Table of contents

A simple approximate approach to the full recursion method of V. Heine and co-workers (1980) for calculating the local density of states in a tight-binding framework is presented. When used to calculate the force on an atom in a distorted lattice, the approach reduces the computation time by two orders of magnitude. The deviations from the full force calculation are typically small (10-20%).

The relativistic corrections (RC) (spin-orbit, Darwin and mass-velocity) are calculated to the p-d gaps of 1T TiSe₂, TiS₂, ZrSe₂ and ZrS₂ using the self-consistent non-muffin-tin OPW band-structure results. RC are found to enlarge the p-d gaps. The corrected p-d gap of 1T TiSe₂ is estimated to be small and positive. RC to the p-d gap of the semiconductor ZrSe₂ improve agreement with the experimental gap. RC are found to be of secondary importance to the p-d gaps of the semiconductors TiS₂ and ZrS₂.

The equilibrium bulk properties of diamond-type semiconductors Si, Ge and alpha -Sn are calculated following recent work on electronic structure and total energy by the self-consistent local pseudopotential method. The calculated equilibrium lattice constants and bulk moduli are presented and compared with experiment.

It is shown that the range of realistic potentials associated with neutral defects in semiconductors is insufficient to give rise to an effective mass-like excited state normally expected for a number of shallow and deep substitutional donors. In particular, it is shown that the state of e symmetry associated with the self-consistent potential of a neutral oxygen impurity in the perfect lattice of GaP does not lie in the forbidden gap.

The effective medium theory is an excellent theory for the effective conductivity of random media, but when the theory is applied to percolation problems the result shows a somewhat unrealistic behaviour, because the effective conductivity by the theory increases exactly linearly from the percolation threshold against the volume fraction of the conductive component. To remove the defect for the theory a simple method to improve the effective medium theory is proposed. The effective conductivity by the improved method increases less than linearly from the percolation threshold and agrees well with the result by computer simulation, both for three and for two dimensions.

Two-dimensional magnetoplasmons in electron inversion layers of Si(100) have been investigated using MOS capacitors with submicron structured periodical gates. The amplitude and position of the magnetoplasmon resonance follows only in general the classical plasmon dispersion. At fields B_c/n(n=2,3,...) where the plasmon frequency is a multiple of the cyclotron frequency there are pronounced changes of the position and strong modifications of the amplitude of the plasmon resonance. The plasmon linewidth is not affected significantly by magnetic fields up to 12 T.

The exact phase diagram of the nearest-neighbour q-state Potts ferromagnet in the fully anisotropic 3-12 lattice is conjectured through a star-triangle transformation. It recovers all the available exact results concerning particular cases, namely: (i) anisotropic square lattice for all q; (ii) anisotropic triangular and honeycomb lattices for all q; (iii) anisotropic Kagome and diced lattices for q=2; (iv) isotropic 3-12 and Asanoha lattices for q=2. It provides proposals for several other planar lattices, in particular for the anisotropic Kagome (and diced) one for q not=2, where it differs slightly from the Wu(1979) conjecture (which also satisfies cases (i) and (iii)). The bond percolation critical probabilities on the 3-12 and Kagome lattices are determined to be respectively p_c=0.739830 ... and p_c=0.522372.

The eigenvalues and eigenvectors of the inverse of the susceptibility matrix are discussed for random spin systems. At a phase transition precipitated by the vanishing of the smallest eigenvalue it is shown that the corresponding eigenvector must be extended, and that the density of states must vanish at zero eigenvalue. Above the transition temperature, generalised Griffiths singularities are associated with the existence of localised states with arbitrarily small eigenvalues. For infinite spin dimensionality the eigenvalue problem is equivalent to an Anderson problem with correlated diagonal and off-diagonal disorder.

The authors show that the Ashkin-Teller model has Ising critical exponents, in the region where the model has two phase transitions. The proof follows from mapping the ground state of the time-continuous Ashkin-Teller Hamiltonian onto that of the Ising chain in a transverse field.

The discontinuous (first-order) transition behaviour of compressible Ising systems described by Hamiltonians of the form H=-J_s Sigma _(ij)S_iS_j-J₄ Sigma _(ij) Sigma _(kl)S_iS_jS_kS_l has been studied for the first time using Monte Carlo techniques for lattices of sizes 100² and 20³. The results have been compared with those obtained using the renormalisation group technique.

The thermodynamics (field-cooled) magnetisation of a vector spin glass is determined within a Parisi-like scheme for small fields near the spin glass transition. Only for reduced temperatures tau <or approximately=-h²3/, substantially lower than the spin glass ordering temperature tau approximately -h², is the profile flat, in broad agreement with experiment and the Parisi-Toulouse hypothesis (1981).

Satellite absorption bands near the 630 nm exciton-magnon combination bands in crystals of the ionic ferromagnet Rb₂CrCl₄ doped with 1.8% and 3.8% Mn²⁺ are identified as electronic excitations of Cr²⁺ coupled to spin flips on isolated Mn²⁺. The energies and relative intensities may be rationalised with a simple molecular field model and an estimate is made of the Cr-Mn ground state exchange constant.

The nuclear spin-lattice relaxation times of ¹H and ¹³³Cs in CsFeCl₃.2H₂O and RbFeCl₃.2H₂O are measured in the paramagnetic region. Both relaxation rates have an activation-type temperature dependence in a wide temperature range together with a maximum at a temperature well above the zero-field 3d-ordering temperature. This behaviour can be satisfactorily described with a diffusive soliton model.

The authors report X-ray photoemission measurements of core level shifts in TaS₂, Fe₁3/TaS₂, Mn₁4/TaS₂ and Ni₁3/TaS₂. The shifts are related to charge transfer from the intercalate 3d ions to the host band structure, and have implications concerning observations of charge density wave amplitudes.

The experimental values of the integral dechannelling function of protons with 1 MeV initial energy are presented. The values have been obtained for the four most open channels of W crystal and six channels of Ge crystal. The dechannelling mechanism due to crystal atom thermal vibrations is discussed. The fact is taken into account that not only the particle momentum fluctuations but also the fluctuations of particle position in the transverse plane after a scattering event give rise to the changes of the transverse energy when the particle is scattered by a displaced chain atom. The correlations of thermal displacements of crystal atoms have been included by examining the result of scattering by an individual atomic string. The correlations have been shown to result in the appearance of the factor (1+ Sigma _j gamma _ij) in the addend ( delta p_{perpendicular to} ²)/2M₁ in the expression of the dechannelling rate (here gamma _ij are the correlation coefficients of thermal displacements of atoms). The integral dechannelling function is calculated using the values of gamma _ij obtained in the framework of the Debye approximation. The contribution from multiple scattering by electrons to the dechannelling is discussed on the basis of the methods developed earlier to calculate the channelled particle energy loss. The comparison with experimental data has shown that the inclusion of the correlations of the crystal thermal vibrations can significantly improve the agreement with experiment. The results obtained may be treated to be a substantiation for the possibility of deriving fresh information about lattice vibrations from the experimental data on the dechannelling.

The damping of collective modes in TbVO₄ near the structural phase transition is calculated with the use of a perturbation method applied to a pseudospin-phonon model. A pseudofermion representation is utilised for the pseudospin operator in order to take into account an intrinsic effect of fluctuation field caused by surrounding pseudospins on a given pseudospin. It is shown that the spectrum of singlet pair excitations splits into a pair of spin waves by the fluctuation field and at the same time it gives the damping of the collective modes of the order of the experimental values. The damping of both the acoustic phonon and the central doublet excitation are also derived by using relationships which hold exactly between pseudospin and phonon Green functions.

The energy levels of the anisotropic narrow-gap semimagnetic semiconductor (Cd_1-xMn_x)₃As₂ in a quantising magnetic field are calculated. Analytical expressions for the cyclotron effective mass and the effective g-factor of conduction electrons are given. The values of the effective mass are practically unaffected by the presence of Mn ions in the crystal while the effective g-factor is greatly modified showing a strong temperature dependence and a pronounced anisotropy.

Virial and Budd-Vannimenus theorems (1973) are generalised and derived unitarily and simplified: for a jellium with an arbitrary background density rho (r) four different but equivalent expressions of the pressure term in the virial theorem are found, containing the total energy E_rho , the electrostatic potential phi _rho (r), the electric field E_rho (r) and the electron density n_rho (r), respectively. The expression with phi _rho (r) generalises the Budd-Vannimenus theorem for arbitrary geometries and background density profiles and the other expressions with E_rho (r) and n_rho (r) give electrostatically equivalent formulations of the Budd-Vannimenus theorem. The jellium sphere is studied especially for the limiting case of infinite radius R to infinity , yielding bulk and surface theorems. The latter involves a correction of a theorem given by Vannimenus and Budd, arising from the necessity to start with a finite system for a consistent treatment of the pressure. Also an expression given by Heinrichs (1979) is corrected.

Earlier investigations making use of a density matrix formalism to study the average resistance of a disordered solid are extended in the 1D case to calculate moments of the resistance within a diagonal-disorder model. Application of the symmetric group greatly simplifies the problem, reducing matrices from of order 2^2N to of order 2N+1 for the Nth moment. The symmetry-reduced matrix enables a transparent discussion to be made of the analytic properties of the mean conductance which is shown to have a number of remarkable properties. Finally, some analytic results are presented in various limiting cases and compared with earlier work.

New information on the magnetic ordering of the iron ions in bismuth ferrite BiFeO₃ was obtained by a study with a high-resolution time-of-flight neutron diffractometer. The observed splitting of magnetic diffraction maxima could be interpreted in terms of a magnetic cycloidal spiral with a long period of 620+or-20 AA, which is unusual for perovskites.

A semi-invariant diagrammatic perturbation formalism is employed to study spin-wave interaction effects in S=1 Heisenberg magnets with single-ion uniaxial anisotropy and in an applied magnetic field. A general two-sublattice model is assumed with both intra-sublattice and inter-sublattice exchange interactions. The theory takes account of the optical branches to the spin-wave spectrum (arising due to the single-ion anisotropy) as well as the usual spin-wave excitations. Expressions are derived for the renormalised energy and damping of all these modes as a function of temperature and applied field in the ordered regime, but excluding the spin-flop phase. Numerical application is given to the metamagnetic system FeCl₂ in its zero-applied-field antiferromagnetic phase. The results are found to be in good agreement with recent one-magnon Raman scattering measurements for this material.

Optical absorption and ESR spectra of reduced vanadium centres in Ca₂NaMg₂V₃O₁₂ are reported. The spectra are interpreted as arising from tetrahedrally coordinated V⁴⁺ and octahedrally coordinated V³⁺. The ESR and optical data are correlated using molecular orbital (MO) theory. The composition of the flux-grown single crystals is analysed and discussed.

The authors develop a theory of solid echoes following a two-pulse RF sequence in orientationally ordered crystals such as solid ¹⁵N₂ and solid H₂ which takes into account the dipolar interactions between nuclei of different molecules. These interactions result in a damping of the solid echoes which is found to depend on the angle and axis of the rotation of the nuclear spins by the second pulse. The theoretical predictions are in quantitative agreement with the experimental results obtained both in solid ¹⁵N₂ and in solid H₂. The authors discuss the use of solid echoes for the study of orientational ordering in molecular solids, and in particular how one can take advantage of the unique possibility offered by these systems of suppressing the damping of solid echoes.

For pt.I see ibid., vol.15, no.23, p.4881 (1982). Following a description of the formation of stimulated echoes in orientationally ordered crystals such as solid N₂ and solid H₂ the authors discuss the exploitation of these echoes for the detection of slow rotational motions in these systems. For solid N₂ at low temperatures where the molecular orientations remain fixed the 'natural' decay of the echoes is very slow as a result of the quenching of the nuclear spin flip-flop transitions between different molecules. The 'natural' decay is also very slow in the orientationally ordered phases of solid H₂ and the authors have used this property to search for residual rotational motion in the quadrupolar glass phase of solid H₂. Such motion would lead to a strong additional damping of the stimulated echoes. The experimental results show that the molecular orientations in the glass phase of H₂ are frozen for time scales up to 10^-2 s. The temperature dependence of the echo amplitudes in the glass transition region clearly indicates a collective freezing of the molecular orientations. A new model of an inhomogeneous dynamical freezing is proposed to account for the experimental results.

Circular polarised emission from F and F_A centres in neutron- or electron-irradiated CaO:Mg is reported. A simple theory of the polarisation, which ignores spin-lattice relaxation, is described which predicts P_c=20% at the level crossing between the triplet states. This result is in close agreement with the experimental results for neutron-irradiated crystals. In electron-irradiated crystals or untreated crystals the level-crossing resonance is much less intense, because many centres are in relatively unstrained regions of the crystal, therefore making no contribution to the level crossing. In such samples a fraction of F and F_A centres which are in centres of high strain are not in thermal equilibrium: these centres are entirely responsible for the level-crossing resonance in the appropriately treated crystals.

LEED I-V spectra are reported at both normal incidence and 9 degrees off-normal incidence for the beta ₂-N ( square root 2 × square root 2)R45° surface phase on W(100) and at normal incidence for the beta ₃-CO ( square root 2* square root 2)R45° surface phase. calculated I-V spectra for structures in which the N adatom is placed in the four-fold hollow site yield a well-defined minimum in the reliability-factor comparison with experimental spectra for a W-N interlayer spacing of 0.49 Å and the W-W surface spacing relaxed back to the bulk value. A comparison between the experimental I-V spectra for beta ₂-N and beta ₃-CO in the ( square root 2 × square root 2)R45° structures shows conclusively that C and O adatoms in the beta ₃-CO state occupy the same structural sites as beta ₂-N adatoms.

CdS_xSe_1-x(0<x<1) films have been grown by pyrolytic decomposition. Complete solid solutions are found to form over the entire composition range. The films are of hexagonal structure. The lattice constants vary linearly with composition. The variation of optical band gap with composition is found to be slightly nonlinear.

The effect of non-parabolic band structure of surface phonons in n-type InSb films has been investigated quantum mechanically in the GHz frequency region. Numerical results show that the amplification coefficient is enhanced for the non-parabolic band structure due to the non-linear nature of the energy band in semiconductors. Moreover, the amplification coefficient depends also on the temperature, the piezoelectric coupling mechanisms, the frequency of sound waves, the electric field, and the thickness of the semiconductor film.

The electron energy loss spectrum of single-crystal CaO has been measured in the range 0-50 eV for primary energies between 200 eV and 1300 eV. Comparison with Im(-1/ epsilon ) calculated from optical data shows good agreement except for the presence of peak in the electron loss spectrum identified as a surface plasmon. Peaks at 1.20 eV and 4.97 eV in the bulk band gap appeared to have their origin in surface states and a sharp peak at the band edge also appeared to have a surface contribution. The peak at 1.20 eV was identified as arising from the presence of defect states induced by electron bombardment.