Table of contents

The approximation for the correlation function G(r,r',t) appearing in the theory of Hubbard and Beeby (1969) has been examined and found to be exact for short times. Further, it has been shown that the recent paper by Tewari and Tewari (1975) is erroneous and misleading, and that their results are greatly inferior to those obtained by Pathak and Bansal, (1973).

The oscillatory long-time tail of the velocity autocorrelation function observed in liquid sodium and rubidium is traced back to a singularity in the spectrum of longitudinal waves emitted by the moving particle. Therefore Schiff's conclusion (1969) that the oscillatory long-time tail is due to the soft-core character of the interparticle potential implies that the same property of the potential is responsible for the long lifetime of short-wavelength density waves in liquid metals.

Magnetic counterflow is presented to account for the anomalous relaxation observed in superfluid helium-3. The difference between the A and B phases are explained as due to the vanishing critical spin velocity in the B phase. The importance of dissipation is emphasized and an experiment to check the validity of the model is proposed.

The authors report experimental evidence that the rate nu at which a negative ion nucleates vortex rings in He II is strongly influenced by ³He isotopic impurity concentrations close to that of the natural abundance. It is suggested that the anomalous temperature dependence of nu observed near 0.3K in earlier experiments in natural ⁴He is a consequence of ³He condensation on the ions, and that the presence of as few as five condensed atoms is sufficient to completely eliminate the bare ion signal in a typical experimental geometry.

For pt.I see ibid., vol.9, p.291 (1976). Reflectivity data on polysulphur nitride (SN)_x are reported in the energy range 0.5-27 eV, and include vacuum-ultraviolet and synchrotron radiation measurements. The transmission spectrum is given for light polarized both parallel and perpendicular to the polymer chain axis, in the energy range 0.5-4 eV. The absorption coefficient, alpha , and the imaginary part of the dielectric function, epsilon ₂, have been calculated from the reflectivity data by a Kramers-Kronig analysis. The energy dependence of epsilon ₂ is compared with that calculated on the basis of the energy band structure given in the previous part.

Comments are made on the paper by Kamimura et al., see ibid., vol.9, p.291, and vol.9, p.L277 (1976), in which it is proposed that the metallic properties of the polymer polysulphurnitride, (SN)_x, are stabilized against a Peierls distortion because two overlapping conduction bands cross the Fermi surface. It is shown that for a one-dimensional metal with two bands crossing the Fermi surface, if the sum of the two Fermi wavevectors equals half a reciprocal lattice vector, then there is a strong tendency toward a Peierls distortion which will double the size of the unit cell. The one-dimensional band structure proposed by Kamimura and co-workers for (SN)_x will almost certainly exhibit such an instability.

An effective-field theory of the spin glass is presented, using only the conventional molecular-field approximation, in order to make the so-called replica formalism of the spin glass transparent.

The static properties of spin glasses are discussed within the Bethe-Peierls-Weiss approximation. The effect of a finite number of nearest neighbours is reflected in the expressions for the spin-glass transition temperature, the order parameter and the susceptibility. In contrast to the results of the classical molecular field approximation, the susceptibility approaches the transition temperature from below with a finite positive slope.

It is shown by Raman scattering experiments in nonaxial CeF₃ that the components of two-fold degenerate phonon states which are split by an external magnetic field are approximately right and left circularly polarized.

A kinetic theory is developed which derives, for example, the effective equation of motion of a polymer molecule entangled with a density of other such molecules. This analysis produces an alternative route to the results obtained previously from statistical mechanics.

The authors calculate the effective equations of motion of shear waves in a gel, consisting of a cross-linked polymer network in a Newtonian fluid. It combines the models used to calculate the shear modulus of rubbers and the viscosity of polymer solutions. The calculation is done only for small-amplitude waves, and includes an allowance for chain entanglements.

The properties of low-energy excitations in a disordered system with localized electrons are discussed. A simple model and a self-consistent method for the calculation of the density of states are proposed. It is argued that in a three-dimensional system there are in fact no low-energy one-particle excitations, but many-particle charged excitations exist and determine the d.c. conductivity of the system. Formulae are given for the density of states of such excitations and for the d.c. conductivity.

A dielectric theory of collective excitations in insulating crystals is formally developed, including exchange and correlation effects by a mean field approximation and lattice defects through a dielectric matrix formalism based on wavefunctions in the Wannier representation. Specific application is made to a simple two-band model, for which an explicit secular equation for the longitudinal collective modes is derived with overlap between Wannier functions on first-neighbour sites being treated perturbatively. The response matrix of the model is easily inverted when overlap is neglected, and an explicit expression follows for the macroscopic dielectric function which also displays the existence of transverse collective modes.

The use of a perturbation method in the study of percolation problems is examined. The specific case discussed is the conductivity of a disordered square resistor network in which bonds are broken at random (bond model). The formalism used is closely analogous to that used in the study of disordered alloys. A detailed discussion of the properties of the Green functions is given, and numerical results are obtained within a cluster approximation. It is found that, with the smallest possible cluster, a significant improvement over the effective-medium theory is obtained.

The conditions leading to the occurrence of the compensation rule in space-charge-limited current studies is discussed. It is shown that this effect is not fortuitous but that it can arise whenever a convergence point exists on current-voltage characteristics. Conditions leading to the appearance of a convergence point in such characteristics are discussed in terms of continuous and quasi-discrete trapping levels. The convergence point is shown to result when the concentration of a discrete (or nearly discrete) trap remains constant.

For pt.I see ibid., vol.7, p.1523 (1974). The matching of matrix element method is used to find a new self-consistent Bose operator expansion for tensor operators in spin systems with isotropic exchange interaction plus anisotropy. Tables are given for all tensor operators relevant for cubic and hexagonal symmetry. A discussion of renormalized spin-wave theory for a system with planar anisotropy shows that the Goldstone theorem is rigorously fulfilled to the considered order of perturbation. It is finally shown that the new expansion introduces wavevector-dependent terms from the single-ion anisotropy into the dispersion relation.

Ten terms have been obtained in the high-temperature series for the fluctuation in long-range order of the Ising model in a transverse magnetic field on the three cubic lattices. This model is relevant to real materials such as singlet-singlet magnetic systems, hydrogen-bonded ferroelectrics and cooperative Jahn-Teller systems. The critical temperature of the system was obtained over essentially the entire range of the transverse field for which a phase transition exists. No crossover to the expected d=4 critical behaviour was observed at T=0.

Exact analytic results are presented for the critical properties of the dilute Ising model on a Bethe lattice, where a fraction p of the sites are occupied at random by spins. It is found that the critical behaviour is the same as that of the pure system (p=1) except for transitions which occur by varying p at zero temperature, where the critical behaviour is different and corresponds to the percolation problem. For T to 0 and p to p_c, the percolation concentration, the zero-field magnetization shows crossover behaviour of the form expected from scaling theories. Outside the critical region, a rapidly convergent numerical method is developed and used to calculate the spontaneous magnetization.

Results are derived for the dynamic correlation functions between a pair of spin operators at any two sites within a semi-infinite Heisenberg ferromagnet at low temperatures, T<<Tc. The correlation functions are found to contain terms describing the effects of the bulk spin-wave modes and the surface spin-wave modes, together with appropriate weighting factors. The results are employed to evaluate the spin deviation in the ferromagnet as a function of temperature and distance from the surface.

A theory is presented for one-magnon light scattering by reflection from the surface of a semi-infinite Heisenberg ferromagnet. Results are deduced for the scattering cross section and for the integrated intensity by making use of results derived in a previous paper (see ibid., vol.9, p.2121, 1976) for the transverse spin-spin correlation functions. The calculations include an evaluation of the scattering contribution from surface and bulk spin-waves. The relative magnitude of these two types of contribution to the total scattering is discussed, treating separately the cases of a transparent ferromagnet and an absorptive ferromagnet.

Using thermodynamic perturbation theory the statistical mechanics of intermediate-valence rare earth compounds is investigated. The Gibbs' free energy is calculated to second order in the Anderson mixing interaction and is shown to diverge logarithmically as T to 0. At high temperatures the susceptibility is approximately of the Curie-Weiss form, chi =C/(T+T_F), where kT_f approximately Delta , the 'width parameter' associated with interconfigurational fluctuations.

Neutron inelastic scattering techniques have been used to study Zn-substituted MnF₂ crystals with average Zn concentrations c=0.22+or-0.02 and 0.7+or-0.1. For c=0.22 the results gave scattered distributions whose peaks were at frequencies less than those of the excitations of pure MnF₂ and whose width was considerably larger than the experimental resolution. The other specimen had a concentration gradient such that one end of the crystal ordered magnetically at 4.2K whereas the other end did not. There were no significant differences between the scattering from the different ends, and it consisted of an overdamped distribution the width of which decreased as the wavevector of the excitation decreased.

In n-irradiated CaO and MgO crystals, triplet-state defects are produced in which two electrons are trapped in the O^2- sites of a linear trivacancy configuration O^2--Ca²⁺-O^2- parallel to the (100) crystal direction. The electronic spins are coupled antiferromagnetically to give a ground-state singlet ¹A_1g for these F⁺-centre pairs, the first excited level ³A_2u being thermally populated at room temperature. Measurements of the ³A_2u state EPR spectrum at 1.4K under optical excitation demonstrates that optical spin alignment memory is induced during the optical pumping cycle.

The proton spin lattice relaxation time was measured for two linear Ni²⁺ salts, TMNC (tetramethylammonium nickel chloride) and TMNB (tetramethylammonium nickel bromide). It was found to be rather small and field-independent. The results are explained by the existence of a large single-ion anisotropy term which does not commute with the total spin and prevents the setting up of a diffusion process. The short-time behaviour of the spin correlation functions was determined by computing the second and fourth moments for two orientations (parallel and perpendicular to the chain axis). From the temperature-dependent proton relaxation rate, the intrachain exchange interaction is shown to be ferromagnetic in both these salts.

The electronic and magnetic properties of RESn₃ compounds (RE=La, Ce, Pr, Nd, Sm, Eu, Gd, Yb) have been investigated using the 23.8 keV Mossbauer resonance of ¹¹⁹Sn. The isomer shifts and quadrupole interactions are nearly the same in all compounds. The transferred magnetic fields and their orientation with respect to the principal electric-field gradient axis at various Sn sites in the magnetically ordered state of RESN₃ (RE=Pr, Nd, Sm, Eu, Gd) have been utilized to get information about the magnetic structure. An evaluation of the transferred fields in PrSn₃ and NdSn₃ shows that the spin density at the Sn nucleus is nearly the same in both compounds.

The electric field in a point-charge lattice of orthorhombic symmetry and of ellipsoidal external shape is obtained in terms of the field in a slab-shaped specimen of the same lattice. This result allows one to extend the applicability of the 'planewise summation method' to cases where otherwise it would give a slow convergence. As an example, the electric field of Na⁺ ions at the NO₂^- sites in ferroelectric NaNO₂ crystals is evaluated.

Brillouin back-scattering measurements on the weak ferromagnet FeBO₃ (T_N=348K) are reported in the temperature range 77-350K in magnetic field up to 6 kG for an incident wavelength of 514.5 nm. From the magnetic field and directional dependence of the magnon frequency, the Dzialoshinski-Moriya field H_DM (1958, 1960) was obtained over the whole temperature range, and precise values were found for the three dominant exchange contributions. The full set of elastic constants is reported.