Table of contents

It is shown that the particular form of the mass current in ³He-A found by Cross (1975) is equivalent to a phenomenological assumption that the current depends only on the traceless part of the tensor Omega _ij introduced by Mermin and Ho (1976) to describe spatial variations of the order parameter. An equation of motion for Omega _ij is derived in terms of the vector C introduced previously by the author (1975) to describe temporal variations of the order parameter. The appropriate generalizations of curl nu _s=0 and the quantization of circulation for ³He-A are derived in terms of Omega _ij, and the nature of possible singularities is discussed.

A detailed LEED study of the clean Si(100)(2*1) surface and the effects of hydrogen adsorption has been made. Adsorption of hydrogen in the presence of a hot filament modifies the structure to give a sharp (1*1) LEED pattern, and the intensity data are consistent with the structure of the silicon atoms being in the bulk structure sites. This observation is in conflict with the only previously reported study of hydrogen adsorption using LEED, and favours certain models for the (2*1) reconstructed surface which have recently been discarded as incompatible with the earlier experimental result of Ibach and Rowe (1974).

The authors propose a generalization of the 'cluster-Bethe lattice' approach of Falicov and Yndurain for the electronic density of states in binary alloys. In the present formulation it is possible to treat the Bethe lattice in any desired single-site approximation. Further, they obtain algebraic forms for the transfer matrices corresponding to the two types of atoms in the cluster, for which only interpolation formulae were previously given by Falicov and Yndurain (see Phys. Rev. B, vol.12, p.5664 (1975)).

The authors have developed a new numerical approach to the Anderson localization problem. It is an efficient procedure for the calculation the participation of ratio, averaged over the entire band. Preliminary results are given for lattices of one to four dimensions.

The authors present and study a simple model that describes the evolution of a quenched magnetic system towards equilibrium (the annealed case). In the adiabatic limit a particular choice for the magnetic interaction allows for an analytic treatment of the problem. Expressions are obtained for the time dependence of basic thermodynamic quantities, as well as that of the local magnetization and spin correlation functions.

The critical behaviour of the weak ferromagnet Fe₃BO₆ has been examined experimentally. It is found that Fe₃BO₆ has critical exponents beta =0.347, gamma =1.4 and delta =4.6. The scaling relation gamma = beta ( delta -1) is fulfilled within the error limits.

The reflection spectra of SrCl₂ and CdF₂ at photon energies below 56 eV have been measured using synchrotron radiation. The data have been subjected to Kramers-Kronig analysis. In compounds with relatively large anionic radius, covalency appears to have the effect of reducing the strength of cationic core excitons. SrCl₂ is an example of this.

The intrinsic luminescence excitation spectrum of CaF₂ has been measured between 8 and 50 eV. The luminescence is due to the recombination of self-trapped excitons. The spectrum is interpreted in the light of recent work on alkali halides and there is evidence of double electron-hole pair creation by scattering at photon energies near to twice the band gap. There is also a reflection-loss enhancement mechanism probably due to a surface effect, leading to conclusions in the Ca²⁺ core excitons.

Principles of calculating the electronic structure of the F⁺ centre in partially covalent solids are discussed. A bond-orbital model of the perfect lattice is described, and the effects of this covalence on the F⁺ centre energy levels and hyperfine interactions are investigated. The effective-charge method of treating covalent crystals is critically examined, and rejected in favour of an ionic ion-size model for variational calculations. The covalence is less important in calculating wavefunctions than in using the wavefunctions to derive hyperfine interactions. Lattice distortions give only small changes in transition energies, but are extremely important in determining the hyperfine interactions.

Fractional parentage for R₅ to R₃ are given for angular momentum states up to I=6. They are used for finding solutions of the T(X)( epsilon + tau ₂) Jahn-Teller problem in the special case of equal coupling, with and without spin-orbit coupling. A series of theoretical bandshapes is given. Theory and experiment are compared for the stress dichroism and magnetic dichroism in adsorption (good agreement) and for the luminescence bandshape (qualitative agreement only) of the F⁺ centre in CaO. The absorption bandshapes for F centres in the caesium halides are also compared with this model, and are quite well accounted for.

Experimental data for the mobility of InSb, doped by nuclear reactions, are presented. This method of doping guarantees a well known number and a random distribution of impurities. The experimental data are shown to agree surprisingly well with the Brooks-Herring formula for ionized impurity scattering. The agreement is discussed in terms of the partial wave method using the Born approximation and Schwinger's variational method to calculate the phase shifts.

A study has been made of the sensitivity to electron radiation damage of the Yb³⁺ sharp line emission spectrum at 77Kin zinc telluride which had been previously implanted by 50 kV Yb⁺ ions and given suitable post-implantation annealing treatment. The Yb³⁺ emission intensity at 1013.6 nm was found to increase with electron damage above a certain threshold energy and, if taken as a monitor of the production of cation displacements, yields a threshold incident electron energy of 145 keV for enhancement ( identical to 5.6 eV zinc displacement threshold energy). Warming the electron-damaged samples to temperatures greater than 160 degrees C allows complete removal of the defects produced by the electron damage. Analysis of the intensity decreases as a function of electron fluence for those Yb³⁺ emission peaks which are reduced by damage show the rare earth excitation process to be indirect.

The experimental elastic reflectivity of ⁴He atoms from liquid ⁴He surfaces behaves as if the ⁴He atoms are reflected from a very smooth elastic potential. The authors explain this anomalous result in terms of Van der Waals forces and coupling to the ripplons which swamps all other processes. Interpretation of the experiments confirms that the surface of liquid ⁴He is diffuse on a scale of 5 AA.

A study of the exchange and correlation component of the one-electron LEED potential was carried out. An analysis of low-energy electron diffraction data from the Na(110) face at T=173K and normal incidence was made to test the different model potentials. A good fit to experimental spectra was obtained with a model based upon Hartree-Fock (core) and Hedin and Lundqvist results for the exchange and correlation potential of a uniform electron gas. The inner potential and absorption are those of a uniform electron gas with the same density as Na (r_s=4). The surface layer is determined to be neither contracted nor dilated with respect to the bulk (110) planes.

A model is proposed to explain the various kinetic processes occurring at a GaAs (100) surface when beams of As₄ and Ga are used to grow GaAs by molecular beam epitaxy. There is a considerable amount of data available on this particular system and an attempt has been made to logically examine the fundamental surface processes and explain them by a semi-empirical model. Reasonable quantitative agreement with experiment, in the temperature range 450-600K, is achieved for much of the experimental data.

An evaluation of the exchange and correlation energy of semiconducting systems has been attempted by using a model dielectric function with a finite static limit and assuming complete translational invariance. The same procedure has been used as in the analogous calculation for the electron gas. The resulting expression has been integrated without further approximations and its limit as epsilon ₀ to infinity has been found to compare satisfactorily with the Nozieres-Pines interpolation formula (1958), for the electron gas. Numerical results are given for electron densities and static dielectric constants corresponding to the group IV semiconductors.

A recently developed renormalization group approach to two-dimensional bond percolation problems is generalized to deal with the percolation conductivity sigma of dilute resistor networks. The critical exponent t, defined by sigma (p) varies as (p-p_c)^t, is related to an eigenvalue of the renormalization group transformation of conductance probability distributions. The transformation and eigenvalue are obtained for various real-space scalings of the square and triangular lattices, resulting in t=1.13+or-0.09. The Last-Kirkpatrick scaling relationship is used to obtain the critical exponent for spin-wave stiffness in the dilute ferromagnet.

The hopping conductivity of granular metals is known to be of the form sigma varies as exp (-(T₀/T)¹2/) in the temperature range 20K<or=T<280K. A theoretical derivation of this relation using the critical percolation conductance method as developed in the context of the variable range hopping mechanism of conduction in amorphous systems, is discussed. Use is made of the empirical fact that the ratio of intergrain separation and grain size is nearly constant for macroscopically homogeneous samples. It is also assumed that the hopping of electrons is predominantly between nearest neighbours. Extension of the treatment to thin films and comparison with previous theoretical work is briefly discussed.

Transmission and photoconductivity measurements, both as a function of intensity and time have been made at room temperature on indium antimonide using CO₂ lasers and on germanium using a hydrogen fluoride laser. In both cases it is shown that the reduced transmission at high intensities is primarily due to the electrons and holes generated by two-photon absorption and not directly due to the two-photon absorption process. Previous work on both materials must therefore be reinterpreted.

In order to improve the understanding of the (g) tensor of D_4h complexes formed with d⁹ ions, using the more realistic molecular orbital approach, the third-order contribution tensor (G) has been calculated. The results obtained have been applied to the analysis of the (g) tensor of (CuCl₄)^2-D_4h complex, also including the second-order contribution tensor ( delta g) arising from the bonding levels B_2g and E_g.

A formulation for disordered Heisenberg spin systems and alloys by the coherent potential approach is rigorously developed to involve cluster effects and off-diagonal randomness. In the momentum representation the diagonal matrix elements of the averaged t-matrix are obtained in a Fourier-analysed form. Equations to determine the unknown Fourier coefficients of the coherent energy are given exactly by requiring that each Fourier coefficient of the t-matrix vanish. An approximating method based on the exact formulation is presented for linear chains in magnetic systems. This applies to general short-range potentials and always retain the translational symmetry.

An effective-medium theory is presented for the substitutionally disordered transverse Ising model above its transition. The equations of motion for the relevant Green functions are decoupled in RPA. The disorder then occurs through a local parameter and can be treated in the spirit of the single-site coherent potential approximation. Fully self-consistent results are computed at the transition for the transition temperature, densities of states and spectral function. Simple features of the results can be understood using a generalized virtual-crystal approximation which accounts for damping due to disorder. Extensions of the theory to include intrinsic damping, more than one spin per unit cell and coupling to phonons are discussed.

The statistical mechanics of uniaxial S=1 ferromagnets with biquadratic exchange is considered in both ferromagnetic and quadrupolar phases using the standard basis-operator method proposed by Haley and Erdos (1972). In the random phase approximation, the collective excitation spectrum and thermodynamical properties of the system are discussed in detail, with stress laid on the role of kinematic restrictions with regard to the operators of the standard basis. The results are compared with those of molecular field theory, constant coupling approximation, and the high-temperature series expansion method. The problem of stability of the quadrupolar ordering is also considered by having recourse to the nonrelativistic analogue Goldstone theorem.

Some quantum effects of the magnon-photon interaction are investigated. A magnon life-time, arising from a radiative relaxation through the absorption and emission of one photon, is found. Multiple scattering of magnons and photons is indicated. The creation of a photon at one spin site and the resonant absorption of the same photon at a later time at a different site is found to lead to a spin-spin real radiation exchange interaction. The predicted effects are large enough to be experimentally observed.

A recent investigation by Nattermann and Trimper, (see J. Phys. A., vol.8, p.200, 1975), of the influence of cubic anisotropy in both the quadratic and quartic parts of an n-component order parameter Hamiltonian is extended in order to examine the decay of the anisotropy near the critical point. In the case where the transition is driven to first order by the anisotropic fluctuations, the 'size' of the first-order transition is estimated. It turns out that this first-order transition becomes experimentally observable only for large values of the lattice anisotropy. The effective and asymptotic critical exponents eta and zeta (the latter characterizes the decay of the anisotropy) are calculated. The competition between the decay of the anisotropy and the occurrence of a first-order transition in investigated. The results give an explanation for the first-order transition in KMnF₃. The extension of this approach to lower-than-cubic symmetry is briefly discussed.

A paramagnetic centre having spin S=2 and C₂ symmetry has been detected in natural amethyst crystals. The only ESR transition observed was the Delta M=+or-4 transition between the lowest two energy levels M=+or-2. Line position measurements at 35 GHz and 16 GHz gave the g-tensor principal value for the C₂ direction g_zz=1.9876+or-0.0006 and the zero-field splitting of +or-2, Delta ₂=10.166+or-0.005 GHz (at 77K). The constants D and E of the second-order zero-field splitting operator DS_z²+E(S_x²-S_y²) could not be determined; however, -D must be greater than 80 GHz and mod 3E/D mod <0.3. The paramagnetic centre could be an Fe⁴⁺ ion on the tetrahedral silicon site of the quartz lattice.

The reflectivity spectrum has been measured for photon energies between 0.03 eV and 12 eV and the optical transmission between 0.03 eV and the absorption edge at 0.95 eV. The real and imaginary part of the dielectric function have been calculated using a Kramers-Kronig analysis and an energy level scheme has been derived. All phonon modes expected by group theoretical analysis have been observed.

Photoelectron spectra of Sn_1/3TaS₂ and SnTaS₂ are reported and compared with spectra of 2H-TaS₂ and SnS. It is possible to trace the charge transfer from Sn to Ta from the observed increase of the occupation of the lowest Ta 5d band and from the observed decrease of the positive charge on Ta. The charge transfer is the same in Sn_1/3TaS₂ as in SnTaS₂. The data indicate the presence of two types of Sn atoms in SnTaS2. The Ta 4f peaks show an asymmetric broadening; and an anomalous intensity ratio of the 4f₇ and 4f_5/2 peaks. These effects are ascribed to shake-up effects involving excitations of 5d electrons. The average relaxation energy of a Ta 4f hole is found to be 1.1 eV.