Table of contents

A Wilson type of 'renormalisation group' calculation shows that the ground state of an s-d exchange Hamiltonian in which a spin-1 impurity interacts with a single scattering channel antiferromagnetically is not a spin-zero state, but is a ferromagnetic spin-¹/₂ state. Numerous other related calculations confirm that the ground state of an antiferromagnetic s-d exchange Hamiltonian is not necessarily an S state. It is suggested that a spin-zero ground state only occurs when the number of antiferromagnetically coupled scattering channels equals or exceeds twice the spin of the impurity.

The initial susceptibility and the average free-energy singularities for a disordered Ising spin system on a Cayley tree have been studied. A set of recursion relations for the probability distribution functions of the effective fields at each generation of the tree is formulated. It is shown that the susceptibility is Curie-like at any temperature, for an equal number of ferromagnetic and antiferromagnetic bonds. The average free energy behaves as h^{2 kappa (T)} where h is an applied field and 1<or= kappa < infinity for 0<or=T<or=T_infinity ; the latter is a finite limiting temperature.

A Heisenberg ferromagnet is considered in which the eigenvalues of S^z and (S^z)² are 1, 0, - lambda and 1, 0, lambda ² where lambda is the asymmetry parameter lying between 0 and 1. It is shown that in this system a quadrupolar phase appears as an intermediate phase even when the ground state is ferromagnetic. The temperature T_q at which the transition from the ferromagnetic to the quadrupolar phase occurs is derived with a molecular-field approximation. Two limiting cases lambda to 0 and lambda to 1 are also examined.

A novel form of the simple mean-field equations for the Ising model with arbitrary interaction is presented. The method involves the development of a pair of self-consistent equations for the average spin at a given site and two spin correlation functions for a given pair of sites; all the higher-order spin correlations are adequately taken into account. A critique of a recent similar approach by Frank and Mitran (1977, 1978) is also given. The formalism presented here can be applied to the estimation of the transition temperatures of spin-glass models as well as to regular three-dimensional arrays of Ising spins. Results obtained for such systems are in close agreement with existing best estimates.

Raman measurements were performed on K₂CoF₄, a two-dimensional antiferromagnet with large uniaxial anisotropy. Two lines at 206.5 and 468 cm^-1 were identified as the AFMR and two-magnon lines respectively. Measurement of the temperature dependence revealed an extremely weak renormalisation of these excitations up to T_N=107.4K.

Recent ENDOR measurements of transferred hyperfine interactions in the linear structure M³⁺-F^--Cd²⁺, where M³⁺=Fe³⁺ or Cr³⁺ and the host lattice is CsCdF₃, have given anomalous results when interpreted by standard ligand hyperfine structure theory. The data have therefore been reinterpreted allowing for polarisation of the F^- ligand by the electric field from its neighbours. This is found to improve agreement between theory and experiment, especially if the fluoride ion is allowed to relax towards the M³⁺ ion, but some difficulties still remain.

High-precision Mossbauer studies of phase transitions require a good drive, a strong source, a multichannel analyser and the associated routing circuitry and very stable and sophisticated temperature controllers. A method is suggested which does not require all these complications and still gives T_c to an accuracy of approximately one in 10^5-6 and the order parameter exponent n to approximately one in 10². The limitations of the technique are also discussed.

Correlated site percolation is studied on the Bethe lattice. Exact results are obtained for the correlated site percolation probability P_n(p) and the concentration of 'dangling sites' on the infinite cluster.

Detailed mechanisms are proposed for the defect reactions occurring in irradiated alkaline earth fluorides. Both pure and doped crystals are considered. For the former, the models rationalise much of the experimental data, particularly the studies of Hayes and Lambourn (1973). The discussion of doped crystals explains the origin of the pronounced effects of trivalent impurities. The mechanism of formation of photochromic centres is discussed and the observed temperature dependence of the stability of these defects is explained successfully.

The electrostatic contributions to the inner elastic constants of HCP metals have been calculated for axial ratios in the range 1.56-1.90, using the Ewald-Fuchs method.

The resonant part of the electrostrictive coupling of the acoustic longitudinal model, which propagates along the polar axis, to the order parameter, has been taken into account in the pseudo-spin model for the ferroelectric phase transition in KDP. Using a Green function method and an RPA-type decoupling scheme, an expression is derived for the velocity of the acoustic mode in the ferroelectric phase. The results are compared with the available experimental data on RbH₂PO₄. The effect of this coupling on the thermodynamic behaviour at the phase transition is discussed.

A Raman study of the three-solid-state phase transitions in diamantane is presented. The low-temperature transition at T_c1=35K is characterised by a zone-centre soft librational mode; this mode has been fitted to a damped harmonic oscillator function, and the damping and static susceptibility of the soft mode obtained as a function of temperature. These results indicate that this transition is almost pure second order, a particularly rare example of such an event in a molecular crystal. The behaviour of a lattice mode at approximately 50 cm^-1 which splits into two at T_c1 indicates a change in the space group. At T_c2=407K, the Raman-active lattice modes are replaced by a broad, overdamped mode which softens rapidly as the plastic phase transition at T_c3=440K is approached from below; the plastic phase gives the characteristic spectrum associated with rapid, isotropic molecular re-orientation.

Spectra of the complex amplitude reflection coefficient of KNO₃ single crystals were measured for all phases between room temperature and 190 degrees C in the spectral region from 15 to 300 cm^-1 by asymmetric Fourier spectroscopy. The complex dielectric function epsilon ( omega ,T) was evaluated from these data. In the room temperature phase II (aragonite structure) the epsilon -spectra correspond to damped classical dispersion oscillators. In the disordered phase I T>128 degrees C, the picture of a relaxation type process coupled to an oscillator gives a good qualitative description of the spectra. The details of the spectra and their change in the transition to the ferroelectric phase III are consistent with Shinnaka's model (1962) of the structure of phase I.

The density of states (DS) of a disordered system with localised electronic states is studied in the vicinity of the Fermi level with the Monte-Carlo computer simulation for the two- and three-dimensional simple model. The minimisation of the total energy with respect to all one-electron transitions is shown to be a good approximation both for the total energy and for the DS. The electron-electron interaction drastically changes the DS in the vicinity of the Fermi level. The DS is shown to have a 'soft' Coulomb gap, and the self-consistent equation fits the results of simulation well. The finite size effect is also studied.

A strong divergence, observed in the relative oscillator strength of the molecular exciton in KCN_x-CKl_1-x, can involve an increase of two orders of magnitude for a nominal variation in the solution concentration x or temperature T. The theory demonstrates that this enhancement can be accounted for by a finite-frequency local field catastrophe of the form described by Lorentz and used to explain ferroelectricity. A crucial role is played by the background susceptibility at the exciton frequency, due to interband polarisability. It is suggested that the strong temperature dependence is connected with the ordering of the CN^- dipoles, which may serve to enhance the interband polarisability. A mean field theory for the phase transitions in pure KCN is also presented.

The longitudinal collective excitations of the electrons in a tightly bound insulator are studied using the dielectric matrix technique. It is found that the spectrum of excited electron-hole states changes radically as the electrons are increasingly tightly bound. A Frenkel exciton and a succession of charge transfer states are found, with the possibility of a plasmon. It is predicted that in electron energy-loss measurements, in practice, only the Frenkel exciton will be seen, and this seems to agree with present experimental evidence on molecular crystals.

Local field effects in semiconductors are studied through the inversion of the dielectric matrix in real space, using a Wannier function basis. The method will be useful when the translational symmetry is broken, e.g. where there are impurities, dislocations or surfaces. The method is applied to the calculation of the potential produced for a static impurity in diamond. The results show the importance of local field effects, which, in this case, appear as oscillations of the potential with the periodicity of the lattice.

Current peaks which appear in unirradiated and UV-irradiated BaF₂:Tb³⁺ crystals during heating from 80 to 400K were investigated. A peak which appeared at 195K without any previous optical excitation, when the crystal was heated in an external field, is attributed to a thermally stimulated polarisation current (TSPC), caused the the rotation of dipoles. After cooling to 80K in an external field and heating without an external field, two ionic thermocurrent (ITC) peaks were observed at 194 and 340K. It is shown that the ITC peak at 194K is due to the reorientation of dipoles, and that at 340K is attributable to the displacement of free interstitial fluorine ions. The effective polarisation temperature for the ITC measurements was found to be approximately 200K, even when the electrical field was applied at higher temperatures.

The dispersion relation for plasma waves, propagation at an arbitrary angle to an external magnetic field, has been calculated on the basis of the Vlasov equation. The energy bands are assumed to be multivalley, non-parabolic and non-spherical. The case of strong degeneracy of the electron gas has been analysed.

The distribution of spins and the thermodynamic properties of random Ising bond models are obtained by the use of the integral equation for the distribution function of the effective fields g(l). The integral equation is derived for a general case in a simple way by the use of the Bethe approximation. From the relation between the magnetisation and the effective field, the phase boundaries between the paramagnetic phase, the glass-like (spin glass) phase (GLP) and the ferromagnetic phase are obtained for the general distribution P(J). For a binary mixture with J_A=-J_B, z=3, the integral equation is solved by approximating g(l) by a superposition of the delta functions. The specific heat and the susceptibility have cusps at the temperature T_G, below which the glass-like phase appears.

USb is a simple type I antiferromagnet, but USb_0.9Te_0.1 shows most unusual behaviour. Studies have been undertaken on single crystals in an attempt to understand this behaviour. Below T_N=203+or-2K an ordering takes place with a wavevector k=(00k) that is nearly commensurate; k=²/₃- delta with delta =0.040 at T_N. At 160K a first-order phase transitions occurs to a commensurate phase k=²/₃. Magnetisation measurements in this phase given a saturated moment of 0.92 mu _B/U atom, which is a factor of three less than that found for USb (2.85+or-0.05 mu _B). The easy axis is <111>; the moments in the other principle directions are given by the cosine law. The only magnetic structure compatible with the present measurements is one described by three square-wave components propagating along the cube edges simultaneously.

The c axis thermal expansion of single-crystal Tb-50% Ho behaves anomalously at several specific temperatures in the antiferromagnetic phase, when the periodicity of the helical spin structure is commensurate with that of the crystal lattice. Mechanisms which may cause the hexagonal anisotropy to influence the lattice expansion are discussed.

Results of the combined EPR and luminescence measurements on white cloudy samples of fluorite, containing hexavalent and pentavalent uranium, are reported. The prevailing U⁵⁺ EPR spectrum, having very low symmetry, is analysed. Studies of the changes of the luminescence and EPR spectra in terms of gamma -dose give a direct proof that the main luminescent U⁶⁺ centre in fluorite has a trigonally distorted octahedral (UO₆^6-) structure. A discussion of the vibronic structure for two luminescent centres is given. The dependence of the luminescence amplitude on the frequency of the chopped pump light in a chronospectroscopic experiment is also interpreted.

Equations are developed for the ferromagnetic resonance condition which take into account the magnetoelastic energy as well as the usual magnetocrystalline energy. In the derivation it is recognised that the crystal lattice assumes a magnetostrictive strain appropriate to the equilibrium direction of the magnetisation, but that this lattice strain does not change in response to the high-frequency precession of the magnetisation. The predicted difference between the effective anisotropy constant measured by ferromagnetic resonance and the value deduced from torque measurements is several times smaller than was predicted by a previous treatment. Experiments on specimens of Co_0.25Mn_0.75Fe₂O₄ are at variance with an earlier report of a substantial difference between anisotropy constants measured by the two methods and the observed difference is certainly much smaller than the earlier theoretical treatment predicted.

The electrostatic polarisability of two-component composite media is studied theoretically using the integral equation method. The polarisability is expanded in terms of potential eigenfunctions. This makes possible the separation of the contribution due to the medium structure from the contribution due to the dielectric properties of the components. Methods of solution are discussed, and calculation of eigenmodes of regular structures are presented. The results are applied to the calculations of light absorption spectra of discontinuous thin films of noble metals.

The room-temperature direct allowed energy gap E_g=3.425 eV was obtained for single crystals of GeS₂ which have an orthorhombic structure. The far-infrared transmission spectrum was measured with unpolarised light in the range of 100-250 cm^-1. The reflectivity spectrum was obtained, also with unpolarised light, in the infrared region between 250 and 600 cm^-1. The reflectivity spectrum was analysed by Kramers-Kronig integration and optical parameters were calculated.

The reflectivity of magnetite (Fe₃O₄) has been measured in the spectral energy range between 0.03 and 12 eV. The optical constants have been determined by means of a Kramers-Kronig analysis. The interband transition spectrum can be interpreted by O 2p to Fe4s transitions and be Fe3dⁿ to 3d^n-14s orbital promotion processes including final-state effects of the atom-like 3d^n-1 configurations.

The following investigation concerns the identification of mechanisms responsible for the blue emission obtained with bismuth-doped lanthanum phosphate LaPO₄(Bi). Observations of absorption, excitation and fluorescence spectra, together with measurements of the decay time from liquid He up to room temperature are presented. The unexpected variation in the fluorescence decay time below 20K makes this sample particularly interesting compared with materials in which the emission and excitation processes could have been attributed to the so called 'bismuth-isolated centre' alone.

Bond lengths and coordination numbers of the nearest neighbours of the central Mn atom in solid KMnO₄ and MnO₄^- in a 0.4 molar aqueous solution have been determined from the extended X-ray absorption fine structure (EXAFS) above the Mn K-edge. In the solution the authors find one shell of four oxygen atoms with a distance of 0.1649+or-0.0005 nm from the central Mn atom. In crystalline KMnO₄ they observe a beating in EXAFS due to the superposition of contributions from two close-lying shells. A comparison of the phases and envelope functions of EXAFS of KMnO₄ and MnO₄^- yields a separation of 0.0125+or-0.0003 nm for these shells. With the bond length in the solution they find three closer oxygen atoms at a distance of 0.1634+or-0.0008 nm and one more distant atom at 0.1759+or-0.0008 nm.

Surface lattice relaxations at finite temperatures are studied on the basis of Verwey's model for rock-salt structured ionic crystals with an (001) surface plane, with particular reference to sodium halide crystals. The temperature dependence of the ionic displacements, mean-square displacements (MSD) and induced moments of the surface ions are obtained in the classical limit with the framework of the extended self-consistent Einstein model. The MSD of cations perpendicular to the surface is found to hardly exceed that of the bulk ions. Unless the degree of rumpling is small at T=0K, the rumpling becomes enhanced and the induced moments of the anions grow at finite temperatures. Brief discussions on the mechanisms of the rumpling are also given.

Photoemission energy distribution curves obtained from single crystals of UTe, UTe_0.12Sb_0.88 and USb in the photo energy range hv<11 eV are interpreted in terms of the densitites of states of the 6d and 5p bands. The fact that the 5f electrons do not contribute to the photoemission spectra is established by observing negative electron spin polarisation for ferromagnetic UTe. The emission intensity of the d states indicates a higher occupancy of the d conduction band for UTe, whereas in UTe_0.12Sb_0.88 and USb the p valence band shifts to lower binding energies and narrows considerably. The participation of 5f electrons in bonding is discussed.