Table of contents

We report the measurements of thermopower, electrical resistivity and thermal conductivity in a complex cobalt oxide Li_0.48Na_0.35CoO₂, whose crystal structure can be viewed as an intergrowth of the O3 phase of Li_xCoO₂ and the P2 phase of Na_yCoO₂ along the c-axis. The compound shows a large room-temperature thermopower of ∼180 µV K⁻¹, which is substantially higher than those of Li_xCoO₂ and Na_yCoO₂. The figure of merit for the polycrystalline sample increases rapidly with increasing temperature, and achieves nearly 10⁻⁴ K⁻¹ at 300 K, suggesting that the Li_xNa_yCoO₂ system is a promising candidate for thermoelectric applications.

The numerical renormalization group (NRG) is employed to study a double quantum dot (DQD) system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U^', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U^'/U. The spin-Kondo effect arising for U^' = 0 (SU(2) × SU(2)) is found to persist robustly with increasing U^'/U, before a rapid but continuous crossover to (a) the SU(4) point U^' = U where charge and spin degrees of freedom are entangled and the Kondo scale is strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz–Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U_c^'. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points; on the overall phase diagram in the (U,U^')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong-coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime, and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.

An interatomic potential for zinc oxide and its elemental constituents is derived based on an analytical bond-order formalism. The model potential provides a good description of the bulk properties of various solid structures of zinc oxide including cohesive energies, lattice parameters, and elastic constants. For the pure elements zinc and oxygen the energetics and structural parameters of a variety of bulk phases and in the case of oxygen also molecular structures are reproduced. The dependence of thermal and point defect properties on the cutoff parameters is discussed. As exemplary applications the irradiation of bulk zinc oxide and the elastic response of individual nanorods are studied.

Amorphous FeCuNbSiB alloys with composition near Fe_73.5Cu₁Nb₃Si_13.5B₉ (the well-studied FINEMET alloy) were annealed at 520 °C for different durations of time, t_A, varying from 3 to 20 min. Detailed investigation of the structure and composition of crystalline phases formed during the initial stages of crystallization in these alloys using techniques such as x-ray diffraction, Mössbauer spectroscopy, scanning electron microscopy, atomic force microscopy and energy dispersive absorption of x-rays, revealed the following. New crystalline phases, tetragonal Fe₃B and hexagonal Fe₂Si, not reported previously, exist in all the nanocrystalline alloys in question in contrast to the well-documented cubic Fe–Si phase with the DO₃ structure which coexists with the Fe₃B and Fe₂Si phases in some compositions only. The crystallization of Fe₃B and Fe₂Si nanocrystalline grains starts at the surface of the ribbons and then proceeds to the bulk whereas the crystallization of DO₃ Fe–Si gets initiated within the bulk. The average size of the nanocrystalline grains of the Fe₃B and Fe₂Si and cubic DO₃ Fe–Si structures in the residual amorphous matrix is around 20 nm but their volume fractions are as low as ≈5%, 10%, and 7%, respectively. The cubic Fe–Si nanocrystals of the DO₃ structure have a silicon concentration in the range 15–20 at.%. The magnetic moments in the amorphous precursor point, on average, are 40° out of the ribbon plane while in the nanocrystalline alloys this angle varies between 2° and 19° depending on the Fe concentration.

We investigated the effects of the external magnetic field on the compositional-fluctuation potentials (APFs) in diluted magnetic semiconductors (DMSs). The APFs in DMSs are divided into two parts: one is the nonmagnetic part usually considered in mixed nonmagnetic semiconductors and the other is the magnetic part caused by the compositional fluctuations of the substituted magnetic ions and the sp–d exchange interaction under the external magnetic field. The APFs in DMSs, thus, depend on the external magnetic field and the temperature as well as the concentration of the magnetic ions; for example in Cd_1−xMn_xTe, the APFs increase with the magnetic field up to about 40 kOe for an Mn concentration of x = 0.2 and 0.3, while the APFs decrease drastically with the magnetic field for x less than 0.05 at low temperatures. After a general discussion of the APFs in DMSs, we calculated the exciton magnetic polarons weakly bound to APFs under the external magnetic field. The calculated results were compared with the experiment on the L₂ photoluminescence in Cd_1−xMn_xTe, with the purpose of revealing the peculiar properties caused by the magnetic part of the APFs.

The dynamic phase transitions are studied, within a mean-field approach, in the kinetic Blume–Emery–Griffiths model under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The behaviour of the time-dependence of the order parameters and the behaviour of the average order parameters in a period, which is also called the dynamic order parameters, as a function of reduced temperature, are investigated. The nature (continuous and discontinuous) of transition is characterized by studying the average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The phase diagrams exhibit one, two, or three dynamic tricritical points and a dynamic double critical end point, and besides a disordered and two ordered phases, seven coexistence phase regions exist, which strongly depend on interaction parameters. We also calculate the Liapunov exponent to verify the stability of solutions and the dynamic phase transition points.

An electron paramagnetic resonance (EPR) study of Er³⁺ ions in single crystals of KTiOPO₄ (KTP) is presented. The EPR spectra show the existence of eight different Er³⁺ centres. The g-matrix has been determined for all eight centres from the analysis of the angular dependences of the spectrum in three planes of the crystal. This study provides strong evidence about incorporation of erbium in the low-symmetry K⁺ sites of KTP. Possible reasons for the appearance of such a large number of Er³⁺ centres are discussed.

The equilibrium structure of the compound Li₃AlB₂O₆ is evaluated via the minimization of the total energy using pseudopotentials and a plane-wave basis within the local spin density approximation (LSDA) in the framework of density functional theory (DFT). The calculated data for the equilibrium structure are in agreement with the experimental ones. The thermal properties of Li₃AlB₂O₆ are consequently calculated within the quasi-harmonic approximation with the Debye model combined with the first principle for which static total energy versus volume can be calculated easily. The equilibrium volume obtained using this model also agrees with the experimental value, so other thermal outcomes gained from this model will provide overall predictions accurately for the temperature and pressure dependence of various quantities such as the equation of state (EOS), the bulk modulus, the heat capacity, and the thermal expansion.

Using the first-principles calculations based on the coherent potential approximation, we study the electronic structure, magnetic moments and the bulk modulus of FeX alloys with IVB group elements (X = Si,Ge,Sn) in the Fe-rich concentration range (x = 0.0–0.25), which form a stability region of bcc-related phases. In agreement with experiment, our calculations reproduce well a peculiar non-monotonous behaviour of the bulk modulus in Fe–Si alloys with increasing Si concentration. Such a dependence is found for all bcc-related disordered and partially ordered Fe–Si phases A2, B2 and D0₃, which is in contrast with an earlier suggestion that the non-monotonous bulk modulus behaviour is related to partial ordering in Fe–Si. In addition, our results predict a similar behaviour in Fe–Ge and Fe–Sn alloys. It is shown that the observed behaviour of the bulk modulus is entirely related to the changes of the magnetic properties with chemical composition.

The magnetization, dc conductivity, and dielectric relaxation of cation-deficient manganese perovskite (LaMn)_0.956O₃ have been investigated. (LaMn)_0.956O₃ shows a ferromagnetic transition around 166 K and a thermally activated dielectric loss peak is observed in the ferromagnetic phase. The transport is thermally activated with a change in slope at the ferromagnetic transition. The temperature dependency of the dc conductivity and dielectric relaxation processes provide evidence of hopping conduction below T_C. The results have been discussed in terms of a hopping process of polarons localized by electron–lattice interaction in tandem with electron–magnon interaction.

A diagrammatic method for the theory of magnetic and resistive properties of manganites has been applied. The Holstein double-exchange model for a narrow band with the strong Hund's rule coupling was studied. In parallel with the Lang–Firsov unitary transformation of the zeroth Hamiltonian, we have realized the diagonalization of Hund's Hamiltonian neglecting the upper triplet. The diagram techniques taking into account the quantum spin fluctuations of the lower quintet and hole state with spin S = 3/2 were developed. The magnetic structure of the ground state and an influence of electron–phonon interaction have been analysed using the first nonvanishing approximation of the perturbation theory. Since a simple self-consistent equation for the Green function is lacking, the approximations for the effective interaction line with strong electron–phonon coupling were used. The influences of quantum fluctuations and electron–phonon interactions on magnetization, the Curie temperature and resistivity were investigated. The calculated temperature dependence of resistivity in the pure double-exchange model agrees well with experimental data.

We are interested, in this work, in determining the Stark sub-level of Er³⁺ ions doping a KY₃F₁₀ single crystal with a molar concentration of 1%. We have used a new method of measurement of energies of the ground level and emitting levels from excitation and anti-Stokes emission spectra recorded at liquid nitrogen temperature. This technique is based on a spectral analysis of the anti-Stokes emissions recorded after selective excitation with a red dye tunable laser. Thus, we could determine the Stark sub-levels of the ground and the principal emitting levels in the infrared, visible and near-UV ranges with a very good precision.

The relationships between incommensurability, charge ordering and magnetic and electric transport properties were studied in La_0.33Ca_0.67Mn_1−yFe_yO₃ (0≤y≤0.06) polycrystalline samples. Incommensurability and charge ordering were directly observed by electron diffraction versus temperature and lattice imaging at low temperature in transmission electron microscopy. Both the charge ordering and the ferromagnetic Curie–Weiss temperature linearly decrease with increasing Fe concentration y. A mean field analysis yields an antiferromagnetic exchange J(Mn–Fe) = −22 K. The undoped samples showed predominantly a commensurate charge ordering superstructure with q-vector 1/3a^* over the whole temperature range<200 K. For doped compositions, the q-vector (1/3−ε)a^* is reduced by 12–15% for 5% Fe doping, as compared to the undoped composition. The low-temperature superstructure of the Fe-doped manganite does not correspond exactly to the threefold cell with lattice parameters 3a, b, c, and defects inducing shifts along the a direction create a disturbance in long-range charge ordering. Jahn–Teller effects on Mn³⁺ centres are proposed to play a crucial part in the superstructure formation as well as in the suppression of charge ordering temperature by doping with non-Jahn–Teller impurity Fe³⁺ on Mn³⁺ sites.

A method is presented of in situ measurements of stacking fault densities in shocked face-centred-cubic (FCC) crystals using x-ray diffraction. Using results from both the second and fourth diffraction orders, wherein shifts in the Bragg peaks due to faulting are accounted for, we calculated fault densities present in a molecular dynamics (MD) simulation of shocked single crystal of copper. The results are in good quantitative agreement with dislocation density measurements inferred directly from the MD simulation. The x-ray diffraction method thus presents a real possibility for experimental determination in real time of dislocation densities in crystals during shock wave passage.

T₁, T_1ρ and T₂ for the ¹H and ²H nuclei in (NH₄)₃H(SO₄)₂ and (ND₄)₃D(SO₄)₂ single crystals grown using the slow evaporation method were measured for phases I, II, III, IV and V. The ¹H T₁, T_1ρ, and T₂ values were found to exhibit different trends in phases II and III: T₁, T_1ρ and T₂ for ¹H do not change significantly near the phase transition at 265 K, whereas near 413 K they change discontinuously. We conclude that the NH₄⁺ and H(SO₄)₂⁻ ions do not play an important role in the III–II phase transition, but do play important roles in the II–I phase transition. The liquid-like nature of the ¹H T_1ρ and T₂ above 413 K is indicative of the destruction and reconstruction of hydrogen bonds. Moreover, the phase transitions of the (NH₄)₃H(SO₄)₂ crystal are accompanied by changes in the molecular motion of the (NH₄)⁺ ions. The variations with temperature of the ²H T₁ and T₂ of (ND₄)₃D(SO₄)₂ crystals are not similar to those observed for the ¹H T₁ and T₂. Our comparison of the results for (NH₄)₃H(SO₄)₂ and (ND₄)₃D(SO₄)₂ crystals indicates the following: the ¹H T_1ρ and T₂ of the (NH₄)⁺ and H(SO₄)₂⁻ ions above T_C1 are characteristic of fast, liquid-like motion, which is not the case for (ND₄)₃D(SO₄)₂; and the ²H T₁ of D(SO₄)₂⁻ in (ND₄)₃D(SO₄)₂ is longer than the ²H T₁ of (ND₄)⁺ in contrast to the results for (NH₄)₃H(SO₄)₂ crystals.

The electronic properties of YbSi are studied by band structure calculation based on the density functional theory within the LDA, LDA+U, and the fully relativistic scheme. When the Coulomb potential is added to the Yb 4f orbitals, the degeneracy between the different f orbits would be lifted and they are split into lower Hubbard bands and upper Hubbard bands. The fully relativistic band structure scheme shows that spin–orbit coupling splits the 4f states into two manifolds, the 4f_7/2 and the 4f_5/2 multiplet.

We have studied structural, electronic and dynamical properties of AuGa₂ and AuIn₂ by employing the plane-wave pseudopotential method within the density functional theory. The structural results are in good agreement with previous experimental and other theoretical results. The calculated electronic band structures for both materials have been compared with the angle-resolved photoemission spectroscopy experiment data along the [100] symmetry direction. Phonon dispersion curves and density of states were calculated by employing a density-functional perturbation theory. The calculated zone-centre optical phonon modes for these materials are in good agreement with experimental data.

The magnetic properties of iron (spin and orbital magnetic moments, magnetocrystalline anisotropy energy) in various geometries and dimensionalities are investigated by using a parametrized tight-binding model in an s, p and d atomic orbital basis set including spin polarization and the effect of spin–orbit coupling. The validity of this model is well established by comparing the results with those obtained by using an ab initio code. This model is applied to the study of iron in bulk bcc and fcc phases, (110) and (001) surfaces and the monatomic wire, at several interatomic distances. New results are derived. In the case of surfaces the variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth, revealing a significant enhancement in the first two layers, especially for the (001) surface. It is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several meV. This is also true for the orbital moment, which in addition is highly anisotropic. Furthermore, it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis. At equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression. The success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries.

There have been many recent experimental studies of rare earth (RE) phosphate glasses, (RE₂O₃)_x(P₂O₅)_1−x, but only two previous reverse Monte Carlo (RMC) modelling studies. The current study reports the first molecular dynamics model of an RE phosphate glass, for Tb metaphosphate glass, with x = 0.25. The model is in good agreement with experimental results for nearest-neighbour distances and coordination numbers, and in reasonable agreement for x-ray and neutron diffraction structure factors. There is a tetrahedral phosphate network, with marked splitting of distances from P to bridging oxygen (O_b) and from P to non-bridging oxygen (O_nb). The phosphate network has tetrahedra denoted Qⁿ (where n is the number of O_b) with an average of n = 2.1 and mostly Q² groups, but with some Q¹ and Q³ groups. Most Tb are coordinated to six O_nb, and the average coordination is N_TbOnb = 5.7, which compares favourably with experimental results that indicate N_RE−O∼6 in metaphosphate glasses with small RE ions. The great majority of O_nb are bonded to only one Tb, but there are a few shared O_nb occurring in Tb–O_nb–Tb configurations. These cause a small peak in Tb–Tb correlations around 4 Å, prior to the main peak around 6 Å. The corresponding Tb–Tb partial structure factor shows promising agreement with a recent experimental measurement using magnetic neutron scattering.

The Mössbauer spectra of akaganeite have always been interpreted considering both the tetragonal structure and the chlorine content. However, very recently it has been suggested that the crystallographic structure is not tetragonal but monoclinic, thus another interpretation for the Mössbauer spectra is required. For this purpose, we have prepared and characterized by several techniques synthetic akaganeite. Our results suggest that the two crystallographic sites required by the monoclinic symmetry are not distinguishable in the paramagnetic state as previously assumed, but they are only discernible in the low temperature magnetic region. At room temperature the spectrum is fitted with two doublets whose origin is related to the chlorine content, i.e. one Fe site assigned to Fe³⁺ ions located close to chloride ions and the other Fe site to those located close to chloride vacancy sites. The low temperature spectra can be adequately fitted with four sextets, whose hyperfine parameters must be subjected to some constraints. The origin of these components is related to the two different crystallographic sites and to the chlorine content. In-field Mössbauer spectrometry at low temperature suggests that the magnetic structure behaves as a system which consists of two asperimagnetic-like structures antiferromagnetically coupled, and not as a collinear antiferromagnet as usually assumed.

The effect of substituting Ti for Mn in the ferrimagnetic perovskite CaCu₃Mn₄O₁₂ has been studied in the series CaCu₃Mn_4−xTi_xO₁₂ (x = 0.3,0.5,1.0,1.5,2.0,3.0). These materials have been prepared in polycrystalline form under moderate pressure conditions of 2 GPa and 1000 °C in the presence of KClO₄ as an oxidizing agent. The crystal structure is cubic, space group (No. 204); the unit cell parameters vary linearly from a = 7.2361(4) Å (x = 0.3) to a = 7.3489(5) Å (x = 3.0) at room temperature (RT). A neutron powder diffraction study has been performed for a selected sample of nominal composition CaCu₃Mn₃TiO₁₂. In the ABO₃ perovskite superstructure, the A positions are occupied by Ca²⁺ and (Cu_2.5²⁺Mn_0.5³⁺), ordered in a 1:3 arrangement, giving rise to the body-centring of the unit cell. At the B positions, Mn and Ti are randomly distributed over the octahedral sites; (Mn,Ti)O₆ octahedra are considerably tilted by 19°, due to the relatively small size of the A-type cations. The Curie temperatures decrease from 331 K (x = 0.3) to 310 K (x = 3.0). The saturation magnetization at 5 K is strongly reduced upon Ti introduction, from M_s = 10.4 μ_B fu⁻¹ (x = 0.3) to 1.0 μ_B fu⁻¹ (x = 3.0). All the samples exhibit negative magnetoresistance (MR), reaching a maximum value of 41% for the x = 0.5 sample at 5 K for H = 9 T; the MR(9 T) at RT is as high as 7% for x = 0.5, and shows an appreciable temperature stability.

Dynamic localization conditions proceeding beyond the nearest-neighbour description have been established by applying the quasi-energy description. The general energy dispersion laws one deals with concern a periodic but commensurable dc–ac field like E₀+E₁f(t), for which f(t) = f(t+T) and ω_B = Pω/Q. Here and ω = 2π/T stand for the Bloch and ac field frequencies, respectively, while P and Q are mutually prime integers. A reasonable centre of band generalization of such conditions has been proposed.

The temperature dependence of resistivity and the bulk modulus are calculated on the Kondo lattice, with ring exchange between localized spins, using the spin-polaron and adiabatic approximation. Peak and zero values of the bulk modulus as functions of temperature and concentration are determined below the temperature of the transition to the paramagnetic state. The effects of the nearest order between transverse spin components and a value of the ring exchange between localized spins on magnetoresistivity are estimated.

We report a novel dielectric anomaly around the Jahn–Teller orbital order–disorder transition temperature T_JT in LaMnO_3+δ. The transition has been characterized by resistivity (ρ) versus temperature (T), calorimetry, and temperature dependent x-ray diffraction studies. Measurements of complex dielectric permittivity ε^* (= ε'−iε'') over a low-frequency range (1 Hz–10 MHz) across T_JT reveal a distinct anomaly. This observation, and the reported relatively high static dielectric constant at T = 0 (ε₀∼18–20), possibly indicate that the orbital order gives rise to intrinsic polarization that undergoes transition at T_JT. The frequency dispersion of the dielectric response at any given temperature, however, reveals that the dielectric response consists of Maxwell–Wagner component, due to interfaces, within such a low frequency range. The T_JT and the nature of the anomaly in ε'(ω,T),ε''(ω,T) at T_JT, of course, vary—from a sharp upward feature to a smeared plateau and then a downward trend—depending on the Mn⁴⁺ concentration of the sample. The observation of an intrinsic dielectric response due to long-range orbital order in LaMnO₃—where no ferroelectric order is possible due to the absence of off-centre distortion in MnO₆ octahedra—may throw a new light onto these classes of materials vis-à-vis multiferroic materials.

A new class of negative refractive-index metamaterials made of metallic spheres arranged in a three-dimensional lattice of helicoidal symmetry is reported. The studied metamaterial possesses several frequency bands which give rise to negative refraction. The proposed structures constitute a viable solution to realizing optical metamaterials since they can exhibit negative refraction in the frequency region of the surface-plasmon excitations of noble metals.

The Ni magnetic moment in the GdNi₂ Laves phase compound is studied in detail by the use of the magnetic Compton profile (MCP) method. Analysis of the MCP, measured at 30 K, reveals that the spin component of Ni 3d electrons coupled antiparallel to that of Gd 4f electrons, and it was confirmed that the Ni retains a spin magnetic moment of 0.16 ± 0.08 μ_B. Furthermore, the total magnetic moment, including the angular momentum component, is found to be 0.23 ± 0.11 μ_B and this value that is obtained is in accord with that derived from direct measurement of the bulk magnetization. Our finding of the existence of the Ni magnetic moment contradicts the well-known fact that Ni loses its magnetic moment in the Laves phase of rare-earth (RE)–Ni compounds. In addition, the magnetic moment originating from the electrons with s- and p-character, which are donated by the Gd and Ni atoms, is also observed and quantified.

Laser ablated transition-metal (TM)-doped In₂O₃ thin films grown under appropriate conditions on both MgO and Al₂O₃ substrates can be well crystallized and ferromagnetic at room temperature. Of all the dopants, Ni seems to be the most promising candidate since doping Ni in In₂O₃ results in semiconducting films with the largest magnetic moment. Films are cluster-free. Magnetic force microscopy measurements confirm that the magnetic signals at room temperature are real. Moreover, compared to TM:In₂O₃ films deposited on MgO, films on Al₂O₃ have smaller grains and those are better connected, so that the film texture is smoother and the magnetic domains are more uniform. The size of ferromagnetic domains is determined to be about 1 µm. The room temperature ferromagnetism in V/Cr/Fe/Co/Ni-doped In₂O₃ films probably originates from the doped In₂O₃ matrices.

It was known that by a duality transformation, interacting bosons at filling factor f = p/q hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating dual 'magnetic field' whose average strength through a dual plaquette is equal to the boson density f = p/q. So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of f = p/q flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux f = p/q per plaquette on five most common bipartite and frustrated lattices namely square, honeycomb, triangular, dice and Kagome lattices. We count the total number of bands, and determine the number of minima and their locations in the lowest band. We also numerically calculate the bandwidths of the lowest Hofstadter bands in these lattices that directly measure the mobility of the dual vortices. The less mobile the dual vortices are, the more likely are the bosons to be in a superfluid state. We find that apart from the Kagome lattice at odd q, they all satisfy the exponential decay law W = Ae^−cq even at the smallest q. At given q, the bandwidth W decreases in the order of triangle, square and honeycomb lattice. This indicates that the domain of the superfluid state of the original bosons increases in the order of the corresponding direct lattices: honeycomb, square and triangular. When q = 2, we find that the lowest Hofstadter band is completely flat for both Kagome and dice lattices. There is a gap on the Kagome lattice, but no gap on the dice lattice. This indicates that the boson ground state at half filling with nearest neighbour hopping on Kagome lattice is always a superfluid state. The superfluid state remains stable slightly away from the half filling. Our results show that the behaviours of bosons at or near half filling on Kagome lattices are quite distinct from those in square, honeycomb and triangular lattices studied previously.

We study the Kondo effect in a quantum dot coupled to half-metallic ferromagnetic electrodes in the regime of strong on-dot correlations. Using the equation of motion technique for non-equilibrium Green functions in the slave boson representation, we show that the Kondo effect is not completely suppressed for anti-parallel magnetization of the leads. In the parallel configuration, there is no Kondo effect but there is an effect associated with elastic co-tunnelling which, in turn, leads to similar behaviour of the local (on-dot) density of states (LDOS) as the usual Kondo effect. Namely, the LDOS shows the temperature-dependent resonance at the Fermi energy, which splits with the bias voltage and the magnetic field. Moreover, unlike for non-magnetic or not fully polarized ferromagnetic leads, only the minority spin electrons can form such resonance in the density of states. However, this resonance cannot be observed directly in the transport measurements, and we give some clues how to identify the effect in such systems.

A spectroscopic investigation of Er³⁺/Yb³⁺ co-doped 50SiO₂–20Al₂O₃–30CaF₂ glasses and transparent glass ceramics containing CaF₂ nanocrystals is presented. The formation of CaF₂ nanocrystals in the glass ceramic was confirmed by x-ray diffraction (XRD) and transmission electron microscopy (TEM). The Judd–Ofelt parameters of the Er³⁺ ions in the glass and glass ceramic have been calculated; they suggested that Er³⁺ ions had been incorporated into CaF₂ nanocrystals in the glass ceramics. The upconversion luminescence intensity of the Er³⁺/Yb³⁺ co-doped glass ceramic was much stronger than that of the Er³⁺/Yb³⁺ co-doped glass. The upconversion luminescence mechanism has been ascribed to a two-photon absorption process for the green and red luminescence and a three-photon absorption process for the blue luminescence.