Table of contents

An excess resistivity has been observed in thin film polycrystalline samples of SnTe with low carrier concentration and is attributed to the additional scattering due to the phonon softening associated with the structural phase transition.

It is shown that a combination of crude mean-field theories developed for pure induced-moment magnets and for conventional spin glasses suffices to give a heuristic explanation of the occurrence of induced-moment spin-glass phases such as found in SeTb at intermediate concentration. The correct sequence of phases is also predicted.

Within a simple Bethe-Peierls-Weiss approximation the authors show by analytical means that a square hole or gap arises in the low-temperature probability distribution p(h₀) of the single-particle excitation fields h₀ at h₀=0 for an infinite-range spin glass. In an externally applied field, the hole remains centred about the zero value of the total field. The reasons for the unphysical low-temperature results occurring in the Sherrington-Kirkpatrick (1978) and Bethe-Peierls-Weiss treatments are clarified in the discussion.

Measurements of Faraday rotation in CdMnTe crystals were performed in magnetic fields up to 150 T. It was found that the optical transitions were shifted to lower energy by an intense magnetic field.

High-resolution absorption and luminescence spectra associated with the creation and decay of excitons bound to neutral donors in germanium are analysed in terms of the Kirczenow shell model (1977). Interparticle interactions in the excited state of the bound exciton, previously observed in phosphorus-doped germanium, are shown to exist in arsenic- and bismuth-doped material. In the luminescence spectra, transitions due to electron-hole recombination within bound m=2 multiexciton complexes are identified.

A previously developed bosonisation scheme is applied to the investigation of the zero-temperature critical behaviour of the XY model in a transverse field. It is shown how this method yields, in a simple and straightforward way, the results previously obtained using cumulants. The meaning of these results is briefly analysed.

Some of the properties of the bond diluted s-state Potts model are examined in this paper, and in particular the phase boundary. It is shown that as s to 1, the model is simply related to the bond percolation problem. By extending the replica arguments of Domany (1978) (which are probably exact), it is shown that near p, the phase boundary behaves as exp(-sK)=(ln s)/(s-1)(p-pc/pc) for all 2-D lattices. The authors also construct a coherent potential approximation that is exact for all lattices as s to 1, and for arbitrary s on Bethe lattices.

A detailed analysis of the X-ray scattering intensity of alpha -AgI has been carried out by an anomalous scattering technique. The two partial interference functions S_ij^dif(Q) for Ag-Ag and Ag-I pairs were estimated using the newly developed theoretical equations of the intensity. The partial distribution functions for I-I, Ag-I and Ag-Ag pairs in this work are consistent with the results obtained from molecular dynamics by Vashishta and Rahman (1978). The intensities of Debye lines were also explained satisfactorily in terms of pair distribution function for Ag-I pairs.

The mean-square displacement of an F^- interstitial and its first and second neighbours are studied using the lattice Green functions and the scattering matrix formalism. The interstitial is treated in the most general way, following the method of Maradudin et al. (1971). The mean-square displacement of the interstitial is found to be three to four times larger than those of the host atoms. The consequences of these results are discussed in the light of the experiments of Willis (1965) and the anomalous values of the mean-square displacements in fluorites at high temperatures, as observed by Thomas (1976).

The lattice dynamics of incommensurate modulated crystals is discussed in the harmonic approximation. The study is based on the symmetry group of such a crystal, i.e. a superspace group. The normal modes may be characterised by irreducible representations of the symmetry group. It is shown that the relevant representations may be labelled by wave-vectors in the Brillouin zone of the basic space group. The reduction of the equations of motion is treated. Finally selection rules for infrared absorption are derived.

A programme of elastic neutron-diffraction experiments has been undertaken to derive (and compare) atomic distribution functions, with high spatial resolution, for the antiferroelectric perovskites SiTiO₃, KMnF₃, RbCaF₃ and CsPbCl₃ in their cubic phase. The study of cubic CsPbCl₃ is presented. Data were collected out to a resolution limit of sin theta lambda =1.2AA^-1, and used in least-squares refinements of parameters describing anharmonic distributions for the Cs, Pb and Cl ions. Two different techniques yield essentially the same conclusions: anharmonicity is very much more significant for the Cl ion than for the metals and, the inharmonic parameters for Cl correspond to a small bulging of its distribution in the directions along which Cl is known to displace on passing to the low-temperature phase.

Earlier work treating solid state phase transitions as thermodynamic instabilities is generalised to include transitions in which the limiting relations between thermodynamic quantities such as the specific heat c_p, thermal expansion coefficients and elastic compliances are not linear. A classification scheme based on thermodynamic behaviour is obtained for solid state transitions which are very close to a bulk instability. A study is made of two continuous transitions of potassium hexachlororhenate. Using experimental data for the specific heat c_p, and for the thermal expansion coefficient alpha ₍₁₁₁₎, these transitions are classified according to the above scheme. It is predicted, for this material, that the critical temperature exponents for the diverging elastic compliance quantities are much greater than those of the specific heat or thermal expansion coefficients.

It is shown that the density can be used as the basic variable for calculating the properties of excited states. The correspondence is not between an eigenstate and its density, as is the case with the ground state, but between the subspace spanned by the number of lowest-energy eigenstates and the sum of their densities. An extension of the Hohenberg-Kohn-Sham theory (1964-5) for excited states has also been developed. The equations derived are similar in form to those for the ground-state density but the interpretation is different. The lowest-order approximation of the present theory coincides with Slater's 'transition-state' theory (1974).

The calcium hexaboride, CaB₆, is a typical semiconducting metal hexaboride. Here two self-consistent APW calculations of its electronic energy bandstructure are reported, in the muffin-tin approximation and in the warped muffin-tin approximation. In both calculations, the local-spin-density approximation is used and the relativistic effects are taken into account. The bandstructure of the muffin-tin approximation is semimetallic. The non-muffin-tin corrections in the warped muffin-tin approximation tends to cause a small, direct energy gap between the valence and conduction bands at the X points in the simple cubic Brillouin zone. The magnitude of the energy gap to 0.3 eV, in reasonable agreement with the experimental value, 0.4 eV, suggested by the temperature dependence of the electrical resistivity. The calculated result for the density of states agrees reasonably well with an experimental result for the XPS spectrum.

APW energy band-structure calculations on ScP have been carried out non-self-consistently for a variety of potentials in order to determine the sensitivity of the results to the exchange-correlation potential adopted. It is found that the X alpha _vi, the Hedin-Lundqvist (1971-2), and the Wigner exchange-correlation potentials give very similar results. Additional calculations have been performed using various values of alpha for the P and the Sc atoms, and also using l-dependent alpha parameters.

Self-consistent non-relativistic augmented plane-wave calculations are performed using the Hedin-Lundqvist (1972) and the X alpha exchange-correlation potentials. Both potentials lead to very similar band structures and charge densities. The self-consistency procedure is found to have only minor effects on the energy bands. The total and partial l-like densities of states are obtained by an LCAO interpolation. Yim et al (1972) found a gap of 1.1 eV from optical absorption measurements and concluded that ScP is a semiconductor. According to the present calculations ScP should be metallic and the experimentally observed optical gap could be explained by direct transitions from the P 3p to the Sc 3d bands.

Using neutron sources giving particles with energies of a few electron volts it is possible that the dispersion of exciton energy bands could be measured directly. Estimates of the cross sections for creation of excitons of both the Frenkel and Wannier type are given. The former give values similar to those for spin wave or electronic transitions but the electronic form factor makes these very small if the momentum transfer Q lies outside the first Brillouin zone. For Wannier excitons the cross section is always reduced by a factor giving the probability that the electron-hole pair are confined to the same atom. At large Q a process via the creation of virtual phonons gives a larger cross section is always reduced by a factor giving the probability that the electron-hole pair are confined to the same atom. At large Q a process via the creation of virtual phonons gives a larger cross section since it avoids the electronic form factor.

The electronic polariton modes of a simple one-dimensional two-band model are discussed. Non-parabolicity of the bands, spatial dispersion and electron-hole continuum states are taken into account.

The explanation of the experimental g-shift of Mg⁺:CaO by means of the (MgO₆) cluster is carefully examined. It is shown that the degree of hybridisation of the ground level a_1g* plays a decisive role on the sign of the g-shift and that, contrary to the conclusions of Boas, Clark and Pilbrow (1976), such a model is unable to explain the experimental g-shift of Mg⁺:CaO in a coherent way, even if third-order contributions are included.

High magnetic field, low-temperature Zeeman measurements of the ⁴A_2g to ⁴T_2g zero-phonon liners of Mn⁴⁺ in Cs₂SiF₆ are reported. The separation of the spin-orbit components of the ⁴T_2g term are established and are found to be an order of magnitude smaller than that predicted by static crystal-field theory. The reduction is explained in terms of Ham quenching of the off-diagonal spin-orbit interaction arising from a strong Jahn-Teller effect. Zeeman polarisations are found to be fully consistent with this Jahn-Teller model. Difficulties are, however, encountered in giving a satisfactory account of the relative intensity of the zero-phonon transitions.

A general theory of relaxation and resonance structure in the magneto-optical spectra of a semiconductor with parabolic energy bands has been developed from first principles by deriving a renormalised quantum transport equation from Liouville's equation. Generalisations and improvements on the earlier theories are illustrated, with explicit application to the magnetophonon resonance damping and the frequency shifting.

The thermodynamics of a classical Heisenberg system with layer structure is investigated by two different renormalisation group (RG) approaches. First for a small inter- to intralayer coupling ratio R=J'/J the interlayer interaction is approximated by a mean-field approach (MFA) whereas the ferromagnetic intralayer interaction is treated in an RG calculation. This approximation scheme breaks down close to the critical and the coexistence curve singularities. Second, a full RF calculation for a strongly anisotropic lattice of d=2+ epsilon dimensions is performed. When a small crystal-field anisotropy of strength DJ is included both approaches confirm a modified scaling assumption for the thermodynamic quantities. For small values of T/J, D and H/J, the usual scaling is violated by powers to which T/J is raised. The scaling functions are calculated for the ordered and disordered phase.

The kinematic inconsistencies for the Hartree-Fock magnon energy renormalisation in a ferromagnet with uniaxial anisotropy are shown to be eliminated by taking into account additional anisotropy terms present in the second-order self-energy.

A simple analytic approach to the dynamics of a magnetically disordered system of classical interacting spins is developed. A transformation in spin space is applied to the system in which the spin field S(r,t) is constant and the equation of the motion for the orientation angles Theta (r,t) and Phi (r,t) of this field is derived. This non-linear equation is linearised and the appropriate damping term reflecting the interaction between modes due to nonlinearity is introduced. The solution is in the form of a propagating mode which switches continuously into a diffusive mode as the wavevector diminishes. The equations obtained are interpreted in terms of the Langevin equation for the random motion. Additionally, the similarities with and the differences between the theory of the spin waves in ordered phase and the hydrodynamical approach are briefly discussed.

An exact solution of the kinetic Ising model in a one-dimensional semi-infinite chain with an enhanced surface exchange interaction J'=J(1+ Delta ) is obtained. For a sufficiently large Delta , two localised modes with even and odd symmetries appear near the surface, the eigenvalues of which are located outside the band of the bulk relaxation spectrum. The critical value of Delta is obtained and the Green function G_m,n( omega ) is also derived.

Crossover behaviour in three-dimensional, uniaxial dipolar ferromagnets is investigated using the spherical model approximation to calculate the effective susceptibility exponent. This enables one to consider both the Ising-mean-field and Ising-dipolar crossovers together. It is found that the temperature at which the latter occurs depends strongly on the spin-wave stiffness as well as the relative dipolar strength.

Mossbauer emission spectra of very dilute Pd(⁵⁷Co) obtained at temperatures down to 18 mK reveal a slowing down of the fast electronic relaxation. The broad paramagnetic hyperfine patterns of the daughter ⁵⁷Fe found in zero external magnetic field below about 65 mK can be described by a random flipping of the giant moment in a cubic surrounding. The spectra with applied external magnetic fields are strongly influenced by longitudinal and perpendicular fluctuations (relative to the axis of magnetisation) of the ⁵⁷Fe hyperfine field. The perpendicular fluctuations acting in the intermediate nuclear spin states in the decay from ⁵⁷Co to ⁵⁷Fe lead to marked changes in the nuclear orientation parameters. It is shown how relaxation parameters can be extracted from the experiment, and a complete description of the procedure allowing a reliable determination of the ⁵⁷Co hyperfine field is given.

Donor-acceptor selective luminescence and luminescence excitation spectra of a specially refined InP crystal grown by the liquid encapsulated Czochralski technique are compared with results recently reported (Dean et al., 1979) for the common contaminant Zn. Carbon is the dominant acceptor in the new crystal with E_A approximately 41.5 meV compared with (E_A)_Zn=48 meV. These excitation techniques provided by a tuneable dye laser provide clean resolution of several acceptor internal excitations whose transition energies are characteristic of the acceptor species, even though no useful information is available from the bound exciton spectra due to excessive spectral broadening. Transitions to two clearly resolved p states of the C acceptor yield p-state binding energies identical to those for the Zn acceptor while the binding energy of a single s state is a little less as expected. The high discrimination of the technique permits the probable identification of a second minor acceptor species as Zn.

High-resolution M_4,5N_4,5N_4,5 Auger spectra of tin and oxidised tin are presented. The fine structure observed in the clean tin spectrum is discussed using a quasiatomic approach. This considers the multiplet splitting as arising from the coupling of the two final-state holes in the 4d band. Calculations of the multiplet splitting produce good agreement with experiment and a simulation of the Auger spectrum is attempted. The Auger line-breadths increase on oxidation and a chemical shift in the line positions of -4.1+or-0.1 eV is observed.