Table of contents

The disparity in the masses of the atomic constituents of GaN means that the usually-assumed mode of decay of a long-wavelength LO mode into two LA modes is forbidden. However, given the available information about the phonon spectrum, it appears that a possible decay route is provided by the emission of a TO and an LA phonon.

Local alignment of a conduction electron's spin with core spins caused by strong ferromagnetic coupling imposes a severe restriction on the Hilbert space. This is incorporated in a representation in which the electron is a composite object. Within a mean-field approximation we find a transition from a ferromagnetic metal to a paramagnetic state at a temperature , the Fermi temperature, i.e., there is a separation of energy scales. The electron Green function exhibits a two-fluid character: a Fermi liquid component associated with the ordered spins which disappears above , and an incoherent component with disordered spins which breaks particle-hole symmetry. Implications for manganites, which exhibit very large magnetoresistance, are discussed.

The Jahn - Teller (JT) system has been studied previously by many authors. It is well known that the potential energy surface for this system contains four equivalent wells in strong coupling. The wells are not isotropic. In the strong coupling limit, the vibrational t-mode splits into an -mode of frequency and an e-mode of frequency . However, it is difficult to incorporate this anisotropic effect into analytical models. Previously, the current authors have used a unitary shift transformation and energy minimization procedure to model many moderately to strongly coupled JT systems. However, the part of the Hamiltonian which produces the anisotropy was not treated fully. We now present a modification of this procedure for the system in which a scale transformation is applied in addition to the shift transformation. This is shown to introduce anisotropy automatically into the problem. We show that the correct frequencies are obtained in the infinite coupling limit. Symmetry-adapted combinations of the states associated with the wells are taken to obtain expressions for the ground state and inversion level. The inversion splitting between them is compared with existing results. We then discuss how the scale transformation method can be applied to other JT systems (for which the limiting frequencies are unknown), such as those in the symmetry which applies to the molecule.

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behaviour is explained, critical exponents are introduced and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behaviour under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.

We have systematically studied the behaviour of the absorption bands due to the O - H bond-stretching vibration and its polarization characteristics in with the use of well characterized crystals. It has been found that the O - H bond-stretching vibrational frequencies, , have a strong correlation with Nb concentration in the crystals as in the case of MgO-doped . The values of shift to the higher-frequency region when the Sc concentration in the crystal exceeds about 2.5 mol%. The magnitude of the frequency shift is smaller and the polarization dependence of the absorption bands due to is weaker in -doped than in MgO-doped . These features are attributed to the difference of the charge between and . We have also proposed an ideal defect structure model for -doped , which is based on the Li-site vacancy model as an intrinsic defect structure model. The observed behaviour of is consistently explained by the proposed defect structure model. This supports the justification of the extrinsic defect structure model based on the Li-site vacancy model for -doped as well as for MgO-doped .

The thermal dependence of the relaxation, order and segregation in the vicinity of a tilt grain boundary in the binary alloy is investigated by means of computer simulation with an empirical N-body potential. Energy minimization is performed in order to estimate the particularly strong relaxation effects in the vicinity of the boundary plane at 0 K. Monte Carlo simulations are carried out for constant chemical potential, number of particles, volume and temperature in order to study the thermal properties of the system. Detail is provided plane by plane, parallel to the boundary, which characterizes the temperature dependencies of the order, segregation, sublattice occupancy and relaxation. The vicinity of the boundary remains strongly affected by atomic relaxation and segregation at all temperatures, although no simple relation between relaxation and segregation is found. The evolution of long-range order and sublattice occupancy are strikingly different in the close vicinity of the boundary plane to those in the bulk. The boundary plane is fully disordered at all temperatures between and , where is the bulk temperature for the order - disorder phase transition. The transition to bulk properties with distance from the boundary is characterized quantitatively.

The influence of the potential model is emphasized by means of a comparison between the results obtained with two somewhat different N-body potentials of similar nature.

The specific heat for AgI-doped CuI has been measured by the method of differential scanning calorimetry. Anomalous specific heats were observed around the transition temperature from non-superionic to superionic phases. These were well explained in terms of the Schottky-type excess specific heat.

The specific heat C of amorphous films was investigated between 0.3 K and 7 K in the superconducting state as well as in the normal state using a modified AC method. The analysis of the data allows one to determine the electronic density of states at the Fermi energy , the density of states of low-energy excitations and the Debye temperature . The concentration dependence of shows a pronounced minimum at x = 60 at.% in comparison to the free-electron model, in agreement with specific heat and UPS measurements and theoretical calculations published recently. The specific heat of the low-energy excitations is of the same order of magnitude as data available from the literature, and shows a linear temperature dependence. increases with copper concentration and the values agree with those published recently.

In addition, the critical magnetic field of the same films was measured. The analysis of these data which should be valid for strongly disordered superconductors yields values of which are about 20% higher than those determined by specific heat measurements. Arguments are given as to why values taken from critical field measurements might be too high.

Finally, the specific heat of an amorphous film was measured. was found to be 30% below the free-electron model value, in contrast to results published previously by Rieger and Baumann who found to be in accordance with the free-electron model.

We present here details of a density-functional-based non-orthogonal tight-binding approach for germanium. This is carried out within the framework of the LCAO ansatz, using a two-centre approximation for the evaluation of the Hamiltonian matrix elements. The Hamiltonian and overlap matrix elements for Ge - Ge, Ge - H are derived using a localized atomic basis set and existing parameters for H - H are utilized. These are tested against results from existing experimental and theoretical data for bulk germanium and germanium surface reconstructions, both with and without hydrogen. In addition we generate the first fully self-consistent ab initio LDA results for small Ge clusters and Ge - H molecules using the AIMPRO program and compare DF-TB results against these. Finally we describe our study of H point defects in bulk germanium. These are the first calculations of this type done on Ge using large fully optimized supercells and confirm self-consistent ab initio calculations done on small clusters. We consequently demonstrate that, despite the extreme simplicity of the approach, it is accurate and highly transferable across a broad range of structural systems ranging from clusters to the bulk phase.

The electronic structures of the ternary alloys Ru - Mn - Z (Z = Si, Ge and Sn) were calculated to examine the relationship between the magnetic properties and the atomic configurations. It will be shown that two types of antiferromagnetic phase are stable for three types of configuration of those alloys, where the Mn magnetic moments are aligned ferromagnetically in the (100) (or (111)) plane and antiparallel along the [100] (or [111]) direction. It will also be shown that Ru - Mn - Z (Z = Si and Ge) can be half-metallic in a ferromagnetic phase.

Spin-polarized MS - and self-consistent charge extended Hückel calculations on as a function of the Cr - distance R have been carried out in order to clarify the origin of the bands detected in the vacuum ultraviolet excitation spectrum of associated with charge-transfer (CT) transitions as well as what electronic orbitals are involved in the jump. With the help of results on other 3d impurities it is explained that the two first transitions peaked at 8.0 and 8.7 eV are the and CT transitions while other transitions involving at least one-orbital without bonding would display a smaller oscillator strength. It is shown that the two referred transitions both exhibit a strong dependence on R ( being about ) whose microscopic origin is explained. Using this R dependence an explanation of the experimental band width W of a CT transition is attempted for the first time. The present analysis indicates that W can be understood simply considering the coupling with the mode, leading to a Huang - Rhys factor S = 20. Also it is pointed out that CT transitions involving the orbital would give rise to a significant decrement in S.

The present results together with experimental data on other 3d complexes indicate that the transitions (where is and ) are probably contained in the broad third band peaked at 12 eV. Also they shed some light on the experimental results of other systems such as and which are briefly discussed.

A study is made of the stability of the possible lattice structures which result from the magnetic-field-induced lattice deformation introduced by Araujo and Khmelnitskii. The deformed lattice may either be the result of a single distortion occurring along a particular direction or of a superposition of distortions in different directions. In a noninteracting electron model the energy variation of the electron system will determine which final lattice structure is the most stable. When electron interactions are considered in the Hartree approximation we find that the energy variation of the electron system alone will not determine which final structure is the most stable. The latter is then imposed by the lattice itself. If the distortion turns out to be unidirectional then the corresponding charge-density wave should be weakly pinned even in the absence of impurities.

We study propagation of excitations in one-dimensional tight-binding chains doped with random impurities that are classical Einstein oscillators. We find that the presence of impurities does not affect substantially the ballistic nature of the electronic propagation. Furthermore, for some oscillator masses, wave propagation is faster than that of the ordered tight-binding chain.

A model of hybridized bosons and fermions is studied beyond the mean-field approximation. The divergent boson self-energy at zero temperature makes the Cooper pairing of fermions impossible. The frequency and momentum dependence of the self-energy and the condensation temperature of initially localized bosons are calculated analytically. The value of the boson condensation temperature is below 1 K and the long-wave spectrum is strongly damped which rules out the boson - fermion model with the initially localized bosons as a phenomenological explanation of high-temperature superconductivity. The intra-cell density - density fermion - boson interaction dominates in the fermion self-energy. The model represents a dirty normal metal, in which localized bosons play the role of impurities.

The critical behaviour of non-linear susceptibility of a two-component composite is studied in this paper. The first component of fraction p is non-linear and obeys a current - field (J - E) characteristic of the form while the second component of fraction q is linear with . Near the percolation threshold or , we examine the conductor - insulator (C - I) limit and superconductor - conductor (S - C) limit . For the C - I limit and , the effective linear and non-linear response functions behave as and , respectively. For the S - C limit and , and are found to diverge as and . Within the effective-medium approximation, the exponents are found to be s = t = 1 and , and . By using a connection between the non-linear response of the random non-linear composite problem and the resistance or conductance fluctuations of the corresponding random linear composite problem, the exponents and are found to be , , respectively, where t(s) is the conductivity exponent in a C - I(S - C) composite, d is the dimension of the composite and is the correlation-length exponent in d dimensions, and are given by , , where characterizes the scaling of the th cumulant of the global resistance (conductance) distribution due to local resistance (conductance) fluctuations in the corresponding linear C - I(S - C) composites, and . We prove that is a monotonically increasing function of while is a monotonically decreasing function of , which have the following special values: and ; and ; and . The critical behaviour of the non-linear susceptibility in a C - I composite is very different from that of the non-linear susceptibility in a S - C composite and some unexpected results of the critical behaviour of non-linear susceptibility in a C - I network are reported in this paper.

The linear magnetostriction has been measured in the intermetallic compounds. The Zener power law, which gives as proportional to the third power of the reduced magnetization, is found to be valid in the ferromagnetic phase of . For x < 1 the compounds are weak random anisotropy magnets, and in the quasisaturated regime induced by a magnetic field is still proportional to , but the exponent p is smaller than three. p increases with the field and approaches three in the high-field limit (12 T). A relation between the violation of the Zener power law and the reduction of the magnetization in the random anisotropy systems is derived, and is compared with the experimental results.

Utilizing the state-independent projection technique, we obtain a general formula for the cyclotron-transition linewidth for anisotropic deformation potential phonon scattering. The formula is applied to calculate the width in Ge at low temperatures. It is shown that the transition between the two lowest adjacent Landau levels makes the most contribution to the temperature and the magnetic field dependence of the width, and the result agrees better with the experiment as the higher-order contributions are included. The width increases with the magnetic field, implying that the interaction of electrons with acoustic phonons increases with the field.

Muon spin-rotation - relaxation experiments were performed at low temperature in transverse, zero and longitudinal field on , , and as an extension of our previous studies of the CeTSn (T = Ni, Pt, Pd) series. In CeNiSn we have proven the formation of weakly dynamic paramagnetic spin correlations, below 1 K which, however, do not lead to long-range magnetic order even at T = 10 mK. For the predicted heavy-hole gas antiferromagnetism is not seen, but rather a reduction of magnetic correlations. Both Pt-doped compounds exhibit no significant enhancement of spin correlations although CePtSn is an antiferromagnet with . The magnetic correlations increase strongly for up to the point of forming a spin - glass-like state at T < 0.9 K. Doping with either 20% Pt or 10% Cu increases the unit cell volume by roughly 1%. Volume expansion in CeTSn is a known cause for a reduction of the hybridization between f electron states and conduction electrons, thereby strengthening magnetic interactions. Yet, the marked differences in magnetic behaviour between replacing Ni in part by either isoelectronic Pt or by Cu, which has two more d electrons, indicates that the dominating effect must be the increase of the d electron density instead.

A model for ferroelectric relaxors such as PMN, PSN and PLZT giving a quantitative description of their properties and phase diagrams is proposed within the framework of the random field theory. In this model, the relaxors are considered as systems with random sites and orientations of electric dipoles, lattice vacancies, antisite ions and other defects as well as impurities embedded into the paraelectric phase, which is proposed to be the `host' lattice for these materials.

The calculations of the temperature which corresponds to the transition from the paraelectric to the ferroelectric phase is carried out as a function of the concentration of lattice defects (point charges and dilatational centres). On the basis of these calculations, the peculiarities of the ferroelectric relaxor phase diagram are discussed. The main features of the phase transition sequence when decreasing the temperature in relaxors with constant dipole and defect concentrations are described.

The Cross superparaelectric model and Burns temperature have been shown to appear in a natural way in the proposed model.

A comparison between calculated and experimental data has been made for the model ferroelectric relaxor PLZT x/65/35. Fairly good agreements between calculated and measured and critical concentrations of lanthanum have been obtained from the model.

From the analytical properties of the third-harmonic generation susceptibility and from its asymptotic behaviour in the frequency variable, a set of eight Kramers - Kronig relations and nine sum rules are obtained. These universal constraints are used to generate a simplified model for the static limit of in insulating systems with inversion symmetry. The static limits of calculated within this model for silicon and germanium are shown to be in qualitative agreement with the experimental data.