Table of contents

We calculate the magnetization as a function of field for an Anderson impurity model for which the lowest configurations are f¹ and f², using the leading order 1/N expansion (where N is the orbital degeneracy). For most values of the valence, except those near two, we find a two-stage crossover in M(H). This is due to an unbinding of the many-body singlet, first to a partially screened magnetic state and then to the full f² moment. At small fields there is a positive deviation from linearity in M(H) near the integer valent limits which is characteristic of degenerate f⁰-f¹ models. This upturn disappears for intermediate values of the valence.

We present measurements of tunnelling conductances (at T=4.2 K) of point contact and planar junctions formed on sodium tungsten bronze single crystals as the carrier concentration is changed through the metal-insulator (MI) transition. We find that the junction conductance is varies as mod V mod ^1/2 on the metallic side, and that as the MI transition is approached, the voltage dependence becomes deeper and changes to a linear dependence ( varies as mod V mod ) in the critical region. We interpret this observed behaviour as being due to evolution of short-range screened Coulomb interactions (giving rise to a square-root cusp in the density of states) in the disordered metallic phase into an Efros-Shklovskii-type Coulomb gap in the insulating phase. The possibility of breakdown of normal Fermi-liquid-like behaviour in the critical region is discussed.

One-dimensional (1D) ballistic constrictions have been made in a two-dimensional electron gas of high carrier concentration (6.5 * 10¹¹ cm^-2) and high mobility (9.5 * 10⁵ cm² V^-1 s^-1) formed at the interface of a GaAs/AlGaAs heterostructure. At least seven ballistic conductance steps were clearly observed at 4.2 K and remained discernible up to 40 K. A 1D subband spacing of 10 meV was found from the electric-field-induced half plateaux in differential conductance. The mobility and carrier concentration of the two-dimensional electron gas were also measured as functions of temperature in order to compare the relative effects on the degradation of the ballistic quantization of Fermi-Dirac broadening at the Fermi energy and the reduction in the ballistic mean free path. The close similarity between the experimental conductance characteristics and those calculated with a simple assumption of the Fermi-Dirac electron energy distribution strongly suggests that this is the principle mechanism in smearing the quantized conductance plateaux.

We report the observation of a spin polarization phase transition of the ⁴/₃ fractional quantum hall state of a high-mobility 2D hole system in a GaAs-(Ga, Al)As heterostructure. Mobilities in excess of 1000000 cm² V^-1 s^-1 are achieved at a density of 0.86 * 10¹¹ cm^-2. The depth of the ⁴/₃ minimum is seen to weaken as the carrier density is increased before disappearing completely. Upon further increase in carrier density the ⁴/₃ minimum is re-entrant and proceeds to strengthen. The ⁸/₃ and ⁷/₃ states are observed to show apparently anomalous behaviour.

The abrupt discontinuity of the background in the semi-infinite jellium results in a decaying oscillatory (Bardeen) spatial response of the electron gas. Related phenomena are the Friedel oscillations around an impurity in a metal, and the Ruderman-Kittel coupling between two localized magnetic moments embedded in a sea of conduction electrons. We have found that the ¹⁰⁹Ag (I= 1/2 ) NMR linewidth in nanometre-sized supported (and therefore isolated) silver particles shows a size effect that may be due to Bardeen-Friedel oscillations. The linewidth is also temperature dependent, in a way that cannot easily be explained as an effect of paramagnetic impurities; we suggest that thermal vibrations, known to have comparatively large amplitudes in small particles, wash out the abruptness in the background-charge discontinuity, and thus diminish the amplitude of the oscillations.

The effect of pressure up to 5.5 GPa on the magnetic behaviour of Gd₂Fe₁₇ has been investigated using the ⁵⁷Fe high-pressure Mossbauer effect technique. We show that the decrease of the average magnetic hyperfine field at 300 K can be well explained by the decrease of Curie temperature with pressure, while the Fe local magnetic moment remains almost stable in this pressure range. The decrease of the isomer shift with increasing pressure indicates a corresponding increase of the s-electron density at the ⁵⁷Fe nucleus, which is mainly caused by the volume compression of the 4s conduction electrons.

We study the domains in an ultrathin magnetic layer with perpendicular magnetization as a function of temperature. The domain spacing is given by the balance between the interface energy and the demagnetizing energy. The demagnetizing energy is calculated in a continuum theory which is valid provided that the domains are large compared with the lattice spacing. The temperature dependence of the interface energy arises from the entropy of the rough walls. This is obtained from the exact results for the two-dimensional Ising model. We predict that the domain size shrinks rapidly as the temperature is raised towards the transition.

The intensity of Bragg reflections depends strongly on the angle of incidence, if a highly collimated beam of X-rays is impinging at grazing incidence on a thin (200-600 AA) polycrystalline antimony layer. In the case of asymmetric grazing incidence diffraction (AGID) the angle of incidence is small, as the exit angle must be large and nearly twice the Bragg angle. The experimental data are analysed on the basis of the distorted wave Born approximation (DWBA), which yields the thickness d and the optical constants delta and beta of the layer. These parameters are compared with those determined from total external reflection data.

We present a high-resolution synchrotron X-ray diffraction study of xenon adsorbed on single-crystal graphite for coverages of two, three and six monolayers. We observe the evolution of the lattice mismatch between the xenon overlayer and a square root 3* square root 3R30 degrees structure commensurate with the underlying substrate. In the case of the bilayer we see a first-order incommensurate-commensurate (IC-C) phase transition at 62.0 K+or-1.2 K, which we demonstrate is consistent with the layer closest to the substrate having locked into the commensurate sites. The role of substrate quality is discussed and we conclude that previous studies on relatively poorer substrates may have favoured equilibrium structures strongly influenced by the surface imperfections. The risk of an insufficiently equilibrated adsorbate is discussed in the context of the very slow kinetics we observe for multilayer xenon on high-quality substrates. For the three- and six-layer adsorbates we observe a systematic increase in lattice mismatch with film thickness and no indication of an incommensurate-commensurate transition. We conclude that the trilayer system consists of many distinct domains approximately 500 AA across, each of which has a random close packed structure.

We present an exact numerical method for obtaining the variation in the density of states associated with the adsorption of wires on a flat surface and with channels cut into an otherwise planar surface. This general method is presented for the determination of the resonances of shear horizontal polarization associated with such surface protuberances or indentations.

Momentum densities of annihilating electron-positron pairs, positron lifetimes, work functions and binding energies as well as electron-positron enhancement factors at the surfaces of simple metals and cadmium are studied. The effect of electron-positron correlations on the surface-state positron annihilation characteristics is set out.

A one-step photoemission calculation scheme for valence electrons is presented which uses (to construct the initial- and final-state wavefunctions) the multi-slice technique, which has been developed for low-energy electron diffraction (LEED). Included in the scheme is the possibility of having an over-layer or an arbitrarily shaped surface barrier, and realizing both the electron and hole life-times by means of an imaginary part to the energy. The photoemission intensity due to surface states can also be calculated separately by the same procedure. The advantage of the scheme is that because the crystal potential is divided into arbitrarily thin slices, problems associated with the frequency used muffin-tin potential do not arise.

A numerical investigation of the single-particle energy spectrum of two-dimensional electrons subject to a periodic potential of square symmetry and a perpendicular magnetic field is presented. Our approach allows variation of both the steepness and the strength of the modulation potential. It is shown that the inclusion of coupling between different Landau levels has a strong impact on the appearance of the subband structure. The possibility of finding experimental indications of the spectrum is discussed in the light of the present calculations.

The reflection of light from a medium with ordered spin structure characterized by the breakdown of time-reversal and parity symmetry is expected to be non-reciprocal even if the net magnetic moment of the medium equals zero. We report on the first experimental observation of spontaneous non-reciprocal rotation and circular dichroism in spin magnetoelectric Cr₂O₃. Non-reciprocal effects were observed below the antiferromagnetic transition temperature T_N=307 K and their temperature behaviour roughly corresponds to that of the order parameter. Observed values of (1-4)*10^-4 for the magnetoelectric susceptibility in the optical range are several orders of magnitude higher than predicted earlier. This increase of the susceptibility is presumably attributable to electronic dipole transitions in the optical range.

The electron density distribution of HCP (hexagonal close-packed) metal Mg is obtained for the first time by the maximum entropy method (MEM). The data used in the analysis are measured by a newly developed synchrotron x-ray powder diffraction with an imaging plate (IP) as a detector. Care is taken in the quality of the specimen and the high counting statistics of the measurement. In the MEM map of Mg, which is the electron density distribution map obtained by the MEM, a surplus of electron charge is seen around the tetrahedral sites (T sites) of the HCP structure, while the electron densities around the octahedral sites (O sites) are much less than the average density of inter-atomic sites. By these surplus electrons, Mg metal forms a honeycomb network in the base plane and shows a kind of electronic layer structure. Since there are no ambiguities of phase determination, it can be said that the MEM map of Mg is constructed purely depending on the experimental data and free from any structural models. In our previous work the same kind of honeycomb network was found in Be, which is also an HCP metal. There is a high possibility that such honeycomb network is one of the structural characteristics of pure HCP metals at the electronic level. More work has to be done to investigate such a possibility and the MEM analysis will play an important role in structural studies at the electronic level.

We present a tight-binding model for the electronic structure of solid C₆₀ using four (one 2s and three 2p) orbitals per carbon atom. The model has been developed by fitting the tight-binding parameters to the ab initio pseudopotential calculation of Troullier and Martins (1992) in the face-centred cubic (Fm3) phase. Following this, calculations of the energy bands and the density of electronic states have been carried out as a function of the lattice constant. Good agreement has been obtained with the observed lattice-constant dependence of T_c using McMillan's formula. Furthermore, calculations of the electronic structure are presented in the simple cubic (Pa3) phase.

A short-range electron-phonon (e-ph) interaction is considered in a many-electron narrow-band system where electron hopping is comparable with the phonon frequency. The behaviour of the polarons as a function of the e-ph interaction strength and the electron concentration is studied within the framework of the mean-field theory using a modified Lang-Firsov transformation and two-phonon coherent states of the phonon subsystem. The small-to-large-polaron transition and the effect of the two-phonon coherent state are discussed.

Some common trends observed in the temperature variation of the thermoelectric power (TEP) of high-T_c materials are theoretically analysed. In the first part of the analysis, we calculate the dominant effect of superconducting fluctuations on TEP, assuming that the conduction process occurs in two dimensions. In the second part of the analysis, we show that, by including the self-energy proposed in the marginal Fermi-liquid hypothesis along with that arising from superconducting fluctuations, one can understand the main features of the temperature variation of TEP. The magnitude of TEP given by the formula derived here is also of the right order.

We present an analytical quantum statistical theory of giant magnetoresistance in magnetic multilayers (current flowing in the plane of the layers) which takes into account both spin-dependent scattering of conduction electrons (s, d or hybridized sd electrons) and spin-dependent potential barriers between successive layers. The model also includes quantization of the momentum of conduction electrons in the direction perpendicular to the plane of the layers (k_z). The influence of the following parameters is discussed: ratio of spin-up to spin-down mean free paths, height of potential barriers between adjacent materials and thicknesses of the various layers. It is shown that the main contribution to the giant magnetoresistance is spin-dependent scattering rather than spin-dependent potential barriers. In fact, if the mean free paths of spin-up and spin-down electrons in the magnetic material are significantly different, the presence of potential barriers (spin-dependent or not) can only decrease the magnetoresistance amplitude. Furthermore, the quantization of component momentum k_z leads to well-defined oscillations of magnetoresistance with respect to thicknesses of the various layers. It should be possible to observe these quantum oscillations experimentally.

We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between v_sigma q and v_rho q, where v_sigma and v_rho are the velocities of spin and charge fluctuations, while spectral weight above v_rho q and below -v_{rho q} is generated by the hybridization of the Fermi surface at +or-k_F by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.

We have calculated the critical exponent of the metal-insulator transition for a three-dimensional network of random wires. The Hamiltonian of this model is not explicitly defined, and so we do not bias our results towards the models with diagonal or off-diagonal disorder, which produce conflicting exponents. The result is s= nu =1.10+or-0.05, which is in agreement with other models using tight-binding Hamiltonians with off-diagonal disorder. We suggest that pure wave interference is not the dominant mechanism for Hamiltonians with diagonal disorder and therefore some other physical process must be responsible for generating exponents of s= nu approximately=1.5.

We consider an optically excited semiconductor as a coherent system of interacting excitons and photons. Within the boson formalism and secular approximation the analytical expressions for the exciton quadrature variances are rigorously derived. The analysis of these variances over the relevant parameter space shows that initially coherent excitons can evolve into squeezed states in a finite-size semiconductor, which must possess both linear and non-linear interactions.

Polarized absorption spectra of Eu³⁺ in single-crystal LiYF₄ have been recorded at 298 K and 77 K in the region from 3900-39000 cm^-1. Symmetry assignments have been made in both D_2d and S₄. Calculated energy levels are obtained by diagonalizing a parametric Hamiltonian that describes the free-ion and crystal-field interactions in a basis of states spanning the 4f⁶ electronic configuration of Eu³⁺. J mixing was taken into account.

This paper presents simulation results on the dynamics of 2D arrays of ultrasmall normal tunnel junctions at finite temperature, focusing on the possible Kosterlitz-Thouless-Berezinskii transition of charge unbinding. In the case of an array with zero self-capacitance, we find a reasonable agreement between simulation results and the theory. We perform finite-size scaling analysis for linear and non-linear conductances. We also study the effects of self-capacitance and random fractional offset charges, which may be relevant to the experimental situation. In both cases, linear conductances show activated behaviour. A random charge distribution with relatively strong disorder could explain the experimental values of the activation barrier energies.

The electron mean free path L in the normal state and the critical temperature T_c as well as the parallel critical magnetic field H_c// and perpendicular critical magnetic field H_{c perpendicular to} were measured in equilayered Cu/Pb modulated films. The modulation period lambda varied from 59 to 1620 AA. Our films were fabricated by thermal evaporation. The electron mean free path in the component layers estimated following the Gurvitch model is markedly shortened as a result of electron scattering both at interfaces and at grain boundaries. The dependence of T_c on component layer thickness was compared with existing theoretical models. Our measurements of the parallel critical fields as a function of temperature revealed the crossover of superconductivity from three-dimensional to two-dimensional behaviour.

The variational wave function proposed by Bartkowski (1972) to treat the ground state of a quantum antiferromagnet is generalized to arbitrary spin. We derive the fundamental equations of this method for the energy and magnetization by using a local cluster expansion. The leading order corrections to the wave function in the limit of either large spin S or lattice dimension D are identified. The good quality of the wave function is confirmed by the ground state energy of E₀ = -0.3340J obtained for the Heisenberg S = 1/2 antiferromagnet on the square lattice. We present results obtained for the system of two planes and for three-dimensional SC and BCC lattices, as well as for the three-dimensional anisotropic Heisenberg model. It is found that the quantum fluctuations in a two-plane system are already closer to a three-dimensional than to a two-dimensional antiferromagnet while a weak interplane coupling in the latter case hardly influences the nearest-neighbour spin correlations within the planes.

The electronic structure of PrNi₅ was calculated using the full potential LAPW method. On this basis the crystal-field parameters were determined and compared with experimental results. The electric field gradient at the Pr nucleus site was also calculated. The problem of the existence of Ni magnetic moments is challenged.

Incoherent Kondo effects have been observed in Ce_xSi_100-x (x = 18, 53, 66 and 87) amorphous alloys produced by sputtering. They show large enhancement of the electronic specific-heat coefficient at low temperatures, being classified as heavy-fermion systems. The magnetic susceptibility reveals a Curie-Weiss law at T>100 K with an effective Bohr magneton number of above 2.45 mu _B. However, the electrical resistivity is large, revealing a Kondo-type logarithmic temperature dependence. The atomic randomness prohibits the coherent Kondo state and the formation of a magnetically ordered state in the Ce-Si amorphous alloys.

Nd³⁺-doped LaF₃, LiYF₄, CsY₂F₇, BaY₂F₈ and BaF₂ crystals were investigated. For scintillator applications, the characteristics of the fast Nd³⁺ 4f²5d to 4f³ emission component is of interest. The effective 4f²5d to 4f³ scintillation decay time under gamma irradiation was found to vary from 5 to 42 ns, depending on the host lattice. Light yields were determined under X-ray excitation. The 4f²5d to 4f³ output from many samples was seriously affected by impurity absorptions. After correcting for these, an estimate was made of the maximum possible 4f²5d to 4f³ light yield to be expected in very pure Nd³⁺-doped crystals. In neither of the cases was a 4f²5d to 4f³ light yield of more than about 1000 photons per MeV of X-ray energy found. In addition to Nd³⁺ 4f²5d to 4f³ emission, Nd³⁺ 4f³ to 4f³ and host emissions were also recorded at wavelengths shorter than 550 nm. A semi-quantitative model is given for the Nd³⁺ 4f²5d to 4f³, 4f³ to 4f³ and host emission intensities.

We describe a semiclassical approach to estimating the absorption of electromagnetic radiation by small conducting spheres, in which the motion of the charge carriers is ballistic. The results are strikingly different between the cases of rough and smooth walled particles. For a rough walled particle the absorption coefficient is proportional to omega ² in the low-frequency limit. For a smooth walled sphere the absorption coefficient has a low-frequency cut-off at omega _c, the angular frequency of a circumferential 'whispering gallery' classical orbit of a carrier at the Fermi surface. At frequencies above omega _c the spectrum consists of a sequence of overlapping resonance bands which combine to give an absorption coefficient proportional to omega ₂ only for omega >> omega _c.