Table of contents

By means of elastic neutron scattering the authors have observed for the first time the polarisation of the ⁵⁹Co-nuclei in the hyperfine field of the ordered electronic magnetic moments through the term (b⁺-b^-) not=0 in the structure factor. The polarisation I of the nuclear moments gives rise to a new Bragg peak in CoF₂ whose intensity is proportional to I²(b⁺-b^-)². At very low temperatures (T<20 mK) I becomes large enough to produce a measurable (001) Bragg peak in CoF₂. The results indicate that they have achieved I=0.18 corresponding to a nuclear temperature of 19 mK. The corresponding (001)-intensity was 1% of the (002) peak.

The authors present numerical solutions of the hypernetted chain equation for the pair distribution function of the classical two-dimensional Coulomb gas over a wide range of couplings, 0.1<e²/k_BT<300. The pair structure and thermodynamics have a behaviour reminiscent of the three-dimensional case.

Room temperature reflectivity and thermoreflectance measurements of 1T VSe₂ below and above the charge density wave (CDW) transition temperature have been carried out. A noticeable change in the thermo-optical response at about 108K has been detected around 1.65 eV which seems to be due to the CDW onset. No evidence has been found of the commensurate CDW transition at 70K.

For pt.I see ibid., vol.14, p.L127 (1981). In three dimensions, there is a transition at a critical value W_c of the disorder parameter from a region of exponentially localised states to a region of extended states. When W decreases to W_c, the authors find a value equal to 0.66 for the critical exponent nu relative to the divergence of the localisation length. On the other side of the transition, they are naturally led to define an 'order parameter' and give its variation against W in the whole region of extended states. In two dimensions, a critical value W_c of the disorder parameter separates a region of exponentially localised states (W>W_c) from a region of 'quasi-extended' states which are non-square summable and fall off as 1/R^{eta (W)}. They give the variation of the exponent eta (W) in the whole 'quasi-extended' region. On the other hand, they show that the divergence of the localisation length when W decreases to W_c is now controlled by an essential singularity. As a conclusion, they describe the striking analogies with their results in any dimension and the behaviour of the 'XY' phase transition model.

The bandwidths for metastable states in a simple model of amorphous semiconductors is evaluated exactly. The region of metastability in the space of the model parameters (phase diagram) is deduced and the subregion corresponding to an infinite range model is indicated. The model predicts both paramagnetic and diamagnetic metastable states and the relationship between them is discussed.

The authors have calculated the internal energy, specific heat and susceptibility chi of random +or-J planar and Heisenberg magnets in two dimensions. In the Heisenberg model, chi is Curie-like at all temperatures studied. By contrast, the planar model chi decreases at the lowest temperatures, and increases strongly with increasing sample size at temperatures from (0.5-1)J. These results are compared with theoretical predictions for model systems with frustration and disorder.

Calculations of the relaxations of oxygen neighbours around Mnⁿ⁺, Feⁿ⁺, Coⁿ⁺ and Niⁿ⁺ impurities (n=2, 3 and 4) in MgO are presented. The values are used in an attempt to account for the enhancement of coupling to T_2u symmetry vibrations when the impurity carries excess charge. Although the correct trend is reproduced the point-ion coupling model fails to give the observed magnitude of the effect. Local hydrostatic, tetragonal and trigonal strains are related to the corresponding bulk strains. It is shown that for divalent impurities the fractional local strains are close to those in the bulk crystal but when the impurity carries extra charge large and symmetry-dependent reductions arise.

Calculations of the changes in energy associated with symmetry-adapted displacements of a central ion and its nearest neighbours (allowing for polarisation of all other ions) provide values of the corresponding force constants. The changes in these force constants when the central perfect-lattice ion is replaced by a foreign ion have been calculated on the basis of shell model interaction potentials for the defect systems Ni²⁺:MgO, Mn²⁺:MgO and Mn⁴⁺:MgO. The results show that simple models for force constant changes introduced by defects, as commonly used in Green function analyses of defect problems, are seriously inconsistent. Nevertheless some agreement is demonstrated between the present calculations of force constant changes and values found from fitting experimental results in Green function treatments.

Energies of formation and migration for Schottky and Frenkel defects in all the alkali halide crystals are calculated from a set of potentials by Sangster and Atwood (1978) and compared with parallel studies using different potential models. Some estimates of volumes of formation and migration obtained by studying variations in the energies with isotropic strains are also presented. For CsCl-structure crystals it is found that in general self-interstitials prefer distorted tetrahedral sites to face- and edge-centred sites but split interstitialcies provide the lowest-energy configurations.

A low-temperature calculation of the influence of the anharmonicity of the phonons on the dynamic structure factor is made for a compressible Heisenberg system. The anharmonicity is caused by the coupling of phonons and spins. The memory function of the displacement relaxation function is calculated to lowest order in the temperature. Only two-magnon processes are found to contribute to the memory function in this limit. The displacement relaxation function turns out to be very simple. The collision processes can lead to a second resonance. In two limits, the results are compared with the results of a continued fraction approximation. The qualitative agreement is good.

The density of states in the valence band of silicon has been calculated numerically using 6*6 and 30*30 k.p Hamiltonians with two different sets of band parameters. The bands are highly anisotropic and non-parabolic due to the small size of the spin-orbit splitting. The accuracy of the calculations is limited by the uncertainty in the band parameters. Because the bands are non-parabolic, the thermal average masses are temperature dependent. The thermal density of states effective mass varies by about a factor of two between low temperature and room temperature, while the thermal velocity mass is nearly temperature independent. It is shown that the dependence of the optical cross sections of deep levels on photon energy should extrapolate to 15 meV below the valence band edge, giving rise to systematic errors in determining thresholds. The additional non-parabolicity found with the 30*30 Hamiltonian is significant for optical cross sections, but not for thermal averages.

It is well known that periodic lattice distortions can occur in metallic systems due to the cut-off of the electron distribution at the Fermi surface. One-dimensional models of materials with strong nesting of Fermi surfaces in three dimensions are commonly employed to investigate such a Peierls transition involving a soft phonon of amplitude u. Calculations which take account of single-particle electronic energies only always give a lowering in energy U_bs from the distortion proportional to u² ln u, and consequently always predict a phase transition at a low enough temperature. This is in disagreement with the results of Halperin and Rice (1968) and of Chan and Heine (1973). The authors show very simply that if the electrostatic interaction between the electrons is included, then U_bs infinity -u² and so whether or not the phase transition occurs depends upon the balance between this term and the normal quadratic forces. They conclude that the Frohlich Hamiltonian is inappropriate for the discussion of this problem.

The three polariton branches connected with the heavy and light excitons in a semiconductor with a four-fold degenerate T₈ valence band, such as GaAs, ZnSe and ZnTe, are considered. Calculation of electromagnetic reflection and transmission coefficients requires two additional boundary conditions. These are taken as homogeneous equations in the exciton fields and their derivatives at the boundary. Reflection and transmission coefficients for normally incident light are derived, and a condition for energy conservation is given in terms of those coefficients. The theory of resonant Brillouin scattering is given. It is assumed that coupling to the acoustic phonons occurs by means of the deformation potential, and the theory is given in a macroscopic linear response formulation. If interference terms can be neglected, the general form of the Stokes cross section reduces to a sum of nine lines, each of which has a skew form.

A many-body calculation of the density of states and the Auger linewidths for the core levels of H, He and Li embedded in an electron gas is presented. In this calculation, relaxed atomic wavefunctions, orthogonalised plane waves for the conduction band and a dynamical response function which includes the orthogonalisation hole around the atom are included. Comparison with other theoretical calculations and the available experimental data is made.

Hopping transport in disordered systems may occur by many-electron hopping excitations due to the Coulomb interaction between electrons. Expressions are derived for the many-electron hopping rates. The most important factors in the derived expression are an activation factor, a factor which is an exponential of the sum of the hopping distances of the electrons participating in the excitation, and a factor which is a measure of the significance of the interaction energy in comparison with the disorder energy. The first two of these factors were also found in previous theories. The theory breaks down when the number of electrons n participating in a hop becomes extremely large. But for typical conditions the theory is valid up to n approximately 100 or more.

The authors have measured the critical electric field above which the charge density wave formed in NbSe₃ at 59K can slide freely in the crystal as a function of defects created at helium temperature by irradiation with 3 MeV electrons. In this case, contrary to those of doping with impurities or with proton irradiation, the depinning electric field is only weakly dependent on the defect concentration.

The effect of the propagation of ultrasound at an angle Theta relative to the direction of a DC magnetic field B in a degenerate semiconductor such as n-type InSb is investigated by using a quantum treatment which is valid at high frequencies and in strong magnetic fields. It is found that the real and imaginary parts of the linear longitudinal conductivity oscillate with the DC magnetic field when ultrasound propagates along the field for both parabolic and nonparabolic band structures. However, if the angle Theta is different from zero, these oscillations diminish for the nonparabolic band structure, and no oscillations can be observed for the parabolic band structure.

The metastable states of the Sherrington-Kirkpatrick model at T=0 are investigated within the 'innocent replica' framework, i.e. within a replica formalism without replica symmetry breaking. The density of metastable states is evaluated in the presence of an external magnetic field, and the energy and distribution of internal fields of the ground state calculated, as a function of the external field. These are found to be in good agreement with the data of Bantilan and Palmer (1980) and Palmer and Pond (1979).

The authors obtain the density of states of a random ferromagnet with long-range interactions, taking into account both diagonal and off-diagonal disorder.

The normal mode problem for the Mattis-Heisenberg model is simplified. A set of random finite difference equations is derived. This reformulation is used for a numerical study of the localisation of the eigenmodes. The averaged inverse participation ratio is calculated in one and two dimensions. Strong localisation effects are indicated but it is difficult to give the results an interpretation in the conventional localisation edge picture.

The authors investigate the temperature renormalisation of the magnetic excitations in FeCl₂, where, owing to the low value of the spin, a careful treatment of its large anisotropic effects appears to be necessary. A self-consistent renormalised theory which is not affected by kinematic inconsistencies is presented for a model Hamiltonian suitable to describe FeCl₂, i.e. including both anisotropic exchange and single-ion uniaxial anisotropy. The correctness of this theory is tested by means of an exact calculation of the self-energy in the T-matrix formalism, which is exact in the low-temperature limit. Explicit calculations have been performed for the temperature dependence of the energy gap (k=0) and the results compared with the experimental (AFMR, neutron scattering) data. The existence of a significant exchange anisotropy seems to be necessary for explaining the AFMR data. Indications are given about the magnitude of this anisotropy.

A detailed study has been undertaken of the shape and intensity of a specific line in the Raman spectrum of squaric acid at the phase transition (T_c=100 degrees C). Although the line is symmetry-forbidden in the high-temperature phase, its persistence points to a local low-temperature symmetry even above T_c. The shape and intensity can be explained within a unified picture involving assumptions about the two-dimensional character of the phase transition. The interplanar correlation function is found to show a temperature behaviour similar to that found for the long-range order parameter.

When a local time-dependent perturbation in a metal is switched on and then off, it is desired to calculate the probability P( epsilon ) for the system to be excited to a state of energy h(cross) epsilon . For a strong but slow perturbation V(t) the authors show that the problem reduces to the calculation of an evolution operator for a time-independent one-body potential W(V(t)) which is a functional of V(t). They calculate W for potentials possessing a time-independent phase-shift representation. For such potentials they calculate the evolution operator, and hence P( epsilon ), for a Fermi sea both at zero and finite temperature. They give simple applications of their results to problems such as X-ray photoemission spectroscopy and energy dissipation of an atom scattered from a metal surface. The relationship to a recent solution of the problem, at zero temperature, using a time-dependent Tomonagon representation is indicated.

The thermal emission of a metal-backed thin film of LiF is observed at the emission angle of 20 degrees . The observed spectra measured at elevated temperatures are analysed by using the response function based on the virtual-mode theory for the ionic film in order to derive the temperature dependence of the lattice dynamical quantities, such as phonon frequency and damping. The dielectric function derived from a theory based on the thermodynamic Green function technique is considered in the spectrum analysis. The estimated temperature dependence is discussed in terms of the phonon anharmonicity. The LST relation including the phonon anharmonicity is derived from the virtual-mode theory.

A simple theory of temperature dependence of photoemission is derived with a view to illustrating the main thermal effects. These prove to be: reduction in amplitudes of peaks due to hole state scattering and reduction in the matrix elements, and the shifting of surface state peaks which the authors attribute to narrowing of the band gap within which the surface state exists. Scattering of the escaping electron is relatively unimportant.

A detailed study is reported of the W (001) (1 × 1) to ( square root 2 × square root 2)R 45° surface phase transition by angle-resolved photoemission, in which data have been collected throughout the surface Brillouin zones (SBZ) of both structures. Assignments of surface states/resonances are made by comparison with calculated spectra, and existing theoretical models for the W (001) surface phase transition are critically examined in the light of the results. Although surface state coupling occurs at the new zone boundary on the Sigma symmetry line, the constant energy contours of these states are not flat along the zone boundary, and it is concluded that charge density wave transition mechanisms are not tenable.

A calculation of the photoemission from Al (100) and (111) surfaces, which includes band-structure effects but neglects screening of the photon field, gives good agreement with experimental results at fixed photon energy; it does not reproduce the observed variation in emission intensity from a fixed initial state as a function of photon frequency. Treating Al as a free-electron gas with a frequency-dependent local dielectric function is also unsatisfactory. However, using the simple hydrodynamic method for non-local screening at a metal surface, in which the surface polarisation charge is treated more realistically, the authors obtain good agreement with the frequency dependence of photoemission both from the Al(100) surface state, and from the Fermi level. This shows enhancement in photoemission below the bulk plasmon frequency, and a minimum at omega _p.