the concentration of sites, characterises the disorder. They find that an Anderson transition takes place at R_c=0.257+or-0.010 and R_c=0.220+or-0.026 for the two models respectively. They also calculate the correlation length exponents in each case, finding v=1.95+or-0.13 and v=1.63+or-0.17 respectively. In two dimensions they do not observe an Anderson transition.

It is shown that covalency provides a negative contribution to the Delta A/sub /k parameters describing the relativistic crystal field (RCF). Estimates of the magnitude of this contribution have been made for Gd³⁺. The results show a reduction in the RCF contributions to the ground S-state splitting of Gd³⁺.

A new approach, called the embedded-molecular-cluster method, is proposed to calculate the electronic structure of point defects in a non-metallic crystal in the framework of the molecular cluster model. The method is applicable to defects with any perturbation radius of the crystal and is based on the concept of the latter as the sum of weakly overlapping structural elements, (atoms, ions, bonds, molecules, etc.). It accounts for Coulomb and exchange interaction between the cluster and the rest of the crystal, as well as (self-consistently) for polarisation of the latter. The present work contains a calculation of the full energy of a crystal with a point defect and arbitrary types of structural elements.

For pt.I see ibid., vol.21, p.5041 (1988). The embedded-molecular-cluster method, as proposed in the authors previous paper for the calculation of the electronic structure of point defects in non-metallic crystals, has been applied in the present work for the case of crystals containing structural elements in the shape of rigid molecules, molecular ions, etc. Using the Green function of perfect-crystal lattice dynamics, equations have been obtained describing polarisation of the remainder of the crystal. The operator V^eff, which accounts for exchange and Coulomb interaction between the cluster and the rest of the crystal, including its polarisation, and is an addition to the Hartree-Fock operator, has been evaluated. Both problems (calculation of polarisation of the rest of the crystal and the solution of the effective Schrodinger equation for the cluster) have to be solved in a self-consistent way. Parameterisation effected for the method has made it possible to express explicitly both the operator V^eff and the response function necessary for evaluating polarisation. A detailed investigation of the lattice dynamics of an ideal crystal allowed the author to connect the parameters of the method with the dynamic matrix of an ideal crystal, i.e. eventually with its phonon spectra and eigenvectors, which can be found experimentally.

A general formulation is introduced to treat the influence of the displacements of some atomic centres on X-ray absorption in the single-scattering curved-wave formalism. This formulation is particularly suited to the study of small shifts, but it can also be used to consider finite displacements. As an application, they investigate the influence of thermal motion and structural disorder on the curved-wave extended X-ray absorption fine structure, thus generalising the Debye-Waller and asymmetry factors.

Dispersion of eigenfrequencies and eigenvectors of lattice vibrations in Ge along the (110) direction is calculated from planar force constants, which are evaluated ab initio using the local density-functional theory and the pseudopotential scheme. The particularity of these vibrations is in the harmonic coupling between the longitudinal and transverse modes which is not predicted by group theory, even in high-symmetry crystals such as Ge. The formalism of lattice dynamics is systematically built in terms of the vibrating (110) planar sublattices-the form suitable for the ab initio determination of force constants-and it is shown how the coupled modes are to be treated in the planar representation. Particular attention is paid to anharmonicity of the vibrations, which the first-principles calculations provide as well. The results are used for comparison with predictions offered by different phenomenological models (i.e. shell model and bond-charge model) and for judging the physical realism of the latter.

Some static and dynamic properties of cooperative Jahn-Teller systems accompanied by a discontinuous structural phase transition are studied on the basis of a coupled pseudo-spin-phonon model with a third-order anharmonic term. The form of the anharmonicity is chosen so as to give a qualitative description for the structural phase transition of CsCuCl₃ on the assumption that the local modes associated with the Jahn-Teller effect propagate along the c axis of the crystal as a one-dimensional phonon. Molecular-field theory gives a set of coupled equations for the order parameters which have a solution with a discontinuous change at the transition point. Frequencies of collective modes are calculated in the random-phase approximation and are shown to be modulated by the anharmonicity. The coupling coefficient of the Dzyaloshinsky-Moriya (DM) interaction is explained to be in proportion to the order parameter on the basis of Moriya's theory. The temperature dependence below the transition temperature T_c and the discontinuous change at T_c of the electron spin resonance (ESR) linewidth are derived when the DM interaction has the dominant contribution to the ESR spectrum.

The functional integral formulation of the Hubbard model (1986) proposed by Kotliar and Ruckenstein (which, at the mean-field level, reproduces the results of the Gutzwiller approach) is used to calculate the one-loop correction to the free energy. The T³ in T correction to the specific heat in the Fermi liquid regime is obtained for the half-filled case and is related to the Landau amplitudes A₀^a, A₀^s that appear at the mean-field level. After parametrising the interaction strength with pressure so as to reproduce the observed effective mass of liquid ³He in the manner of Vollhardt (1984), the calculated variation of the T³ in T term with pressure is found to be in excellent agreement with the experimental results of Greywall (1983).

An ion moving with supercritical velocity in superfluid ³He emits beams of quasi-particle excitations. The beams are, as a consequence of triplet pairing, spin polarised and show a particle-hole branch imbalance. Hence supercritical ions are potential generators of polarised excitations for scattering experiments with quasi-particle beams. The energy and angular dependences of the spin polarisation and the particle-hole imbalance are calculated. Furthermore the question of whether the critical velocity is lowered by bound states at the ion is investigated.

Employing selective monochromatic laser excitation, the photoluminescence in ZnSe_1-xTe/sub /x alloys with Te concentrations 1%<or=x<or=2.3% is investigated. The structured emission band is interpreted as being due to recombination of excitons localised at different types of small Te clusters. The energy spectrum of these excitons is inhomogeneously broadened. The details of exciton-lattice interaction revealed under resonant excitation of these exciton states strongly favour the model of large-radii excitons tightly bound through the hole. For excitation above the exciton gap, resonant Raman scattering by longitudinal optical (LO) phonons is observed. The measured degree of polarisation is used to discriminate between this process and the narrow-line LO resonance luminescence found under selective excitation of the localised states. The smooth transformation from Raman scattering to resonance fluorescence indicates that, owing to strong interaction between the cluster and band states, no energy gap exists between the free and localised exciton states.

The effect of compensation in doped semiconductors is studied. Results are obtained for the whole range of concentrations although the calculations are only completely justified in the region of intermediate and large concentrations. The impurity band is described by the Hubbard Hamiltonian. The electronic interaction related to different ions is calculated using the Hartree-Fock approximation. The potentials of the ionised and neutral impurities are screened differently. The diagonal terms of the Hamiltonian are considered to be random variables following a Gaussian distribution. The off-diagonal disorder is treated in the Matsubara and Toyosawa approximation (1961). The density of states and the Fermi energy are obtained for different values of the compensations and concentrations. The results for the Fermi energy coincide with theoretical models and numerical simulations developed by Efros et al. (1972, 1979), valid for low concentrations and the whole range of compensations, within the context of the classical impurity band.

Adiabatic and radiative effects accompanying interactions of a kink with a point-like impurity are studied by means of the perturbation theory within the framework of a model of a damped DC-driven charge-density-wave system based on a perturbed sine-Gordon equation. A threshold (maximum) value of the DC voltage (external drive applied to the system) admitting capture of a kink (charged soliton) by an impurity is found. The maximum voltage allowing the existence of pinned states of the kink is also found, and the corresponding dependence of the density of released kinks on the voltage is evaluated, provided that the coordinate of an individual impurity relative to an underlying lattice is a uniformly distributed random quantity. It is demonstrated that this dependence gives rise to an additional peculiar branch of the current-voltage characteristic (CVC) of the system. The energy emitted by a moving kink during its collision with the impurity is calculated. It is shown that, provided that the level of direct dissipative losses is sufficiently low, the radiative losses render the CVC hysteretic.

The photoconductivity spectra and the carrier drift mobilities of MnO single crystals are measured at various temperatures from 83 to 299 K in the spectral region from 300 to 650 nm by the synchronous detection and transit time methods. The photoconductivity spectra show the photoconductivities associated with the intrinsic inter-band excitations and with the crystal-field adsorptions of Mn²⁺ ions. The photocarriers are both electrons and holes with high drift mobilities. The results are discussed in terms of recent theories describing the band gaps and the electronic structures of the 3d transition-metal compounds.

TbPO₄ shows two successive magnetic phase transitions, the lower of which is connected with a Jahn-Teller induced reduction of crystal symmetry. In both phases, the magneto-electric (ME) effect (which is larger that in other known ionic crystals) was measured to determine the temperature and magnetic-field dependence of the elements of the ME susceptibility tensor. Calculations in mean-field theory taking into account exchange, dipole and Jahn-Teller interactions, a static external field and ME coupling yield quite satisfactory agreement with the measured temperature variation of the elements. Considerable differences exist in the field dependence indicating the deficiency of the theoretical model.

For pt.I see ibid., vol.21, p.2749 (1988). Very careful studies of infrared spectra of crystals of magnesium, zinc and iron fluoride are reported. Using several models and methods, the authors discussed the experimental infrared spectra temperatures from 10 to 300 K in a previous paper. Using a full shell model with both ions polarisable, the optical frequencies and elastic constants are calculated and compared with existing data. Dielectric properties such as effective charges, ionic polarisabilities, dielectric constants and infrared mode strengths are determined. These models are applied to the study of the behavior of B_1g, A_2u and E_u modes, and C₄₄ and C_s elastic constants with temperature in ZnF_. They show that, above 100 K, this behaviour can be explained by the change of some short-range force constants, while, below 100 K, it is necessary to take into account the increase of the effective charge Z_F. Lastly the authors have calculated the contribution of the second-order processes to the infrared spectra. Comparison with experimental data allows a precise interpretation to be made of supplementary IR bands. These results explain the difficulties encountered in trying to represent the IR data by a classical oscillator model particularly for the E_u spectrum in ZnF₂ and FeF₂.