Table of contents

In bootstrap percolation, sites are occupied at random with probability p, but each site is considered active only if at least m of its neighbours are also active. Within an approximation position-space renormalisation group framework on a square lattice the authors obtain the behaviour of the critical concentration p_c and of the critical exponents nu and beta for m=0 (ordinary percolation), 1,2 and 3. They find that the bootstrap percolation problem can be cast into different universality classes, characterised by the values of m.

A nuclear magnetic resonance technique is described which can greatly amplify weak spectral features in the wings of NMR spectra at low temperatures. Partial saturation of the strong central part of the spectrum is detected due to symmetrical pumping of wings of low amplitude on each side of the spectrum. Symmetrical pumping avoids the bottleneck which occurs when one wing only is irradiated. The technique has been applied to the observation of weak tunnel sidebands in the spectrum of methyl malonic acid.

An ODMR study at 1.6K shows that the 3.4 eV luminescence of Y₂O₃ originates in a triplet state. The results are consistent with an intrinsic trapping mechanism for excitons. The nature of the trapping mechanism is discussed. Results of an ODMR study of SC₂O₃ are also reported, using the 3.6 eV luminescence.

A theoretical model is presented for the calculation of projected range distributions of energetic implanted ions in multilayer targets. In this approach, which is based on the energy distribution of the implanted ions at different depths within the target, the angular deflection of the penetrating ions is taken into account. The calculations employ the power-law approximation for the nuclear scattering cross section and results are presented for large angular scattering of 20 keV aluminium implanted into germanium and for small angular scattering of 355 keV arsenic implanted into silicon. A range profile is also derived for 20 keV boron implanted into a substrate coated with a layer of silicon nitride to demonstrate the effectiveness of the model as applied to non-uniform target substrates. These projected range distributions are compared, where possible, with other theoretical calculations and/or experimental results.

The dynamical properties of a simple model of phase transitions are discussed using Mori's method. The response function is extended to the second order and the temperature behaviour of the memory kernel in the vicinity of T_c(T<or=T_c) is estimated. It is found that the central peak may be observed in addition to the soft-mode peak, at least in the case of the so-called displacive limit, and that the frequency of the soft mode does not vanish at T_c.

In this the first in a series of two papers the authors provide a detailed exposition of a self-consistent symmetrised matrix method which is well suited to the study of localised defect systems in diamond-like and zincblende semiconductor crystals. The technique requires the full exploitation of the defect symmetry and they show how a group theoretical analysis can be used to great advantage for defects with T_d, D_2d and C_3v point-group symmetries. When implemented, the technique is equivalent to a finite-cluster method employing many hundreds of atoms-typically between 300 and 1400.

For pt.I see ibid., vol.17, p.2575 (1984). The authors present the results of their calculations on the ideal and reconstructed vacancy and divacancy in silicon and the ideal and Jahn-Teller distorted cation and anion vacancies in gallium phosphide and zinc selenide. For the silicon vacancy they find that the charge density profile, the defect potential and the Jahn-Teller parameters are all in agreement with the existing results obtained from the self-consistent Green function methods. They also present a consistent description of the silicon dangling bond. An analysis of the localised structure of the divacancy in silicon is given, and they argue that the electron-lattice coupling at the divacancy should be significantly weaker than that at the single vacancy. The authors provide a comprehensive description of the dangling-bond states of vacancies in GaP and ZnSe and a coherent analysis of their results is presented. They predict a strong and systematic variation in the Jahn-Teller coupling constant across the periodic table, and their results are briefly compared with the existing experimental data.

Existing magneto-optical data on shallow donors in InSb subjected to high magnetic fields and strong hydrostatic pressures are analysed theoretically using variational wavefunctions and taking into account the realistic energy band structure. The data are successfully described assuming that, in addition to a pressure variation of the effective mass, the static dielectric constant varies from 16.4 at zero pressure to 14.8 at 9 kbar. It is argued that the strong pressure dependence of the dielectric constant of InSb is due to the narrow-gap band structure of the material.

The authors have calculated self-consistent total-energy surface for hydrogen present interstitially as H⁺, H⁰ and H₂ in crystalline silicon and diamond. The dissimilarities of the two materials are more evident than their similarities, for they show molecular hydrogen to be the stable form in silicon, and atomic hydrogen to be the stable form in diamond in the absence of impurities. The energy surfaces for H⁰ and H⁺ are complex, with minima too small to trap the atoms when zero-point energy is taken into account. They discuss their results in relation to other theories and to the normal and anomalous muonium ( mu ⁺e^-) experiments.

The low-field drift mobility of electrons scattered by background and remote impurities, and by acoustic and polar optic phonons, is calculated for quasi-one-dimensional (Q1D) semiconducting structures using the relaxation time approximation. Approximate analytic expressions are derived for the momentum relaxation rate for the various scattering processes by assuming a 2D infinite potential well at the interfaces between the thin wire and cladding and using a momentum conservation approximation. The electron mobility is evaluated numerically in the size quantum limit and is found to be enhanced over the mobility of a 3D system if the phonon scattering is the dominant mechanism and if the transverse dimensions of the wire are large enough. The limitations of the present model are discussed in detail.

Simplified expressions for the fourth-frequency-moment sum rules for the longitudinal- and transverse-current correlation functions have been obtained for a two-dimensional classical Coulomb fluid interaction with a logarithmic potential. The numerical results for these sum rules are presented as a function of wavenumber k for Gamma =2, 10 and 40. Using the exact result for the triplet correlation function for Gamma =2, it is found that the error involved in the use of the superposition approximation is about 5% for 0.4<or=k<or=4.0. Sum rules and a simple mean-field theory are used to study the plasma wave dispersion for Gamma =72. Results are in close agreement with recent molecular dynamics calculations.

The authors study the effect of metastability on the spin wave propagation in spin glasses. The magnetic excitations in a given local minimum are described by the excitations of the Mattis-Heisenberg Hamiltonian. They are led to consider, within this picture, a spin glass as a disordered antiferromagnet that cannot sustain long-range magnetic order owing to frustration.

The authors calculate the ground state susceptibility chi ₀, to leading and next-leading order in a 1/n expansion, for the N-fold degenerate Anderson model in the integral valent limit. From this and perturbational results they are able to calculate the Wilson numbers W(N), which relate to chi ₀ and T_K, to first order in 1/N.

Properties of both ferromagnetic and antiferromagnetic one-dimensional chains have been used in discussions of magnetic systems in which the strongly anisotropic nature of the interactions permits them to be considered (above any three-dimensional ordering temperature) as quasi-one-dimensional systems. A chain in which both symmetric (Heisenberg) and antisymmetric (Dzyaloshinksi-Moriya) interactions are present provides a further example that can be used to model some magnetic systems. One specific soliton-like excitation in such chains is shown to have properties relevant to the low-temperature behaviour of weak ferromagnetic materials. Linear coordination polymers provide appropriate examples of these materials and comparison is made with experimental data available on CoBP.

Ferromagnetic resonance (FMR) measurements on the magnetic quasi-one-dimensional systems (C₆H₁₁NH₃)CuCl₃ (CHAC) and (C₆H₁₁NH₃)CuBr₃ (CHAB) in the region 8< nu <75 GHz and at a temperature of 1.25K are presented. The experimental results can be described quite well by a classical mean-field model assuming that, in a first approximation, the ferromagnetic chains behave like independent entities. A comparison of this model with the experimental results yields accurate values for the exchange anisotropy. These values indicate a pronounced easy-plan anisotropy for CHAB, whereas for CHAC the inferred anisotropy is clearly orthorhombic. These results are in fair agreement with previously reported measurements of magnetisation and specific heat.

Ferromagnetic resonance measurements are presented on the quasi-one-dimensional S=¹/₂ ferromagnetic compound (C₆H₁₁NH₃)CuCl₃ (CHAC), indicating the existence of magnon bound-state resonances (MBR). In addition to the normal ferromagnetic resonances several extra modes were observed in the temperature region 1.2K<T<4.2K and at various frequencies (18 GHz< nu <75 GHz). It is shown that these extra resonances can be interpreted in terms of Delta m=+or-1 transitions between magnon bound states. The experimental results are compared with three theoretical models: the S=¹/₂ ferromagnetic xxz and xyz models and a semiclassical model which shows the possibility of inducing transitions between envelope soliton states in ferromagnetic resonance experiments. The three models give qualitatively similar results for the low-lying excited states of the magnetic chains in CHAC. The experimental results can be described best by the S=¹/₂ ferromagnetic xyz model.

Heat capacity data are presented for KTaO₃ doped with various amounts of Li. Two anomalies are resolved at low temperatures: a peak of c/T³ versus T at 10K similar to one found in pure KTaO₃ and in many ferroelectrics; and a kink in c/T³ versus T at 30K only in samples heavily doped with Li. These findings may be explained in terms of a random internal field coupling non-linearly to lattice modes. Internal fields are produced by off-set charges and when these charges become mobile with rising temperature the fields average to zero and the lattice modes are allowed to vibrate in a bias-free manner. The charges responsible for both anomalies in KTaO₃ are believed to be of extrinsic nature: electrons dissociated from unknown donors are responsible for the 10K anomaly while intentionally doped Li ions substituting for K at an off-centred position induce the 30K anomaly.

Temperature-dependent positron annihilation lifetime and Doppler broadening experiments were performed on single crystals of 2H-TaSe₂ to search for effects from known charge-density-wave (CDW) phase transitions. Thermally generated equilibrium vacancy formation in 2H-TaSe₂ could apparently be detected as well. Positron lifetime spectra were measured over the temperature range 10-787K. Two lifetimes were observed, a short-lived component which was assigned to positron annihilation in the perfect lattice, and a long-lived component from annihilation in vacancy-like defects. The intensity of the long-lived component was seen to increase as a function of temperature above 300K, while the short-lived lifetime decreased, consistent with the two-state trapping model of the positron. The positron lifetimes in the perfect lattice, and in the thermally generated vacancies, were found to be 0.173+or-0.015 ns and 0.378+or-0.008 ns respectively. The apparent activation energy for the thermally generated defects was found to be 0.12+or-0.03 eV. Doppler broadening spectra which were observed in the temperature range 20-300K exhibited no abrupt change of shape coincident with known CDW phase transition temperatures. However, anisotropic lattice expansion effects associated with 2H-TaSe₂ were observed. The application of positron annihilation techniques to the study of CDW systems is discussed in light of these results.

Thin discontinuous films of lead, of thickness 10-100 AA, were evaporated onto 120 AA copper films in order to examine the superconductivity and localisation effects. The temperature and magnetic field dependences of the resistance were studied. It was found that the addition of lead on the copper film increased the spin-orbit interaction, and that the inelastic scattering time was shortened at 10K due to the additional contribution of phonons of from the lead. Superconducting fluctuations in some films were observed far above T_c (T>or approximately=3T_c). The results are described well by localisation theories and by Larkin's theory of superconducting fluctuations.