Table of contents

The backbone of the infinite percolation cluster is shown by Monte Carlo studies to be a fractal object, on short length scales. Its measured fractal dimensionality d_B, at two dimensions, is found: d_B=1.68+or-0.02. Numerical calculations for the anomalous diffusion on the backbone are also performed on the same samples. The value of the spectral dimensionality d_B, extracted from the power law behaviour of the average number of distinct visited sites, is obtained: d_B/2=0.625+or-0.005. Both results show clearly fractal-to-Euclidean cross-over above the percolation threshold. A general relation between fractal and spectral dimensionalities pertaining to the infinite percolation cluster and to the backbone is also given and checked numerically.

Exact calculations of the spin-spin correlation function q_j in the localised-electron limit of Gutzwiller's (1963, 1965) variational approximation to the Hubbard-model group state, for rings with numbers of electrons N=4(2)18, strongly suggest that q_j varies as (-)^j/j at large separation j between the spins. Monte Carlo calculations for N up to 100 reproduce this behaviour.

The magnetic phase transitions of high-stage MoCl₅-graphite intercalation compounds have been investigated by magnetic susceptibility and spontaneous magnetisation measurement in the temperature range 16 mK<or=T<or=4.2K. The experimental results show that the successive magnetic phase transitions occur at T_cl and T_cu. The upper transition temperature T_cu is not dependent on the stage number (N) of these compounds (T_cu=1.60K), which suggests that the magnetic ordering between T_cl and T_cu is two-dimensional. The lower transition temperature T_cl shifts to lower temperatures as the stage number increases from 3 to 5 (T_cl=690 mK for N=3, 500 mK for N=4 and 400 mK for N=5), which gives an evidence for the three-dimensional magnetic ordering below T_cl.

A phenomenological theory of the incommensurate phase transition which occurs close to the alpha - beta transition in quartz is presented. This theory assumes that the coupling between the soft optic mode of the alpha - beta transition and the acoustic modes play an important role in the formation of the modulated structure. According to the values of the phenomenological parameters, different kinds of incommensurate structures can form, in particular single-k or triple-k structures. The available experimental data concerning the quartz transition are discussed.

A band structure calculation using well localised orbitals obtained in a self-consistent manner has been performed on NiO. The localisation of the orbitals allows the treatment of both the valence and the lowest conduction bands by the tight-binding method. The details of the crystal potential are presented. The charge densities calculated from the crystal one-electron function show the ionic nature of the compound and reveal the deviation from the perfect ionicity (ionicity 1.65). The asphericity of the nickel ion resulting from the cubic crystal field appears clearly. The crystal-field parameter Delta associated with the difference in the average energies of the e_g and t_2g bands compares well with the experimental value and is mainly due to the covalency.

For pt.I see ibid., vol.16, no.35, p.6713 (1983). The imaginary part of the relative dielectric functions epsilon ( omega ) has been computed in the electric dipolar approximation using a band structure calculation. The separate evaluation of the various band-to-band transitions allows the assignment of the main peaks of the curve. The reflectivity and absorption curves were then deduced and compared with the experimental results. The first absorption peak for NiO has been attributed to 2p to 3d transitions.

A simple analytic local pseudopotential has been suggested for silicon. This pseudopotential has four adjustable parameters ( beta ₁/ beta ₂, C₁, C₂, C₃) of which two are taken to give the values of W(111) and W(311) used by Cohen and Bergstresser (1966) and beta ₁/ beta ₂ is taken from Animalu and Heine (1965), leaving one parameter which the authors choose to obtain a fit. The band structure, reflectivity spectrum and valence density of states were calculated on the basis of this pseudopotential and compared with the experimental results and the corresponding non-local pseudopotential calculations. It is shown that the local pseudopotential approach to silicon can give at least as good results as the more complicated non-local approaches of recent years. This is due to the inclusion of form factors for larger reciprocal lattice vectors (g²>(2 pi /a)²11) which other workers have taken as zero. From the results of the present paper it becomes apparent that an adequate estimate of the influence of non-local features can be made only after investigations of the possibilities of the local pseudopotential.

The formation and break-up of the acoustic solitary-wave polaron from a free electron and acoustic phonons in one dimension is described. In an electric field the polaron moves as a massive rigid classical particle. Energy dissipation by acoustic phonons is weak, the mobility in the continuum limit is infinite, and the polaron drift velocity is the velocity of sound. The theory is applied to polydiacetylene and explains the experimental ultra-high mobility and saturated drift velocity found in that material by Donovan and Wilson (1981).

Three new approximations for the dielectric function of a uniform electron gas with a dynamical local-field correction are developed within the framework of the double-time Green function method. An essential property of these approximations is their self-consistency, as well as the incorporation of correlations between electrons with antiparallel spins in addition to ordinary correlations of the Hartree-Fock type. An analysis of the behaviour of the local-field correction at large wavevectors is carried out in the limits of large and small frequencies. It is shown that the high-frequency approximation satisfies exactly the sum rule for the third frequency moment of the function Im epsilon ^-1(q, omega ). The low-frequency approximation obeys the Niklasson sum rule, while the mean-frequency approximation leads to a self-consistent static structure factor.

Considers the effect of long-range Coulomb interactions on the properties of a model quasi-one-dimensional conductor. Use of the bosonisation method allows the author to obtain an essentially exact solution of the problem. Most spectacularly, for g₁>0(g₁ is the intrachain backward scattering constant) there is a metallic region in the phase diagram between the regions of density-wave and superconducting instabilities. In addition, the Coulomb interaction enhances the tendency towards density-wave ordering, whereas the superconducting fluctuations are suppressed. The implications of these results for current theories of (TMTSF)₂X superconductors are discussed.

Although gallium in low concentration in ZnSe acts as a shallow donor, complex compensation effects occur if its concentration is increased, so the resistivity begins to increase with increasing impurity content. Slow wavelength scanning of the photocapacitance, infrared quenching of photocapacitance and transient photocapacitance have been used, therefore, to study the incidence of defect levels in Schottky diodes formed on ZnSe:Ga. All the devices exhibited an acceptor level 0.55 eV above the valence band, which is attributed to the self-activated acceptor complex (V_Zn-Ga_Zn)'. With increasing gallium content the concentration of this acceptor appears to decrease, and a new shallower acceptor 0.40 eV above the valence band was observed in devices of ZnSe doped with 50 ppm gallium. For comparison, and as a control, the same photocapacitance techniques were used to place the copper acceptor 0.67 eV above the valence band.

The authors give numerical results for the asymptotic form of the magnetic isotherm M(H) at T=0 for weak and strong fields for the j=³/₂, ⁵/₂ and ⁷/₂ Coqblin-Schrieffer model (1969). These are derived from integral equations based on the exact diagonalisation of the model. The low-field results indicate a clear change in qualitative behaviour of the model with j. They all show a positive initial curvature which increases with j and contrasts sharply with the behaviour of the standard Kondo model j=¹/₂. In high fields the leading terms in an asymptotic expansion in log (g mu H/T₁) have been calculated. From these results the Wilson numbers, which relate the zero-temperature susceptibility to Kondo temperature T_K, as defined by the high-temperature series expansion in log T/T_K, have to be calculated for the j=³/₂, ⁵/₂ and ⁷/₂ models. The j=⁷/₂ results are applied to the compound YbCuAl. Using the single parameter determined from an earlier fit to the T=4.2K magnetic isotherm the authors find excellent agreement with the high-temperature susceptibility over a temperature range from 140 to 1000K. The results explain the apparent reduction of the moments of the Yb ions from their free-ion values.

Phase diagrams are derived, in the context of the infinite-range model of Sherrington and Kirkpatrick (1975) for spin glasses with single-ion uniaxial anisotropy. Special attention is given to the case where magnetic ions with competing anisotropies are dissolved in the same host. In general four distinct phases are possible: a paramagnetic phase, and three spin-glass phases in which longitudinal and/or transverse spin degrees of freedom are frozen. For mixed anisotropies, a rich variety of phase diagrams is predicted as a function of the anisotropy strengths and the concentrations of the magnetic ions. In nearly all cases where the anisotropies compete two consecutive transitions are predicted, in which first longitudinal and then transverse spin degrees of freedom freeze out (or vice versa) as the temperature is reduced. These double transitions should be observable in rare earth systems such as YEr_1-yTb_y and YEr_1-yDy_y.

Dynamical aspects of the 2D Gaussian Ising spin glass are studied by a Monte Carlo simulation. The relaxation times tau _i of individual spins in the system are determined by analysing their autocorrelation functions. The distribution of In tau _i turns out to be broad, and rather homogeneous, and with the decreasing temperature its upper limit increases more rapidly than expected from the simple Arrhenius law. These tau _i are shown to reproduce excellently most of the qualitative features of the total spin relaxation function and the complex AC susceptibility observed experimentally in various spin-glass systems. The authors argue then that the change of the tau _i distribution by temperatures originates from the cooperative aspect of spin clusters, which themselves are by no means rigid even in the limited temperature range investigated.

Investigates the bicritical dynamics of one-dimensional bond-diluted kinetic Ising models in the percolation limit at criticality. A wide class of single-spin-flip dynamics is applied and domain boundary diffusion arguments are used to identify the dominant processes producing flipping of the ordered finite chain segments constituting the diluted chain. Exact expressions for the rate of flip as a function of length of segment are obtained and are used to derive corresponding expressions for the decay of equilibrium correlations, and of the magnetisation (from a non-equilibrium uniformly magnetised initial state) in the chain. The results are in agreement with those of earlier rigorous calculations restricted to the special case of Glauber dynamics.

The effect of uniaxial (100), (111) and (110) stresses on the EPR fine-structure lines of Cr³⁺ on octahedral Ti⁴⁺ sites in SrTiO₃ and Mg²⁺ sites in MgO have been measured at 300K. The spin-lattice strain coefficients G₁₁ and G₄₄ were determined. From them, the authors deduced the intrinsic superposition-model parameters b₂=2.37+or-0.04 cm^-1 and t₂=-0.36+or-0.01 in SrTiO₃, and b₂=2.34+or-0.01 cm^-1 and t₂=-0.12+or-0.11 in MgO, respectively. A substantial dependence of G₁₁ strain coefficients on charge misfit between Cr³⁺ and the substituted ion was found as has been calculated theoretically by Sangster (1981). The small negative t₂ exponents and positive b₂ reported here are interpreted as resulting from the three occupied t_2g orbitals of the ⁴A_2g ground state of Cr³⁺ as compared with the ⁶A_1g of Fe³⁺. A consistent analysis yields a maximum of the positive b₂(R) of Cr³⁺ at R_max=2.102+or-0.005 AA in MgO, whereas the negative b₂(R) of Fe³⁺ has a minimum at R_min=1.7+or-0.2 AA. The deduced b₂(R) dependence is confirmed for trigonal LaAlO₃ and Al₂O₃, where the known b₂⁰(Fe³⁺)/b₂⁰(Cr³⁺) ratio and sign are quantitatively accounted for.

Phase transitions and complex permittivity were determined at 35 GHz for the organic compounds: ((CH₃)₄N)₂CoCl₄ and ((CH₃)₄N)₂ZnCl₄. A differential thermal analysis confirmed the observed microwave transition in the first compound.

The surface energies and work functions of the disordered binary alloys of alkali metals are calculated using the density functional formalism and the variational principle for the energy. Vegard's law for the volumes is assumed. To calculate the structure-dependent pseudopotential contribution the virtual-crystal approximation and the linear relation between the Wigner-Seitz radius and the core radius of the Ashcroft model potential is used. The calculated variation of the work function against the concentration of the constituents is in good agreement with the measurements for Na-K, K-Rb and Rb-Cs systems.