Table of contents

Precise measurements of the specific heat of CsMnF₃ near its Neel temperature (T_N) are reported. A detailed analysis of the critical singularity shows evidence for a crossover behaviour near T_N. This observation is an experimental verification of the spin dimensionality crossover phenomenon from a three-dimensional Heisenberg-like behaviour far from T_N to a three-dimensional XY-like behaviour in the near vicinity of T_N.

Transitions identified with emission of electrons and holes from Cr²⁺ and O centres in GaAs have been followed as a function of hydrostatic pressure up to 8 kbar. The pressure coefficients of the complementary energy sums are 4.7+or-1.5 and 3.0+or-1.5 MeV kbar^-1 respectively. It is concluded that the dominant transitions to conduction band are weighted to the higher bands near X and L, rather than to low density of states minimum at Gamma , confirming earlier assignments of peaks obtained by rapid photocapacitance spectroscopy (White et al., J. Electron. Mater., vol.5, p.91 (1976) and J. Appl. Phys., vol.47, p.3230 (1976)).

The Hartree-Fock conduction band structure of solid neon is computed by the APW method. The logarithmic derivatives used have been obtained directly from the static-exchange electron-atom scattering phase shifts. A detailed comparison is made with the existing literature, where the HF conduction bands are obtained with the use of different schemes.

For phosphorus doped silicon near 20K, it has been observed that the time required for breakdown to occur after application of a strong electric field is a function of the time elapsed since the last breakdown. A theory is developed which shows that the breakdown time is sensitive to the occupation of excited donor states. Good agreement between theory and experiment makes it possible to measure the lifetimes of two states believed to be the 2S state and the upper 1S groundstate. As the temperature was varied from 20K down to 17K, these lifetimes changed from seconds to minutes, in serious disagreement with rates calculated from phonon cascade theory.

An analogy is considered between long-range properties of the Green function G of an electron moving in a random potential, near the mobility edge, and those of spin-spin correlation functions, obtained for a random Ginzburg-Landau Gaussian model. The absence of a 'ferromagnetic' long-range order in the latter model is related to the short range of the average G. The average squared modulus may become long ranged. This long range is analogous to a 'spin-glass' like phase. This 'spin-glass' transition deviates from mean-field theory for dimensionalities d<4. Renormalisation group, the epsilon expansion and the n to 0 replica trick are used to analyse the appropriate fixed points. For few impurities, no fixed point can be reached, probably because no localisation edge exists. For larger disorder, the 'isotropic', n=0 fixed point may be reached, and is interpreted as probably leading to percolation. For still larger disorder, the Anderson transition may result.

A ¹⁶¹Dy Mossbauer study has been performed on the cubic equiatomic compound DyMg. From the value of the hyperfine parameters, the isomer shift in the intermetallic compounds of dysprosium and the magnetic properties of the heavy rare-earth-magnesium system are discussed.

Computer simulation data for liquids with generalized Lennard-Jones potentials are analysed with the aim of elucidating the key features required of a liquid for it to support a short-wavelength, collective density excitation. The data suggest that, for high densities, both the repulsive and attractive components of the Lennard-Jones potential must be modified substantially for such a mode to exist, and that softening the potential core does not in itself suffice to induce the correlation necessary for a liquid to support a mode. Viscoelastic theory is shown to provide a good description of the dynamical properties and to provide a useful condition for the existence of a collective density excitation.

A calculation of the Van der Waals binding energy between layers of a hexagonal layered structure is presented. The results are used to estimate the interlayer binding energy of graphite, using measured mean and derived anisotropic polarisabilities. The agreement with experimentally measured binding energy is satisfactory indicating that Van der Waals forces are indeed the dominant binding mechanism between layers.

Keyes' model for the electronic contribution to the elastic constants has been extended to the rhombohedral group Vb semimetal bismuth, and the magnitude of the effect calculated using parameters taken from the literature. The theory predicts that an increase in the free electron density should decrease C₁₁, C₆₆ and C₄₄ and increase C₁₂ and C₁₄. These predictions have been tested by measuring the elastic constants of single crystals of bismuth heavily donor-doped with tellurium (10¹⁹-10²⁰ electrons cm^-3); the experiments were performed between 4.2K and room temperature by the ultrasonic pulse echo overlap technique. In general, doping of bismuth with tellurium causes the expected decrease in the ultrasonic wave velocities and the elastic constants vary in the manner predicted by the theoretical model. An increase in the free electron concentration causes C₁₁ and C₆₆ to decrease, C₁₂ to increase, while the variation of C³³ is negligible.

A lattice dynamical model for crystalline iodine has been investigated. The simple bond charge (SBC) model developed by Parr and co-workers (1968, 69, 71 and 73) for free molecules has been adapted for the iodine molecular crystal to take account of intermolecular as well as intra-molecular covalent bonds. Mode instabilities of previous models are absent from the present calculations. Acceptable agreement with experimental dispersion relations has been achieved using model parameters consistent with the basic concepts of the SBC model. The results strongly support the validity of the SBC model for the covalent bonds between halogen atoms.

The contribution of tunnelling states of helium atoms to the heat transfer between liquid helium and a solid is theoretically investigated. It is shown that the heat transfer is appreciably enhanced by the tunnelling of the helium atoms close to the boundary. Taking the suitable energy distribution function, it is shown that the efficiency of heat transfer becomes rather strong for a temperature above about 0.1K. This theory is applicable to the case of the heat transfer between a solid and solidified ³He, ⁴He, H₂ or D₂.

An unsatisfactory aspect of an earlier low-energy electron diffraction structure analysis of a clean Ag (110) surface has been eliminated by preparing a new surface. The structure of clean Ag (110) was substantially confirmed to correspond to truncation of the bulk crystal but with 10% contraction of the first interlayer spacing. This conclusion was reached both by visual and quantitative (r-factor) evaluation of the correspondence between theory and experiment. Possible explanations of the earlier discrepancies are discussed.

A self-consistent theory for electron correlations formulated so as to satisfy both the compressibility and spin susceptibility sum rules within the framework of the so-called generalised random phase approximation, is used for studying numerically correlation effects on electron gas properties at metallic densities. The physical implication of the self-consistency requirement in the theory is discussed from the diagrammatic viewpoint of perturbation theory.

Positron annihilation in a single crystal of VO₂ is investigated by analysing the Doppler broadening spectra in the insulator and metal phases. The anisotropy in the energy distribution, for emission parallel and perpendicular to the crystal c-axis, at room temperature is 2.4+or-0.1% for k=0, and it vanishes at k=4.0+or-0.1 mRad. The changes in the spectra on passing from the insulating to the metal phase are found to be gradual and spread over tens of degrees. The change in the direction parallel to the c-axis is within the statistical error, while the changes in the two perpendicular directions are about 0.5% and have opposite signs.

The amplitude and period of magnetic moment oscillations (de Haas-van Alphen effect) in semiconductors with a one-dimensional superlattice are calculated by means of the semi-classical approximation. The effect of finite thickness of crystal along the direction of the superlattice is also analysed.

Some important corrections are reported to a previous paper with the above title by Baker (see ibid., vol.1, p.1670 (1968)) which fortunately do not alter its general conclusion. However, there are significant changes in some of the details. In particular the covalency parameters are considerably larger than was previously suggested.

The localisation energy of excitons bound to neutral donors and acceptors is studied using Green function and configuration interaction techniques. The configuration interaction calculation gives localisation energies which are much higher than experimental values. It is argued that much of this correlation energy can be quenched by fluctuations in the degenerate ground states, and lead to a degeneracy dependence for the correlation energy. This mechanism can explain how the J=^1/2 acceptor bound exciton level can lie below the J=^3/25/₂ levels for hole-attractive central cell potentials, and can also explain the level structure observed for multiple bound excitons. When the valence band degeneracy is allowed for using the spherical model of Baldereschi and Lipari (1974) it is found that for the neutral donor bound exciton, states derived from the hole in S_3/2P_3/2P_5/2 levels are close in energy. The quantum fluctuations imply that the domain of the canonical density matrix is larger than that spanned by eigenstates of the Hamiltonian.

The polaron in polyatomic crystals, where several longitudinal optical modes of the lattice vibrations are present, is discussed. The effective mass m_H*, obtained in the Haga-type approximation is given by m_H*/m=(1+ Sigma _i alpha _i/12)/(1= Sigma _i alpha _i/12), where m is the bare mass and alpha _i is the Frolich type coupling constant between the electron and the ith mode of the longitudinal optical phonon. Therefore, the effective mass correction is not generally expressed as a simple sum of the mass correction due to the individual modes of the longitudinal optical phonon.

For pt.III see ibid., vol.10, p.2141 (1977). The quantum transport theory formulated in the coherent-potential approximation in the first paper of this series (1977) is applied to a model random alloy, which is much simplified and yet retains some general essential features of a long-range non-local potential. The effects of the vertex correction and the non-locality of the potential on the conductivity are investigated numerically and the features of them are discussed in detail.

The authors study phase transitions in the isotropic non-degenerate Hubbard Hamiltonian with renormalization group techniques using the epsilon =4-d expansion to first order in epsilon . The functional obtained from the Hubbard Hamiltonian displays full rotational symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences for the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalisation of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed.

The cumulant method, originally applied to NMR lineshape problems by Kubo, (1962) can be extended to treat spin echoes. The echo relaxation is shown to depend on the conventional spin torque correlation function and the symmetry properties of the coupling Hamiltonian. For the dipole-dipole interaction the author demonstrates that the echo decays identically to the free induction decay, while for diffusion in a field gradient the echo decays in the familiar cubic form. The same result is shown to follow from spin diffusion produced by the Heisenberg exchange Hamiltonian. In the motional narrowing region both the free induction decay and the echo decay exponentially with the same relaxation time assuming a perfect NMR magnet.

The authors discuss the self-trapping of a carrier or exciton in an insulator. The qualitative differences between small self-trapped molecular polarons and dielectric polarons are stressed. They point out that, for the formation of a molecular polaron or self-trapped exciton, a potential barrier must be penetrated or surmounted by the configuration coordinate, leading to a delay in the self-trapping process. This does not exist for dielectric polarons. The observable consequence of delay time before self-trapping is discussed, and applications are made to alkali halides and to SiO₂.

The magnetisation of the nearly two-dimensional weakly anisotropic ferromagnets (C_nH₂dn₊₁NH₃)₂CuCl₄ has been studied by means of Cu and Cl nuclear magnetic resonance. The hyperfine interaction of Cu and Cl nuclei and the Cu²⁺ spin direction were determined. The field dependence of the magnetisation has been measured in the range 0 to 10 kOe. This allowed the intralayer exchange integral J to be determined using simple spin-wave theory taking into account experimental magnetic anisotropy and interlayer exchange. The temperature dependence of spontaneous magnetisation measured in the range 1.4 to 4.2K is well described by the theory using this J value.

The zero-field splittings of the praseodymium non-Kramers ground state doublet in PrMN have been studied by specific heat and electric susceptibility measurements down to 0.1K. The electric dipole moment of the Pr ion in the plane perpendicular to the three fold symmetry axis was found to be 0.73*10^-31 C m, much too small to provide significant electric dipole-dipole interactions between Pr ions. The zero-field splittings are attributed to random local fields due to crystal imperfections, but the susceptibility data could not be well fitted with a gaussian distribution. Instead, satisfactory agreement was obtained with a Holtsmark distribution, as expected for the local fields due to a random configuration of charged defects. The conclusions are in broad agreement with those obtained in EPR studies by Sells and Bloor (1976). The magnitudes of the splittings ( approximately 0.1 cm^-1) imply the suppression of long-range order by random local fields.

The shapes, positions, the near-edge and the far-edge structures of the L₃ absorption discontinuity of gadolinium in the metal and in its sesquioxide, hexaboride, monosulphide, fluoride, chloride, bromide, nitrate, sulphate acetate and oxalate are reported. All the spectra are marked by a small peak at the beginning of the absorption, a pronounced white line in the immediate vicinity of the main discontinuity, and fine structure extending up to about 115 eV on the high-energy side. The observed chemical shifts and other features of the spectra are discussed.

The leading term in a semiclassical expansion of the quantum mechanical cross section for potential scattering is obtained for those cases where the classical cross section shows either a fold or an umbilic (hyperbolic or elliptic) type catastrophe. As an intermediate step a narrow wave packet approximation is derived by decomposing the S-matrix into transition amplitudes for wave packets and by expanding the modulus of these amplitudes for large mass.

N_6,7O_4,5O_4,5 Auger spectra have been observed from the clean surfaces of Tl, Pb and Bi using Mg K alpha X-ray excitation. The observed spectra are in good agreement with quasi atomic multiplet structure calculations in which the initial and final states are treated in jj and intermediate coupling respectively.