Table of contents

A scaling analysis for some random walk properties (range, renewal theory) on percolation clusters is outlined. Numerical simulations performed in the Bethe lattice case are in good agreement with the predictions of the scaling theory. The values d=⁴/₃ and d=4 for the spectral and fractal dimensions are also confirmed.

Reports on thermal evidence for the existence of the phase transition from the incommensurate charge density wave state to the undistorted form of 1T-TaS₂. The effect of the transition on the reflectivity spectra is discussed in terms of a metal-insulator transition.

The heat capacity of the solid electrolyte Ag₂₆I₁₈W₄O₁₆ has been determined between 78 and 300K by adiabatic calorimetry. Three transitions occur, two first order (198.5 and 248.6K) and another more gradual transition producing a lambda-shaped peak at 275.6K. The results agree well with those of an earlier study by differential scanning calorimetry.

The experimental results of Mathiot and Edelin (1980) for the diffusivity of In in GaSb are interpreted in terms of two parallel diffusion mechanisms involving the divacancies (V_Ga-V_Sb) and (V_Ga-V_Ga). This interpretation provides a better fit to the experimental data than the V_Ga diffusion mechanism proposed by D. Mathiot and G. Edelin (1980).

It is pointed out that the approach of Lee et al. (see ibid., vol.15, p.L469, 1982) for the computation of the ground state energies of shallow donors in Si and Ge is similar to a spherical band approximation in the light of an earlier work by Tefft (see Bull. Am. Phys. Soc., vol.13, p.710, 1968).

Measurements of the inelastic mean free path in two-dimensional indium oxide films are reported. The results suggest that the phase-breaking time in this material varies as T^-1, which agrees with the dependence predicted by several theoretically known scattering mechanisms. On the other hand, the actual values of the inelastic mean free path, at the same temperature, seem to be essentially independent of the films bulk resistivity. This latter feature may suggest the existence of a phase-breaking mechanism characterised by a scattering time that is proportional to the resistivity.

In this article the authors examine the analytic structure of the Bethe ansatz solution for the ground state energy of the symmetric Anderson model as a function of the interaction U. They find that the energy is analytic for all real U and examine also the strong coupling limit U to infinity .

The author investigates the use of the phenomenological renormalisation group transformation in the nearest-neighbour square Ising model by means of correlation lengths defined by the moments of the pair correlation function.

An improved treatment of the problem of non-additivity in superexchange is proposed. It is stressed that the description of the interference does not require the postulation of any new superexchange mechanisms.

Electron spin resonance (ESR) measurements are reported for Cr⁺ ions occupying octahedral symmetry sites in MgO. The spin Hamiltonian parameters are: a=(4.18+or-0.02) mT; A=(1.86+or-0.02) mT; g=1.9997(4). These monovalent ions are produced in additively coloured MgO by optical excitation at 77K in the wavelength range 250-600 nm, presumably by the photoconversion of Cr²⁺ ions. The Cr⁺ state is stable at 77K but decays on warming to room temperature. Photoconversion of F centres to F⁺ centres also proceeds during optical excitation, mainly but not exclusively in the F band. Such optical excitation is found to change the effective spin-lattice relaxation time for F⁺ centres. There is no correlation between the optical creation of Cr⁺ ions and the photoconversion of F to F⁺ centres.

The ESR parameters of vanadium species in oxide-type matrices are reviewed and a reassignment of the paramagnetic vanadium species in aluminophosphates from V⁴⁺ to VO²⁺ is proposed.

For ODMR spectra observed by monitoring the recombination emission from donor-acceptor pairs, it is usually assumed that signals which correspond to increases in emission intensity can be attributed to the donors and acceptors directly involved in the radiative transitions. It is shown that such an interpretation can be in error if energy transfer is important.

The influence of long-range interactions between particles on the commensurate-incommensurate phase transition is investigated. The local theory (Landau theory, elasticity theory) is shown to be invalid at large distances. The effectiveness of different long-range interactions is examined. The electrostatic forces appear to be ineffective in three dimensions. A new resonance phenomenon is predicted for the longitudinal incommensurate structure.

A Raman scattering study of the non-ferroic and of the improper ferroelastic structural phase transitions (SPT) in the perovskite-type layer compound RbAlF₄ is reported. It is shown that the SPT occurring at T_cl=551K (D_4h¹ from or to D_4h⁵) and at T_c2=282K (D_4h⁵ from or to D_2h¹³) are related to displacive mechanisms owing to the occurrence of one and two soft phonons below T_c1 and T_c2 respectively. The results are consistent with a first-order character for the SPT at T_c1 and a second-order character for that at T_c2. Moreover, in the tetragonal D_4h¹ and D_4h⁵ phases, the Raman spectra exhibit a number of features which cannot be explained by the selection rules at q=0. In particular, one of these additional lines exhibits a soft-mode behaviour above the T_c2 transition, while the condensing phonon is a zone-boundary mode. Such features are imputed to the loss of translational symmetry caused by the existence of intrinsic structural disorder.

The diatomic Toda lattice, a linear chain with exponential interaction and alternating masses, is coupled to different heat baths at the two ends. The non-integrability of the system leads to a quasi-ergodic behaviour. It is shown numerically that a stationary linear temperature gradient is supported by the chain. The conductivity coefficient kappa depends on the mass ratio and the temperature of the heat baths, but not on the chain length. The theoretical values for kappa compare reasonably well with experimental results in BN and MgO.

Studies quasiclassical solutions of a quantum system, a crystal electron in a uniform steady electric field. Classical solutions can be formed from wavepackets of Houston functions or Stark states which are tightly localised in both position and crystal momentum. The position and momentum can be localised initially within the uncertainty principle. However while the momentum uncertainty is conserved with time the position uncertainty oscillates with the Zener period. It is maximal as the inflection points of the band structure. The departure from the initial value of the position uncertainty depends on the band structure and is inversely proportional to the field. For fields lower than approximately 10 kV cm^-1 the electron can only be tightly localised for times short compared with low-field scattering times. For fields higher than approximately 10 kV cm^-1 the electron can be tightly localised throughout the whole Zener orbit.

In pt.I (see ibid., vol.15, p.1939, 1982), a self-consistent cluster CPA, generalised to take into account the effects of clusters, was developed. Off-diagonal disorder and short-ranged order were also taken into account. In this paper the method has been applied to calculate the density of states of the valence band of ternary random III-V semiconducting alloys.

A method is developed to calculate the localisation length in disordered systems. It can be considered to be a generalisation of the method of Herbert, Jones and Thouless (1971-2) for one-dimensional systems, to wires and nu -dimensional lattices. The localisation length can be calculated under some assumptions when the disorder has a Lorentzian probability distribution. No localisation transition is found, that is the localisation length is finite for arbitrarily small non-zero values of the disorder. For other distributions a perturbation expansion is developed, which is valid for large values of disorder and small energies. The dominant term and the first-order correction are calculated.

The luminescence at 0.839 eV in GaAs:Cr is interpreted as a split ⁵E-⁵T₂ transition within the Cr²⁺ ion. The degeneracies are removed by first- and second-order trigonal-field and spin-orbit-coupling perturbations. The parameters appearing in the effective Hamiltonians for ⁵E and ⁵T₂ are all deduced from the high-resolution photoluminescence spectroscopy of Barrau and co-workers (1982); the fit of the energy levels and oscillator strengths provides a very accurate solution. The electronic and Jahn-Teller parameters are deduced. These results lead to a complete interpretation of the magnetic field Zeeman splittings of Eaves (1980), Killoran and co-workers (1980). The accuracy of the interpretation of all the experimental results represents an important improvement on previous models. In particular, the authors show how the interpretation of the ground state a ⁵E (C_3v) is a poor approximation to the results presented.

Coherent medium theory for a master equation description of transport on random lattices is extended to includes scattering in clusters larger than two sites (or one bond) exactly. Bond and site-averaged numerical calculations for the square lattice show some features of transport are improved by this method but that larger clusters are needed in order to obtain exact long-time properties.

The current in a semiconductor under a high electric field is studied by solving the Liouville equation. The formal theory is developed using the Stark ladder representation, and the infinite series of a perturbation expansion for the weak electron-phonon coupling is evaluated. The effect of an electric field on the scattering matrix is studied in terms of the self-energy due to higher-order scatterings. It is shown that the real part of the self-energy, as well as the imaginary part, has a role in the transport properties. The results are applied to the velocity overshoot and the ballistic effect in a short semiconductor device. It is found that the velocity overshoot is realised by the inelastic nature of the scattering while the ballistic effect arises from the variation of the self-energy with time or the correlation effect.

Measurements of the Hall effect and magnetoresistance of four tin-doped bismuth samples in the temperature range 4.2-300K and in magnetic fields up to 6 T have been made. The resistivity data are converted to conductivities. These are reported and used to evaluate the temperature dependence of the excess carrier density and of the thermopower. The evaluation is performed with the Fermi energy as the only adjustable parameter within the pseudo-parabolic model which the authors have previously introduced. The excess carrier density is found to decrease with temperature, and this feature is used to analyse the data in terms of an acceptor energy level. A relation valid for all samples is found between this level and the Fermi level. For the thermopower agreement is found between the calculated values and the experimental ones reported in the literature.

The effect of screening by conduction electrons on the magnetoelastic coupling due to the crystal field in the Laves-phase rare-earth (RE) intermetallics is calculated and applied to REAl₂ compounds. The Thomas-Fermi and Hartree approximations for the screening are considered. Tetragonal, orthorhombic and rhombohedral strains are considered through the distortion of the lattice and of the screening and ligand-ion charge densities. The effect of the screening on magnetoelastic parameters is substantial. The introduction of conduction band exchange is able to modify the sign of the tetragonal parameter compared with the bare-ion point-charge model. The Friedel oscillations of the crystal potential modify the sign of the rhombohedral mode as well. A comparison with available magnetoelastic data for the compounds NdAl₂, PrAl₂ and TbAl₂ is presented and good agreement with calculations is obtained if conduction electron band exchange is envisaged.

The neutron scattering cross section and neutron polarisation for scattering by single magnons are calculated for a ferromagnetic Heisenberg Hamiltonian with various kinds of anisotropy. Although in a one-magnon theory if it is not possible to distinguish between exchange and single-site anisotropies for an easy-axis system using this technique, it is found that is possible to distinguish between an exchange anisotropy and a single-site anisotropy for an easy-plane system by measuring the neutron polarisation at different scattering wavevectors. It is also possible to distinguish between easy-plane systems and easy-axis systems by measuring the neutron scattering cross section for scattering of a completely polarised beam of neutrons for one particular scattering wavevector.

The ladder approximation is performed for metamagnets with uniaxial and exchange anisotropy and the following exchange couplings: in-plane nearest-neighbour ferromagnetic coupling J₁, in-plane, next-nearest-neighbour antiferromagnetic coupling J₂, and small interplane antiferromagnetic coupling J'. Taking J₂ into account encounters non-trivial difficulties but the authors have tackled this problem because a suitable lattice-dependent value of J₂=J₂ causes the long-wavelength magnon dispersion curve to become a quartic power of the wavevector instead of a quadratic one, so one can expect dramatic consequences. In effect this is the case: the results the authors obtain for FeBr₂, which has just the convenient ratio J₂/J₁ to fit the situation described above, give weak renormalisation and damping for the uniform mode, while for FeCl₂ dramatic variances, at least from a quantitative point of view, do not arise with respect to previous approaches, where J₂ was neglected. Such a result cannot be inferred on the basis of a finite-order perturbation theory which, on the contrary, would suggest a heavier renormalisation when the dispersion curve is more flat for small wavevectors, as in FeBr₂.

Phase diagrams are derived, at the mean-field level, for spin glasses with uniaxial anisotropy. Exchange anisotropy and single-ion anisotropy are considered separately. The critical anisotropies at zero temperature are expressed in terms of the internal field distributions for Ising and planar systems, avoiding the replica method. The phase diagrams are qualitatively similar for the two models except that for 'easy-axis' exchange anisotropy two consecutive transitions are predicted as a function of temperature for all values of the anisotropy, whereas for single-ion anisotropy two transitions are predicted only when the anisotropy is sufficiently weak.

The EPR spectrum of 'as grown' SrF₂:Mn crystals has been measured. In addition to the well known signal due to cubic Mn²⁺ ions a new Mn²⁺ signal having trigonal symmetry has been observed. The EPR data have been explained using the spin Hamiltonian H=g mu _BS.H+D(S_z²-¹/₃S(S+1))+AS.I+H_SHF with S=⁵/₂, I=⁵/₂ and the z axis along a (111) direction. The values obtained for the parameters are: g=2.004+or-0.005, mod D mod =1615+or-10 MHz, mod A mod =265+or-10 MHz with A and D having the same sign. The evolution of the EPR spectrum when measured at different temperatures is also reported. A linear dependence of D on temperature has been found. Changes induced by thermal treatments and low-temperature X-irradiations are given. A tentative model for the manganese centre responsible for the trigonal EPR signal that consists of a fluorine vacancy next to a substitutional Mn²⁺ ion is proposed.

Presents measurements of the one-magnon Raman scattering spectrum from antiferromagnetic FeF₂, which show a temperature-dependent asymmetric lineshape with a pronounced tail on the high-frequency side. The degree of asymmetry, and also the overall linewidth, increase with temperature over the temperature range studied (up to ¹/₂T_N, where T_N=78K). It is shown that the mechanism responsible for the linewidth is the scattering of a magnon by the disorder at finite temperatures in the longitudinal spin components. This gives rise to a damping Gamma ( omega ) that is frequency dependent, and hence a lineshape that is asymmetrical. A good empirical description of the lineshape is obtained using a high-density perturbation expansion method. The theoretical estimates of the linewidth are smaller than the experimental values, and we discuss how these estimates may be affected by the presence of optic magnon modes.

The secondary emission, due to recombination of excitons in the vicinity of the indirect band bottom is investigated, where excitons relax their kinetic energy through multiple scatterings with acoustic phonons and a nonradiative decay process. In this case, the secondary emission can be separated into the two parts: the Raman scattering (RS) and the hot luminescence (HL). The spectral lineshape of the HL directly reflects the exciton distribution near the band bottom. The distribution has been calculated by the Fokker-Planck equation with the source term of exciton supply through the indirect absorption process. It is shown that the excitation spectrum of the RS line and the spectral structure of the HL strongly depend on the two quantities: the kinetic energy of an exciton with the sound velocity and the nonradiative decay rate. General features of RS, HL and their relationship are studied for a system with material constants appropriate to BiI₃, since the experiments show that this is an ideal system for the authors' purpose.

Mean free paths associated with the scattering of electrons and holes are derived from experiments on impact ionisation in wide-gap semiconductors using the lucky-drift model. It is found that the mean free path for an electron or hole in any semiconductor obeys a simple universal law which implies a common phonon energy for electron and hole scattering and a dependence of mean free path on threshold energy ( lambda varies as E_i^-12/). The latter dependence is plausible in terms of a simple view of scattering of high-energy carriers in a nonparabolic band. This universal model is derived on the basis of experimental data reported by various authors in Si, Ge, GaAs, and InP. Results for GaSb and its alloys appear to be anomalous, whereas data from GaInAs in InGaAsP tend to support the model. The model predicts the ratio of ionisation coefficients k= beta / alpha and its dependence on field and temperature. It is shown that k in any semiconductor is determined by only the ratio of threshold energies of electrons and holes. A comparison with reported values is made and brief discussions of the spin-orbit resonance effect in AlGaSb and of the enhancement in GaAs/AlGaAs multilayers are given.