Table of contents

The identification of magnetic quantum critical points in heavy fermion metals has provided an ideal setting for experimentally studying quantum criticality. Motivated by these experiments, considerable theoretical efforts have recently been devoted to re-examining the interplay between Kondo screening and magnetic interactions in Kondo lattice systems. A local quantum critical picture has emerged, in which magnetic interactions suppress Kondo screening precisely at the magnetic quantum critical point (QCP). The Fermi surface undergoes a large reconstruction across the QCP and the coherence scale of the Kondo lattice vanishes at the QCP. The dynamical spin susceptibility exhibits ω/T scaling and non-trivial exponents describe the temperature and frequency dependences of various physical quantities. These properties are to be contrasted with the conventional spin density wave picture, in which the Kondo screening is not suppressed at the QCP and the Fermi surface evolves smoothly across the phase transition. In this article we discuss recent microscopic studies of Kondo lattices within an extended dynamical mean field theory (EDMFT). We summarize the earlier work based on an analytical -expansion renormalization group method, and expand on the more recent numerical results. We also discuss the issues that have been raised concerning the magnetic phase diagram. We show that the zero-temperature magnetic transition is second order when double counting of the Ruderman–Kittel–Kasuya–Yosida interactions is avoided in EDMFT.

The density profile and order parameter of a fluid of hard axially symmetric ellipsoids confined in between two parallel hard walls is obtained by using the density functional theory. The required input direct correlation function of the homogeneous fluid is calculated by the variational method introduced by Marko (1989 Phys. Rev.39 2050) and the modified closest approach method proposed by Rickayzen (1998 Mol. Phys.95 393). Here the restricted orientation model, ROM, is extended to study a fluid comprising molecules which can be aligned in more than six directions, making it more representative of a normal fluid. The density profiles, the average number density and order parameter are obtained for different values of density and elongations. The results are in agreement with the previous theory and available Monte Carlo simulation results.

Diluted solutions of a single, electrically charged polymer chain, its monovalent counterions and two kinds of multivalent salts are investigated. In particular, the influence of the salt concentrations and valences on the mean effective charge per monomer, total inner energy, radius of gyration and various pair correlation functions of the monomers and free ions are analysed. The calculations show that it is the four-valent and three-valent ions, oppositely charged to the monomers, that mostly occupy the space around the polymer and tremendously increase their number there compared to that in the bulk. Furthermore, reductions in the polymer size and effective charge per monomer appear, especially for increasing amount of the four-valent salt. Thus, there is an evidence for polymer conformational changes associated with the ion condensation onto the chain.

Co₄₃Fe₂₀Ta_5.5B_31.5 bulk glassy alloy has the best glass-forming ability (GFA) among the Co-based glassy alloys, and the highest strength (the compressive true strength σ_f = 5185 MPa) among all known bulk crystalline and glassy alloys. With the aim of synthesizing new Co-based bulk glassy alloys with much higher strength and much larger GFA, we investigated the effect of Mo and Si additions on the enhancement of σ_f and GFA in the Co–(Fe, Mo, Ta)–(B, Si) system. The small amount of 2 at.% Mo added to the Co–Fe–Ta–B glassy alloy resulted in obtaining an ultrahigh true fracture strength of 5545 MPa and high Young's modulus (E) of 282 GPa. By further adding 1 and 2 at.% Si, Co–(Fe, Mo, Ta)–(B, Si) bulk glassy alloys were synthesized in the diameter range up to 3 mm, and they exhibited σ_f of over 4450 MPa and E of over 227 GPa. In addition, the ultrahigh-strength glassy alloys simultaneously exhibited excellent soft magnetic properties, i.e., saturation magnetization of 0.32–0.35 T, low coercive force of 0.7–1.1 A m⁻¹, and high effective permeability of 3.9–4.77 × 10⁴ at 1 kHz. The improvement of GFA and σ_f is interpreted to result from the enhanced atomic bonding nature by adding Mo and Si.

We have reported the dc conductivity as well as the ac conductivity in the frequency range 10 Hz–2 MHz for xAgI–(1− x)(0.5Ag₂O–0.5MoO₃), glass-nanocomposites in the temperature range 100–303 K. We have compared the conductivity and its activation energy for the molybdate nanocomposites with those of the borate and phosphate glasses. We have analysed the ac conductivity using the power law model. We have observed that both the dc conductivity and the crossover frequency obtained from the power law model show an activated behaviour. We have also observed that the power law exponent is almost independent of AgI doping content. Furthermore, the concentration of the mobile Ag⁺ ions is found to be independent of temperature as well as the AgI content in the compositions.

I investigate superconducting states in a quasi-2D Holstein model using the dynamical cluster approximation. The effects of spatial fluctuations (non-local corrections) are examined and approximations neglecting and incorporating lowest order vertex corrections are computed. The approximation is expected to be valid for electron–phonon couplings of less than the bandwidth. The phase diagram and superconducting order parameter are calculated. Effects which can only be attributed to theories beyond Migdal–Eliashberg theory are present. In particular, the order parameter shows momentum dependence on the Fermi surface with a modulated form and s-wave order is suppressed at half-filling. The results are discussed in relation to Hohenberg's theorem and the Bardeen–Cooper–Schrieffer approximation.

We performed two-dimensional molecular dynamics simulations of cohesive discs under shear. The cohesion between the discs is added by the action of springs between very next neighbouring discs, modelling capillary forces. The geometry of the cell allows disc–disc shearing and not disc–cell wall shearing as is commonly found in the literature. Does a stick–slip phenomenon happen though the upper cover moves at a constant velocity, i.e. with an infinite shearing force? We measured the forces with which the discs acted on the upper cover for different shearing rates, as well as the disc velocities as a function of the distance to the bottom of the cell. It appears that the forces measured versus time present a periodic behaviour, very close to a stick–slip phenomenon, for shearing rates larger than a given threshold. The discs' collective displacements in the shearing cell (back and ahead) are the counterpart of the constant velocity of the upper cover, leading to a periodic behaviour of the shear stress.

Samples of n-type CdGeAs₂ were produced by intentional doping with indium, selenium, or tellurium impurities. A near-edge photoluminescence (PL) band from heavily In-doped CdGeAs₂ samples shifts to higher energy and becomes broader with increasing electron concentration. The observed shifts in peak energies are compared to predictions for donor–acceptor pair and free-to-bound (electron–acceptor) recombinations including band filling, band tailing, and band gap shrinkage effects due to the high doping levels. For n>2 × 10¹⁸ cm⁻³, the free-to-bound PL transition related to a shallow 120 meV acceptor level is dominant. A lower energy PL band due to deep acceptors and normally seen for p-type samples is the only emission observed from less n-type samples (n∼10¹⁶–10¹⁷ cm⁻³) doped with indium, selenium, or tellurium impurities. Transitions involving the deep acceptor level are not present in the PL for heavily In-doped CdGeAs₂ crystals, which suggests that the deep acceptor may be a Cd vacancy.

The optical and vibrational properties of bare and CdS shelled CdSe nanocrystalline particles are investigated. To confirm the formation of such nanocrystals in our samples we estimate their average particle sizes and size distributions using TEM measurements. From the line profile analysis of the HRTEM images the core–shell structure in the particles has been confirmed. The blue shift in the optical absorption spectra, analysed using theoretical estimates based on the effective bond order model, establishes the electron confinement in the nanoparticles. The main aim of this paper is to show the unique characteristics of the nanocrystals (which are absent in the corresponding bulk material), such as confinement of optical phonons and the appearance of surface phonons. Making use of the dielectric continuum model we are able to match the experimental and theoretical values of the frequencies of the surface phonons. We believe that our studies using optical probes provide further evidence for the existence of core–shell structures in CdSe–CdS type materials.

The macroscopic symmetry of Pb(Mg_1/3Nb_2/3)_1−xTi_xO₃ (PMN–PT) crystals with x = 0.25–0.5 has been studied by optical microscopy. Precise data on the temperature dependence of the birefringence and optical extinction directions have been obtained. Two different low-symmetry phases separating rhombohedral and tetragonal phases have been observed in the compositional range x = 0.3–0.47. The optical extinction in the range x = 0.3–0.37 is consistent with Cm space group symmetry, while for x = 0.37–0.47 Pm symmetry is appropriate. Gradual rotation of the optical indicatrix has been found at temperatures just below T_c in crystals with x = 0.27–0.3. A refined phase diagram is presented.

The tunnel splitting of the methyl librational ground states in the hydrogen bonded tetramethylpyrazine–chloranilic acid (TMP–CLA) complex are determined for temperatures T≤28 K by high resolution neutron spectroscopy. Three tunnel modes are resolved at T = 2.4 K. Their relative intensities show that the crystal structure must be different from the proposed space group. Tunnelling and methyl librational modes from the measured density of states are combined into rotational potentials. There are discrepancies of activation energies calculated for these potentials and those obtained from quasielastic scattering of neutrons at T≥50 K due to structural differences in the two respective temperature regimes. Rotational potentials in TMP–CLA are significantly weaker as in pure TMP.

We have developed a full potential Korringa–Kohn–Rostoker (KKR) Green function method. Three improvements which make the full potential treatment efficient and practical are reported. One is a method for constructing the Green function which satisfies the Wronskian relation exactly. The second is including the contribution of the non-spherical part of the potential in the wavefunctions correctly by use of a modified recursive integral equation. Thirdly, we propose a method that completely eliminates the contribution of irregular solutions of the Schrödinger equation to charge/spin densities. In order to check the reliability of the method, we calculated the electric field gradient (EFG), which is sensitive to how the potential is treated. We have performed EFG calculations for hcp metals and sp impurities in Zn and Cd with the present method. The results are in good agreement with experimental data and show that the full potential KKR method is reliable enough for EFG calculations.

We present a detailed comparison between ONETEP, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron calculations shows that only the largest available Gaussian basis sets can match the accuracy of routine ONETEP calculations. Results indicate that our minimization procedure is not ill conditioned and that convergence to self-consistency is achieved efficiently. Finally, we present calculations with ONETEP, on systems of about 1000 atoms, of electronic, structural and chemical properties of a wide variety of materials such as metallic and semiconducting carbon nanotubes, crystalline silicon and a protein complex.

The temperature- and pressure-induced structural phase transition in PbTiO₃ is studied with the isoenthalpic–isobaric molecular-dynamics method, using an effective two-body interaction potential. The tetragonal to cubic transformation is successfully reproduced with both temperature and pressure. The behaviour of lattice parameters, vibrational density of states, and phonon anharmonicity with temperature and pressure are in very good agreement with experimental data. Two- and three-body correlations were analysed through pair distribution functions, coordination numbers and bond-angle distributions.

To explain the remarkable oscillations observed in the x-ray magnetic circular dichroic absorption spectra from Gd/Cu multilayers at the Cu K edge, ab initio calculations have been made using the fully relativistic Korringa–Kohn–Rostoker formalism including the spin–orbit coupling. The result reproduces well the oscillatory profiles in the near-edge region, but the peaks and valleys do not correspond to those in the difference density of states for the unoccupied Cu 4p band above the Fermi level. We find small spin and orbital moments on the interfacial Cu sites, which decay towards the core of the Cu layer. Surprisingly, neither the spin nor the orbital moments die out on the Cu sites four atomic layers away from the Co interface. This extended polarization is ascribed to the hybridization of the Cu 4p and the Gd 5d states. The accuracy of the calculation is supported by the near-bulk spin and orbital moments found on the Gd sites away from the interface.

The SIESTA approach based on pseudopotentials and a localized basis set is used to calculate the electronic, elastic and equilibrium properties of P 2₁/c, Pbca, Pnma, Fm3m, P4₂nmc and Pa3 phases of HfO₂. Using separable Troullier–Martins norm-conserving pseudopotentials which include partial core corrections for Hf, we tested important physical properties as a function of the basis set size, grid size and cut-off ratio of the pseudo-atomic orbitals (PAOs).

We found that calculations in this oxide with the LDA approach and using a minimal basis set (simple zeta, SZ) improve calculated phase transition pressures with respect to the double-zeta basis set and LDA (DZ–LDA), and show similar accuracy to that determined with the PPPW and GGA approach. Still, the equilibrium volumes and structural properties calculated with SZ–LDA compare better with experiments than the GGA approach.

The bandgaps and elastic and structural properties calculated with DZ–LDA are accurate in agreement with previous state of the art ab initio calculations and experimental evidence and cannot be improved with a polarized basis set. These calculated properties show low sensitivity to the PAO localization parameter range between 40 and 100 meV. However, this is not true for the relative energy, which improves upon decrease of the mentioned parameter. We found a non-linear behaviour in the lattice parameters with pressure in the P 2₁/c phase, showing a discontinuity of the derivative of the a lattice parameter with respect to external pressure, as found in experiments.

The common enthalpy values calculated with the minimal basis set give pressure transitions of 3.3 and 10.8 GPa for and , respectively, in accordance with different high pressure experimental values.

Both differential scanning calorimetry and powder neutron diffraction have been applied to investigate an oxygen isotope effect on the metal–insulator (MI) transition in layered cobaltites RBaCo₂O_5.5 (R = Pr, Dy, Ho and Y). For all the compounds it was found that ¹⁸O substitution increases the transition temperature T_MI by about 2 K. A small negative isotope-effect coefficient α₀∼−0.06 indicates that a delocalization of the pd σ holes in the Co³⁺ high spin state (rather than a spin-state transition) can be responsible for the MI transition, in agreement with density-functional calculations (Wu 2003 J. Phys.: Condens. Matter15 503).

The emission and excitation spectra as well as decay of emissions of alkaline-earth fluoride crystals doped with CdF₂ were investigated in the 2–24 eV range at temperatures in the range 8–300 K. Emission bands at 4.2 and 3.5 eV, respectively, were found under excitation into the Cd absorption region in CaF₂–Cd and SrF₂–Cd crystals at low temperatures. Both emission bands have slow luminescence decay times of microsecond timescale. No Cd-related emission was found in BaF₂–Cd crystals.

The calculations of the geometrical configurations of excited triplet Cd²⁺ centres and the Cd-related electron transitions were carried out by using the ab initio Hartree–Fock method. The results of experiments and calculations lead us to the conclusion that the observed Cd²⁺ emission bands are due to the triplet–singlet transitions from the Cd s-states to the nearest fluorine ions. The calculated energies are in good agreement with experimentally observed ones.

Phosphorus, the current standard n-type dopant in diamond, has been correlated with isotropic, trigonal and tetragonal paramagnetic centres, suggesting that it may undergo a symmetry lowering distortion, perhaps of a Jahn–Teller type. We present first-principles calculations for examining the energetics of various sub-group symmetries of the on-site, tetrahedral donor, and show that C_2v, C_3v and D_2d conformations reduce the total energy and conform to the Jahn–Teller theorem. We also present a qualitative explanation of the resulting quantum-mechanical states. The small amount of energy saved by the distortion may indicate a dynamic Jahn–Teller effect.

Electronic properties of straight carbon nanotubes under an external electric are investigated, following a single-π-orbital tight binding approximation. Metal–insulator transitions in metallic tubes and energy gap modulations in semiconducting ones were found due to the action of the electric field. Reductions in the tube symmetry operations induced by the field are manifested in the energy spectrum as a function of the angle determined by the field direction and equivalent in-plane atomic positions along the circumferential direction. We find that particular energies in the spectra exhibit a periodic oscillation with this dephasing angle. The range and position of those energies, as well the amplitude of the oscillation, can be properly manipulated by changing the strength and direction of the applied electric field.

The electron transport through a monatomic metallic wire connected to leads is investigated using the tight-binding Hamiltonian and the Green function technique. Analytical formulae for the transmittance are derived and M-atom oscillations of the conductance versus the length of the wire are found. Maxima of the transmittance function versus the energy, for a wire consisting of N atoms, determine the (N+1) period of the conductance. The periods of conductance oscillations are discussed and the local and average quantum wire charges are presented. The average charge of the wire is linked with the period of the conductance oscillations and for M-atom periodicity there are possible (M−1) average occupations of the wire states.

We present a fully nonequilibrium calculation of the low-temperature transport properties of a single molecular quantum dot coupled to the local phonon mode when an ac field is applied to the gate. The resonant behaviour is shown in the time-averaged differential conductance as the ac frequency matches the frequency of the local phonon mode, which is a direct consequence of the satellite-phonon-peak structure in the dot electron spectral function. Different step structure with and without the external irradiation is found in the I–V curves, and oscillation behaviour is found in the step height as a function of the irradiation intensity.

The specific heat of single-crystal PrMnO₃ was investigated from 2 to 200 K under different magnetic fields up to 8 T. A Schottky-like anomaly observed at low temperature was gradually shifted to higher temperatures by magnetic fields. The first four singlets of the Pr^3+ 3H₄ ground multiplet in PrMnO₃ are given for the first time by fitting the specific heat of Pr³⁺ ions below 40 K under zero field. By analysing the field dependence of the first singlet of Pr³⁺ ions, the Pr–Mn exchange field is found to be negligible, which is consistent with the magnetic anisotropy of Pr³⁺ ions revealed in the magnetic measurement. At T_N, the cooperative antiferromagnetic ordering of Mn³⁺ spins shows up as λ-shaped anomaly, which is lowered and broadened in magnetic fields. The magnetic entropy near T_N is estimated by subtracting the contributions to specific heat from Pr³⁺ ions and lattice vibrations. It was found that the fraction of entropy above T_N in the total entropy increases with the fields due to the enhancement of spin fluctuations by magnetic field.

It is shown that non-Heisenberg exchange interaction should be taken into account to reproduce the magnetic phase diagram of La_1−xA_xMnO₃ (A = Ca,Sr) using only effective exchange parameters and spins. The formation of the four-spin exchange arises from carrier hopping and coincides with the critical concentration metal–dielectric transition. The two- and four-spin exchange parameters are determined by Monte Carlo simulations.

We report on the structural and magnetic properties of newly synthesized Heusler alloys, Ru_2−xFe_xCrSi, which have quite recently been shown to be candidates for ferromagnetic metals with high spin polarization from band structure calculations. Polycrystalline samples of Heusler alloys Ru_2−xFe_xCrSi were prepared for 0.5≤x≤1.8. They were found to have L2₁ structures for 0.5≤x≤1.5 and B2 for x = 1.8. Magnetic measurements showed that they are ferromagnets. The Curie temperature for x = 1.0 was found to be 370 K. The Curie temperature tends to increase with increasing Fe concentration x. The saturation magnetic moment increases almost linearly as x increases. For higher Fe concentration the saturation magnetic moment is close to 2 μ_B per formula unit, which is theoretically expected.

The polymerization of pyrrole in an aqueous medium in the presence of nanodimensional Fe₃O₄ using ammonium peroxodisulphate (APS) as oxidant results in the formation of polypyrrole–Fe₃O₄ nanocomposites. Characterization of the composites was carried out by Fourier transform infrared spectroscopy, x-ray diffraction, scanning and transmission electron microscopy. The magnetization data exhibit a small hysteresis loop at room temperature. The Mössbauer spectra at room temperature reveal the doublet structure, characteristic of the superparamagnetic phase in magnetite (Fe₃O₄). The composite samples reveal ordered semiconducting behaviour. Polypyrrole is the dominating component in the transport process of the nanocomposites. A very large dielectric constant of about 11 000 at room temperature has been observed. The interface between polypyrrole and Fe₃O₄ plays an important role in producing a large dielectric constant in the composite.

Barium sodium niobate (Ba₂NaNb₅O₁₅) is a tungsten bronze structure that exhibits a complicated sequence of six structural phase transitions, including three incommensurate (IC) phases. The phases are unusual in that all but the highest temperature P4/mbm structure are ferroelectric. Unlike the situation for most incommensurate insulators, in which ferroelectricity develops at low temperatures along the modulation direction, the polarization direction in barium sodium niobate is orthogonal to the modulation(s), permitting some unusual phenomena. In the present study we analyse the thermal and dielectric behaviour at the Curie temperature T_C near 830 K as well as that at the Ccm 2₁–IC(1q) transition near 543 K, the IC(1q)–IC(2q) transition near 565 K and the IC(2q)–P4bm transition at 582 K. The entropy change at 565 K is related to the wall roughening model of Rice et al (1981 Phys. Rev. B 24 2751). Data near T_C = 830 K indicate close proximity to a tricritical point, and discussions of critical exponents are presented, all of which are found to be mean field. Because of Na vacancies, transition temperature variation is found among specimens Ba₂Na_1−xNb₅O₁₅  (830 K< T_C(x)< 865 K), and the system appears to be describable by the disordered exclusion model as a slightly first-order intrinsic system whose dynamics are suppressed by weak disorder. Near T_C the specific heat C(T) is compared with the random bond prediction of Harris (1974 J. Phys. C: Solid State Phys. 7 1671): C(T) = C₀(T)/[1+bx²C₀(T)], where C₀(T) is the intrinsic specific heat of the vacancy-free crystal varying as (T_C−T)^−1/2 and x is the sodium vacancy concentration. In agreement with Harris's model, the shifts in T_C(x) are to lower T with increasing x and scale as x; the broadening scales as x²; and the effective critical exponent remains unchanged at α = 1/2.