Table of contents

We study the equilibrium spin configuration of the 2D Hubbard model for a low degree of doping, x, when a long-range magnetic order is still present. We show that the conventional planar spiral phase has negative bosonic modes and is therefore unstable. The novel equilibrium state that we find at low doping is incommensurate and non-coplanar with the inverse pitch of the spiral varying as square root x; nevertheless this state has a dominant peak in the susceptibility at ( pi , pi ).

As-grown MgNb₂O₆ single crystals grown by the Czochralski method show a deep-blue colour due to the presence of broad optical absorption in the visible spectral region. The absorption of the samples is modified by thermal treatments in air and in vacuum. By heating in air the samples become transparent and by heating in a 1*10^-2 mbar vacuum a complex and broad absorption is induced. An energy band gap of 5.25+or-0.15 eV has been determined. Oxidized samples have an absorption edge at 4.20 eV (at 15 K) but some pre-edge absorption is also present. This latter absorption and the associated photoluminescence emission with a maximum at 2.5 eV are attributed to interstitial Nb ions or Nb ions in Mg lattice sites. The optical absorptions induced by X-ray irradiation and vacuum reduction have been discussed in terms of the defects introduced. An absorption band at 2.30 eV induced by X-ray irradiation is attributed to holes trapped in oxygen (O^--bound small polarons). The absorption band at 1.69 eV has been attributed to an electron trapped in Nb⁵⁺ ions (Nb⁴⁺ small polarons). Another absorption observed at 1.20 eV has been ascribed to a Mg-related electron trap centre. The possible presence of bipolaron centres and other electronic traps is discussed. A comparison with the optical absorption bands observed in LiNbO₃ crystals has been established.

A thermodynamic model for solids under pressure is developed by assuming the universal equation of state and that under zero pressure the free energy is equal to the harmonic crystal (Debye) free energy. The model is applied to gold. In the case of nanocrystals this model reproduces the observed enhancement of the isobaric heat capacity and of the thermal expansion. Our model calculations are free of the ambiguities and inconsistencies connected with the Gruneisen equation, which was used in previous theoretical work.

Giant quantum oscillations (GQO) of the coefficient of ultrasonic absorption by normal metals subject to a magnetic field during a 2 1/2 -order phase transition (PT-2 1/2 ) is discussed the simplest case of the appearance (disappearance) of a spheroidal Fermi sheet associated with the phase transition is considered. For electron energies much higher than the threshold energy, the absorption coefficient is found to show GQO which are not only periodic in inverse magnetic field (the Gurevich-Skobov-Firsov (GSP) oscillations) but also in electron energy (with the magnetic field kept constant) or the size of the cavity (Z) created during the phase transition.

The bistable (shallow-deep) defect systems associated with trivalent impurities (In, Ga, Y and Sc) in CdF₂ are studied. The equilibrium lattice relaxation around the defect and the wavefunction of the electron bound to the impurities are determined by minimizing the energy of the defects. The impurity-fluoride interatomic potentials determined using the electron-gas model of Gordon and Kim are used, and the defect electron is treated by the extended-ion method. In order to compare the deep and shallow states using the same discrete lattice model, a very large cluster of atoms is treated. Two groups of trivalent impurity centres are found. With In and Ga, there is a low, but clearly identified, potential barrier which separates the deep level from the shallow one. In Sc and Y, only a simple shallow level state is obtained. The analysis of the result shows that the difference is to be attributed to the short-range potential of the trivalent impurity centres. On the basis of present work, we predict that Tl³⁺ would exhibit similar bistable behaviour.

Applying the finite-size scaling in conformal field theory, we evaluate the correlation functions and susceptibilities of a 1D Hubbard model with 1/sinh(kr) hopping and repulsive interaction in an external magnetic field. The error introduced in our approximation scheme should be exponentially small in the thermodynamic limit. Incidentally, we provide the generalization of previous work on critical exponents to the case where the right and left Fermi velocities do not coincide.

The antiferromagnetic instability of heavy-fermion alloys with conduction band impurities is examined in the single-site coherent-potential approximation with the strong correlation treated by the slave-boson technique of Kotliar and Ruckenstein. The variation of the paramagnetic-antiferromagnetic phase boundary with the impurity concentration is studied in the case of isoelectronic doping. Our results show that the isoelectronic doping favours the formation of antiferromagnetism if the impurities increase the cell volume, thus suppressing the c-f mixing, which is in agreement with experimental observations in Ce(Cu_1-xAg_x)₆ and Ce(Cu_1-xAu_x)₆. The obtained phase diagram can also be used to explain the effect of nonisoelectronic substitutions of Al for Cu in CeCu₆.

The hyperfine fields and magnetic properties of amorphous and crystallized R_xNd_4-xFe_77.5B_18.5 (R identical to Y, Pr, Cd or Dy; 0<or=x<or=4) alloys have been investigated by means of magnetization measurements, zero-field spin-echo nuclear magnetic resonance (NMR) and the Mossbauer effect (ME). It is found that the Curie temperatures of amorphous alloys change slightly on the addition of R, but the coercive fields of crystallized alloys decrease monotonically with increasing x for R identical to Y, Pr and Gd. A small addition of Dy increases the coercivity; full substitution of Nd by Dy leads to low coercivity owing to the formation of the magnetically soft Dy₃Fe₆₂B₁₄. NMR, ME and X-ray diffraction indicate that the samples with R identical to Pr and Gd for 0<or=x<or=4 and R identical to Y and Dy for 0<or=x<or=2 consist of Fe₃B with a body-centred tetragonal (BCT) structure and a small amount alpha -Fe. Furthermore, the NMR results indicate that the ¹¹B hyperfine fields of BCT Fe₃B increase linearly from 25.3 kOe (34.7 MHz) to 26.3 kOe (36.0 MHz) on the addition of Dy or Gd, but that of alpha -Fe does not change with increasing R concentration; the Mossbauer spectra show that the relative intensity of the subspectrum corresponding to ⁵⁷Fe at Fe_III(8g) sites in BCT Fe₃B is about 5% weaker than those of the other two, implying that about 5 at.% Fe atoms in this site are substituted by other atoms. According to this, it may be reasonable to assume that R atoms enter into BCT Fe₃B.

The magnetic properties of icosahedral Mg₄₂RE₈Zn₅₀ (RE identical to Gd, Tb, Dy, Ho or Er) quasi-crystals have been investigated. These quasi-crystalline phases have a face-centred icosahedral lattice with a highly ordered Frank-Rasper-type structure as identified by electron diffraction and X-ray diffraction. The temperature dependence of DC magnetic susceptibility obeys a Curie-Weiss law in wide temperature ranges. The effective magnetic moments mu _eff are close to those of free RE³⁺ ions and their paramagnetic Curie temperature Theta _p is negative, indicating that the RE-RE exchange interactions are predominantly antiferromagnetic. The value of Theta _p which is the sum of all exchange interactions is almost in proportion to the de Gennes factor. At low temperatures, spin-glass behaviour has been observed in the icosahedral Mg₄₂Gd₈Zn₅₀ and Mg₄₂Tb₈Zn₅₀ quasi-crystals and their spin freezing temperatures T_f are 5.5 K and 7.6 K, respectively.

Electron paramagnetic resonance (EPR) Of Cr³⁺ ions has been observed in single crystals of sodium ammonium sulphate dihydrate (SASD) doped with chromium. At 300 K the spectrum is relatively simple, exhibiting two main different sites, labelled alpha and beta . The spin-Hamiltonian parameters for these sites have been measured. The relative concentration of different paramagnetic sites shows marked sensitivity to unknown factors in the crystal growth. On lowering the temperature the spectrum becomes very complex, making detailed study of the various sites, and changes at any phase transition, impossible to elucidate. None of the spectra shows a marked change at the ferroelectric transition temperature, T_c=92 K.

Some crystals of chromium-doped sodium ammonium sulphate dihydrate (SASD) appear to be divided into regions of darker and regions of lighter blue coloration. Crystal specimens cut from the darker regions have been investigated. Their EPR spectrum exhibits, in addition to the beta -site previously measured, a new site, labelled beta ' because of its similarity to the beta -site. The spin-Hamiltonian parameters of the beta '-site have been measured at 300 K, and the temperature dependence of the spin-Hamiltonian parameter D has been measured from 300 K to 77 K. In contrast to the alpha -site described previously, the beta '-site shows a marked doubling below 92 K, corresponding to a change in D. The temperature dependence of the dielectric susceptibility shows a marked change at 204 K, only very slightly noticeable in undoped SASD, which correlates with a change of slope in the temperature dependence of D measured by EPR.

Simple (CuO₂, CuO) and complex superconducting (YBa₂Cu₃O_7-x, La_2-xSr_xCuO₄) copper oxides have been investigated by ⁶¹Cu(⁶¹Ni) emission Mossbauer spectroscopy. A linear relationship between the quadrupole coupling constant for ⁶¹Ni and the calculated lattice electric field gradients is established, and the contribution of the Ni²⁺ valence electrons to the coupling constant is determined. Magnetic fields are observed at ⁶¹Ni nuclei in those cases when the copper sublattice shows magnetic ordering.

Parameters of the tensors of the electric field gradient (EFG) created by lattice ions at the rare-earth metal (REM) sites in RBa₂Cu₃O₇ (R is a REM or Y) and La_2-xSr_xCuO₄ (0<x<0.3) have been determined by means of ¹⁵⁵Eu(¹⁵⁵Gd) emission Mossbauer spectroscopy. The EFG tensors at the REM sites have been calculated in the point charge approximation. The experimental and calculated EFGs are shown to be in good agreement when holes are supposed to be mainly in sublattices of the chain and Cu-O plane oxygen for RBa₂Cu₃O₇ and La_2-xSr_xCuO₄, respectively.

A comparison is made between X-ray absorption spectra at the sulphur K edge for CdS in wurtzite and zincblende structures. Differences between the polarization dependences of the X-ray spectra are expected due to the differences in symmetry for the two modifications. Multiple-scattering calculations in both structures are compared to published spectra and allow us to interpret a strong dichroic effect in the wurtzite structure. The intensity of a specific resonance is related to the middle-range order around sulphur atoms and potential applications of this fingerprint analysis are proposed.

Superconductivity for the Y(Ni_1-xPt_x)₂B₂C compounds is reported. X-ray diffraction patterns of the Y(Ni_1-xPt_x)₂B₂C compounds were indexed on the basis of the modified ThCr₂Si₂-type structure. With increasing Pt concentration the lattice parameters a and c and unit-cell volume v increase linearly. The expansion of unit-cell volume for YPt₂B₂C is about 18% compared with that for YNi₂B₂C, whereas the superconducting transition temperature decreases monotonically from 15.2 K for YNi₂B₂C to 10 K for YPt₂B₂C.