Table of contents

Exact results on the single spin-flip Glauber dynamics of six coupled Ising spins are presented. The dynamical behaviour is found to be governed by the number of nontrivial local energy minima. In the fully frustrated paramagnetic case there are no diverging relaxation times. In the ferromagnetic case there is one long-lived mode. In the spin glass case there may be several diverging relaxation times. The longest relaxation times follow an Arrhenius law with the energy barrier determined by the energy needed to invert the ground state configuration.

The authors investigate the effect of adding annealed vacancies to systems which exhibit long-period modulated phases in one space direction. Concentration waves are formed which mirror the ordering of the underlying lattice. They expect the results to be relevant to the behaviour of polytypic substances and thiourea.

The authors describe the physical basis and experimental techniques of inelastic electron tunnelling spectroscopy. A discussion of the essential features of quantitative theory shows how to set about detailed analysis of spectra. The power and versatility of the technique are illustrated by accounts of a variety of applications, and suggestions are made about the directions in which the field will develop.

With the help of density measurements obtained from neutron transmission data an attempt is made to describe the authors' previous small-angle scattering critical fluctuations in K-KBr, in terms of an improved order parameter, i.e. the volumic fraction. Critical scattering data on the system K-KF are presented and analysed in this framework. A qualitative estimate of the excess-volume behaviour of these solutions is then given.

Measurements are reported of the X-ray scattering from KTaO₃ with 1.6% and 5% of Li substituted for K and, for comparison, with 1.7% of Nb substituted for Ta. Both KTaO₂:5% Li and KTaO₃:1.7% Nb are found to undergo transitions to states with long-range ferroelectric order on cooling. However, the low-temperature state of KTaO₃:1.6% Li does not possess long-range ferroelectric order when cooled in zero applied electric field. The measurements are in agreement with an electric dipole glass or spin glass analogue description of the low-temperature phase of KTaO₃:Li for Li concentrations below about 4%.

The authors describe, compare and analyse a series of microcalorimetric experiments and computer simulations focusing on the temporal behaviour of the excess energy in supersaturated solid solutions, e.g. quenched Al-Zn alloys with different compositions. Both systems, real samples and computer models, show a qualitatively very similar behaviour. The main common features are the scaling of the data corresponding to different compositions, temperature and even systems, and its consistency with a combination of simple power laws. These facts confirm and extend some previous conclusions about the microscopic mechanisms present during the temporal evolution of the system. They also estimated equilibrium energy values in the case of the binary alloy or Ising model.

An exact real-space rescaling transformation is used to calculate the local Green's functions and the densities of states for a semi-infinite nearest-neighbour tight-binding system with a adatom and an impurity atom located at an arbitrary distance from the surface. The influence of both the surface and impurity atom characteristics on the adatom density of states can be determined in a simple manner.

A comparison is made between the recursion method and the equation-of-motion method in terms of flexibility of application, efficiency of execution and transparency of interpretation. The two methods are so similar that, in most cases, refinements invented for one method are found to be practicable in the other as well. In principle, they are of comparable efficiency but elementary implementations of the equation-of-motion method are somewhat less efficient.

Extensions of the conventional Stevens operators O_kq to negative values of q and their transformation properties are reviewed and reconsidered. Transformation matrices with k=1 to 6 and -k<or=q<or=+k for a general rotation ( Phi , Theta ) of the frame of coordinates are derived by computer using ALTRAN and the corresponding matrices for the operators T_lm. As a special case a transformation which is particularly useful in EPR studies is considered. In the interest of transcription accuracy, the computer-derived transformation relations are reproduced from camera-ready computer output. The present results for k=3 and 5, all q, and k=6, q=1 and 5, are new. A number of inconsistencies in the earlier papers are pointed out for k=2, 4 and 6. The concept of 'normalised' Stevens operators O'_k^q is extended to k=3 and 5 where numerical coefficients relating both sets of operators are given. The transformation matrices for the normalised Stevens operators can be read in a straightforward way from the expressions for the conventional operators. The conclusion is that both the conventional and normalised Stevens operators do transform consistently contrary to some earlier opinions.

The Cr¹⁺ level in GaAs (the so-called two-electron trap level) is investigated using optical absorption and de Haas-Shubnikov measurements for a series of heavily doped n-type samples with Fermi levels up to 120 meV above the conduction band edge. The level is shown to have the form of a broadened distribution of width 26 meV centred at 45 meV (4K) above the band edge. Analogues with intermediate-valence and Kondo systems are briefly discussed.

The authors derive a continuum representation of the spin-one operators which provides the mapping of the spin-one anisotropic Heisenberg chain onto the Luttinger model. They show a schematic phase diagram of the Hamiltonian, and calculate a general two-spin dynamic correlation function at finite temperatures, valid in the massless domain of the Hamiltonian. This can be applied to obtain the transverse dynamic form factor, and results are compared with neutron scattering data on CsNiF₃. The behaviour of the transverse correlation function is shown to be governed by a critical exponent eta _u^+or- which is a measured of quantum effects in the system, eta _M^+or- to 0 being the classical limit. Existing data on CsNiF₃ are shown to be in the classical regime, and they make suggestions for further experiments to search for quantum fluctuations. They also indicate the limits of applicability of the quantum sine-Gordon theory to CsNIF₃.

The problem of the lower critical dimension (LCD) of spin systems in random fields is discussed. The different theoretical predictions for the Ising case-i.e. LCD=2 from considerations of domain wall roughening but LCD=3 from diagrammatic renormalisation-are related to different results for the spectral function Delta (q) of the dressed static-field fluctuations-i.e. LCD=3 is obtained if Delta (q) diverges as xi ^eta with increasing thermal correlation length xi , while LCD=2 corresponds to a non-divergent Delta (q). This difference is analogous to the difference between the true value of the dynamical critical exponent z of a pure ferromagnetic spin system and the 'conventional approximation' z=2- eta . In this way, the weak point of the arguments leading to LCD=2 is discovered, namely the neglect of certain 'mode couplings' between fluctuations with different q or, more pictorially, the neglect of 'domains within domains', and thus the result LCD=2 is seen to be no longer credible. The domain argument leading to LCD=2 are modified by replacing the bare fields by 'dressed' ones; in this way, they are reconciled with the field theoretic result LCD=3.

Computer simulation is used to demonstrate explicitly the ground-state spin canting which occurs when a ferromagnet with competing exchange interactions is diluted. At low concentrations the dominant impurity clusters are next-nearest-neighbour vacancy pairs. The transverse components of the surrounding spins can be viewed as pseudo-spins. Interactions between pseudo-spins are also studied and shown to have the frustrated character to suggest pseudo-spin-glass order within the ferromagnetic bath.

Results of numerical studies on the equilibrium scaling stiffness energy for 2D nearest-neighbour Heisenberg systems at T=0 are presented. The authors first consider the percolation problem and estimate the critical exponent for the spin wave stiffness to be close to 1. They then consider systems in which -J-bonds appear with probability x and +J-bonds with probability (1-x). The scaling stiffness energy, a measure of sensitivity to changes in the boundary conditions, disappears exponentially with x at x_c approximately=0.13 (an estimate for large systems). This value of concentration is identified as an upper boundary of the usual ferromagnetic phase. Nevertheless the magnetisation persists above x_c and disappears at X_c approximately=0.30 when the system enters into the spin glass phase. The region between x_c and X_c is identified as corresponding to the Gabay-Toulouse mixed phase in which the system looks like a spin glass but has some non-zero magnetisation. This interpretation receives further support from studies of the two- and four-spin correlation functions in local energy minima. The correlations decay exponentially, at least on small distances. The correlation lengths of the two-spin correlations start to drop at x_c. The spin components parallel to the magnetisation are actually less correlated than the transverse ones.

A theoretical formulation for the cyclotron resonance linewidth in n-InSb at low temperatures has been developed. The present formulation consists of two competing scattering mechanisms, long-range ionised-impurity scattering and short-range multiple impurity scattering, and yields a minimum in the linewidth as a function a magnetic field, as observed experimentally. The magnetic field position corresponding to the minimum observed corresponds to a radius of the Landau orbit, almost equal to the correlation length between impurities.

In p-type GaP:Zn the two luminescence bands at 0.95 and 1.20 eV can be excited with light below the gap energy. They are due to two independent donor-acceptor recombinations. In the 0.95 eV emission the donor is the doublet PP₄ anti-site as seen from ODMR. The excitation spectrum of this emission follows the density of valence band states of T₂ symmetry with a threshold energy of 1.25 eV. In the 1.2 eV emission the donor is a triplet PP₃Y_P anti-site, the acceptor an impurity with S>¹/₂ bound to the PP₃Y_P, probably at an interstitial site. A likely acceptor could be Fe³⁺, which is present as an impurity in the crystal. In the ground state PP₃Y_P is a spin doublet and the proposed acceptor would then be Fe₁²⁺. The authors suggest that Y_P is Ga on a nearest P site (Ga_P) forming a (P_GaGa_P) anti-structure pair.

Magnetic short-range order in the one-dimensional Heisenberg ferromagnet CsNiF₃ has been investigated by linear magnetic birefringence and optical phase retardation measurements The short-range order was found to extend beyond 120K. The contributions of out-of-plane fluctuations and of the interchain interaction have been recognised. The values of the photoelastic coefficients and of the lattice dilatations are also reported.

The optical absorption spectra of Yb²⁺ in a range of potassium and sodium halide crystals are described and analysed. Attention is focused on the strongly allowed 4f¹⁴ to 4f¹³5d transitions. Excellent general agreement is obtained between theory and experiment provided that a correction based on the nephelauxetic effect is included. Parallel linear dependencies for the potassium and sodium halides are established between a parameter Delta , representing the energy difference between the centre of energy of the excited 4f¹³5d configuration and the 4f¹⁴ ground state, and the lattice parameter d. Similar dependencies are established between the crystal-field parameter Dq and d.

Three types of single centres (O_h, C_4v, C_3v) have been identified in SrF₂:Eu³⁺ and energy level schemes have been established for them. The two types of cluster that predominate in CdF₂:Eu³⁺ and CaF₂:Eu³⁺ are not found in SrF₂:Eu³⁺. Anomalous behaviour of the cubic (O_h) centre common to the other alkaline-earth fluorides is observed, and additional species connected with the C_3v centres appear above 0.1 mol.% dopant concentration.