Table of contents

The effect of nonequilibrium phonon occupation on the transient response of the drift velocity and electron temperature to a step uniform electric field of moderate strength is calculated for single- and multi-layer GaAs-AlGaAs heterosystems, by using a balance equation approach. Interesting ballistic and overshoot behaviour is observed in almost all the cases examined. Although the drift velocity overshoot is only slightly modified by a finite phonon relaxation time, tau _p, up to 3.5 ps, the electron temperature is greatly enhanced and the approach to a steady state is significantly prolonged.

The electronic structure of a quasi-crystalline lattice generated by almost-periodic tilings of the line is examined. The author finds that the wavefunctions and the spectra are characterised by a continuous set of scaling indices and calculates their alpha -f( alpha ) spectrum. Eigenfunctions at special energies are considered in detail. The spectral scaling properties are compared with previous results for spectral dimensions valid near the band centre and the band edges.

In the classical approximation the Heisenberg rhombohedral antiferromagnet shows infinite degeneracy of the ground-state energy corresponding to infinite inequivalent iso-energetic helices whose wave-vectors Q belong to lines in the reciprocal space, called 'degeneration lines'. In absence of anisotropy the spin wave energy spectrum shows 'soft lines' vanishing for all wave-vectors falling on the degeneration lines. These soft lines destroy long-range order (LRO) at any finite temperature. The authors show that the zero-point motion, which is generally expected to contrast with the onset of LRO, favours in this case a single wave-vector removing the infinite degeneracy of the ground state, so LRO is restored by quantum disorder.

New ternary compounds of the type YbXCu₄, where X=Al, Ag and Ga, have been prepared. The compounds with X=Al and X=Ga are found to have the hexagonal CaCu₅-type structure while the compound with X=Ag has the cubic MgSnCu₄-type structure. Magnetic susceptibility measurements reveal that Yb is in a nearly trivalent state in YbAlCu₄, but in a divalent state in YbGaCu₄. The susceptibility of YbAgCu₄ shows a broad maximum at around 33 K, but follows a Curie-Weiss behaviour at high temperatures with an effective moment close to that of Yb³⁺. Thus both the structure type and the valence state of Yb appear to be strongly influenced by the nature of the X atom in YbXCu₄ compounds.

Recently observed luminescence spectra in the alloy semiconductor quantum-well system InGaAs/InP show an enhancement of the electron-hole (e-h) recombination oscillator strength at the electron Fermi energy (E_Fe). This enhancement is explained, using a generalized e-h pair propagator and static screening, as due to multiple e-h scattering and recombination of the electrons at E_Fe with the small number of optically excited holes which have wave-vector components of the order of k_Fe (the electron Fermi wave-vector) due to localisation effects. The localisation is taken to rise from alloy disorder.

The author derives a distribution function for the drift velocities in a glass-forming liquid. The distribution function is of the familiar Maxwell-Boltzmann form except that the temperature in the denominator of the exponent is replaced by T-T₀ for a wide range of temperatures greater than T₀. This is due to the combined operation of two mechanisms: firstly a freezing mechanism described elsewhere which leads to a microscopic resistance varying as (T-T₀)^-1 for T>T₀; secondly a stochastic process which leads to a restricted thermodynamic equilibrium. He also discusses the use of this distribution function in calculating the viscosity with an eye to understanding the empirical Vogel-Fulcher law. He argues that it is important to take into account mechanisms operating over large length scales.

The ground-state energy of the free polaron is calculated, using the Fock approximation. A new model Hamiltonian involving an electron in a harmonic potential of cylindrical symmetry in the presence of a variational magnetic field, internal in origin, is used. This magnetic field, which has no physical existence, introduces the possibility of symmetry breaking. This approach is shown to be equivalent to that of Peters and Devreese (1982), who used path integrals to study the properties of the polaron in a magnetic field, if the variational parameters of their model action are chosen to match those of the author's model and if the magnetic field in the model action is used as a variational parameter whose origin is internal. Using that approach, a strong-coupling ground-state energy much lower than the usual one is found (E₀=-0.1658 alpha ²). It is shown that such a low value cannot be obtained from the adiabatic approximation because a model spectrum having a degenerate ground state has been used. His results call into question the assumption that the energies obtained from the Fock approximation or from the Feynman integrals are upper bounds to the polaron ground-state energy in the case of model actions or Hamiltonians involving magnetic fields.

The form of the current density operator, involving a velocity operator and suitable for use in band-conduction calculations, is used here to calculate the conductivity in a system of localised electronic states. In the site representation, it has zero diagonal matrix elements. Using a relationship between diagonal and off-diagonal elements of position and electron-phonon interaction valid for this system, the authors show that their result is equivalent to a similar Green function calculation of Manucharyants and Zvyagin (1974), where the time derivative of the dipole moment operator was used as the current operator. In doing the calculation, they are able to emphasise the equivalent role played by diagonal and off-diagonal elements of position and electron-phonon interaction. They confirm that the same result is attained when a canonical transformation is performed to remove the diagonal elements of electron-phonon interaction from the Hamiltonian.

A new analysis of the thermo-electric power of a system of electrons in random localised states with electron-phonon interactions is given. A field-theoretic approach is used to calculate the energy current operator and an exact expression for the thermopower is written down. An approximate form is calculated, using a Green function technique, which has a nontrivial contribution from the transported interaction energy, as well as from the electrons.

It is shown that the Holstein-Primakoff boson representation of spin operators leads to the same soliton excitations, in the anisotropic Heisenberg chain, as the classical treatment of spins, if one retains the terms up to products of six Bose operators.

Neutron diffraction experiments were carried out in the temperature range from 1.5 to 295 K on a polycrystalline sample of manganese(II) oxalate dihydrate MnC₂O₄.2D₂O, a system composed of linear chains of oxalato-metal groups. In the course of this study the monoclinic space group C2/c has been confirmed and structural parameters have been refined, using the Rietveld profile-fitting procedure. An appreciable change ( approximately=2%) of the lattice constant a in the temperature range from 100 to 295 K has been observed. At 1.5 K the neutron diagram reveals a group of weak and closely spaced Bragg reflections arising from the magnetic ordering of Mn²⁺ ions. Indexed on the basis of a magnetic unit cell with lattice constants a_m=6a, b_m=2b and c_m=c the observed structure is best described as an antiferromagnetic cone spiral, which the cone axis perpendicular to the b-c plane and the value of the magnetic moment equal to (3.7+or-0.4) mu _B. The resulting fundamental and spiral components are equal to (1.6+or-0.1) mu _B and (3.4+or-0.4) mu _B, respectively. The temperature dependence of the magnetic reflection 511 yields T_N=2.60+or-0.05 K. On the other hand, the temperature dependence of bulk magnetic susceptibility exhibits a rounded maximum in the vicinity of 10 K. A consistent description of the magnetic behaviour of MnC₂O₄.2D₂O at low temperatures has been achieved by assuming that intra-chain interactions between magnetic ions are much stronger than the inter-chain couplings. The fit of the magnetic susceptibility based on Fisher's results (1964) for a linear Heisenberg chain yielded J/k_B=-1.22+or-0.01 K.

Further experimental and theoretical studies of the thermally detected EPR spectra observed in chromium-doped GaP crystals are described. Several resonances are attributed to strain-stabilised Cr³⁺ ions and some others to Cr³⁺ ions in zero- or small-strained sites. It is concluded that the Cr³⁺ ions occupy isolated substitutional sites.

Specific mechanisms involving conventional crystal fields and excitations to other sites are presented which lead to effective anisotropic orbit-orbit interactions. The method of relativistic operator equivalents then leads to contributions to the Hamiltonian which are not only nonscalar but also spin dependent. A comparison is made between the matrix elements of one-body and two-body operators with the same resultant spin and orbital ranks for f⁷ and d⁵ configurations. In a number of cases two-body operators possess matrix elements between spectroscopic terms whereas one-body operators with the same resultant ranks do not.

Resonant polaron behaviour, related to the interaction of conduction electrons with optical phonons in the presence of crossed magnetic and electric fields, is described theoretically and compared with recent experimental data. Green function techniques are used to treat the situation in which real phonon emission is possible, which is the case in the crossed-field configuration. It is shown that weak electric fields influence the amplitudes and widths of the polaron branches, and their positions slightly also. On the other hand, sufficiently strong electric fields destroy the resonant-polaron splitting and pinning.

(Anti)ferromagnetic resonance and magnetisation measurements have been performed on the magnetic quasi-one-dimensional compound CuCl₂.TMSO at temperatures well below the 3d ordering temperature. The experimental results can be described quite well by a classical four-sublattice mean-field model. The exchange anisotropy with the sublattices is found to be predominantly of the XY type and amounts to about 2% of the intra-sublattice exchange interaction J/k_B=39+or-6 K. The coupling strength between the sublattices is obtained as -0.57 K in the crystallographic a direction and 0.03 K in the crystallographic c direction.