Table of contents

The coherent potential approximation for disordered alloys is usually derived by starting from an averaged periodic crystal. It is shown that it is also obtained by starting from the atomic limit, within a similar selfconsistent single site approximation.

A brief discussion is presented of the use of auxiliary field techniques in a functional integral formulation of many body theory. By using a Lagrangian representation for the Green functions from the outset a description is obtained in which true and auxiliary fields are treated on a more nearly equal basis than in partition function methods. The interacting fields are shown to have physical significance, their propagators leading to linear response functions of the true system. A diagrammatic representation analogous to that of a true interacting field problem is shown to follow in a straightforward manner. Transformations among fields are considered.

Measurements of the specific heat of TlBr between 5 and 290 K are reported. These are believed to be accurate in an absolute sense to within 1% at 290 K, falling to 5% at 5 K. The Gruneisen parameter has been calculated as a function of temperature between 290 and 30 K, and at T=0. In spite of a similarity of gamma _infinity and gamma ₀ between 2 and 3, a marked variation of gamma with temperature independence of gamma in caesium halides. Thermodynamic analysis reveals features of a frequency spectrum which accord qualitatively with the concept given by an application of the shell model. The quasiharmonic approximation has been applied to the calculation of the maximum frequencies nu _D(n) of the Debye distributions having the same nth moments as the spectrum in the real crystal for -3<or=n<or=6.

The cancellation theorem of Cohen and Heine is derived in an exact form using a phase function approach. The new form of the theorem enables precise statements to be made about how far the zero to which we cancel the potential is arbitrary, and in certain circumstances to detect over cancellation. The latter phenomenon is ascribed to the influence of the core states and an expression derived for the maximum repulsive potential we can expect when we have over cancellation.

The rotating sphere method of studying magnetoconductivity, when applied to pure aluminium is greatly disturbed by slow and persistent mechanical oscillations whose frequency at low fields (<¹/₂T) follows the helicon frequency and varies as B, but at higher fields increases more slowly to a maximum and ultimately falls again. This variation, including a fall as B^-1 at high fields, is explained by assuming the sphere not to be rigidly fixed but elastically held, and, through flexure of the supporting rod, capable of rotation about a horizontal as well as a vertical axis. Damping by a dashpot is not wholly effective until the supporting rod is made rigid enough to eliminate rotation about a horizontal axis.

Shubnikov-de Haas oscillations have been observed in rho _xx(H) with single-crystalline graphite and in rho _zz(H) with well oriented pyrolytic graphite. Exposure to fast neutron bombardment at approximately 303 K up to a total dose of 1.12*10¹⁷nvt produces electron acceptors which lower the Fermi energy, thus expanding the hole Fermi surface and contracting the electron Fermi surface. The long period (ca. 2.1*10^-5 G^-1) previously associated with majority electrons (m*_c=0.039 m₀) is reduced by pre-irradiation, while the short period (ca. 1.6*10^-5 G^-1) which had been attributed to majority holes (m*_c=0.061 m₀) is increased. Electron and hole assignments must therefore be interchanged, with electron states now appearing at point K and hole states near point H of the Billouin zone.

It is proved that the density of states is analytic in the region in which Anderson (see abstr. A37378 of 1970) has shown that the transition from localized to nonlocalized electron states should occur. There is some discussion of the implications and generalization of this result.

The magnetoresistance of the simplest linear networks-(1) the 'opening network' where large and small orbits couple into a chain, and (2) the 'closing network' where open orbits close via a small orbit-is calculated when phase coherence is negligible on the large orbits and described by a 'relaxation time' tau _p on the small orbits. Large-angle scattering is also introduced. In general, quantum oscillations-resonant for (1) and sinusoidal for (2)-appear in only the 'H² component' of the resistance (unless n_e=n_n). The field and temperature dependences of the oscillations are discussed.

For pt. I see ibid., vol. 4, 458 of 1971. Large-amplitude (5-50% of the total resistance) quantum oscillations in the magnetoresistance of tin are described, and discussed in terms of the coupled orbit networks produced by magnetic breakdown on the pseudopotential model of the Fermi surface, and the specimen calculations of the preceding paper (to be referred to as I). Slow oscillations (f=1.7*10⁶G) from orbit delta were restricted to localities: (a) H near (001) and perpendicular to (110) or (100) and (b) H at 22 degrees from (001). Both line shapes, resonant for (a) and sinusoidal for (b), and field dependences agreed with predictions of I, although very careful field setting was required to obtain the best T* value, 0.4 K, or the largest amplitudes. A little nearer the c axis than (b), the slow oscillations were principally second harmonic of delta with a comparable amplitude of fast oscillations, reflecting complex networks in this region.

The resonant reflection of sound from the surface of a paramagnet placed in a magnetic field is calculated. The conditions under which such reflection of sound is observed are discussed.

The theory of two-magnon Raman scattering in an antiferromagnet, given by Elliott and Thorpe, (abstr. A15401 of 1970) is extended to the spin-flop phase. Application is made to the perovskite and K₂NiF₄ structures and the lineshape predicted. The main features are a broadening of the line and the appearance of additional structure, together with a decrease in intensity.

The absorption spectra at liquid helium temperature of divalent impurities Ti d², V d³, Cr d⁴, Co d⁷ and Ni d⁸ in zinc selenide are presented. Values of the crystal field parameters B and Delta are derived from the spectra. The variation of Delta through the 3dⁿ series has not been explained by present theories: it is suggested that a new approach, based on bond charge, may be more fruitful.

Hydrogen or deuterium has been diffused into calcium fluoride crystals containing various rare earths. The fundamental and second harmonic vibrational transitions of the hydride ions have been examined by infrared absorption measurements at 77 K and 4.2 K. It is found that a fraction of the hydride ions form close pairs with the rare-earth impurities, and the localised vibrations of these hydride ions give rise to satellite absorption lines around those from similar ions in unperturbed fluoride ion sites. For crystals containing ytterbium and europium impurities thermal treatments alone produce centres which are interpreted as Yb²⁺-H^-(s) and Eu²⁺-H^-(s' pairs of two types, depending on whether the hydride ion occupies a first or second neighbour F^-(s) site.

Measurements of the change in anisotropy field and ferromagnetic resonance linewidth due to doping magnesium ferrite and manganese ferrite with cobalt are reported. A large effect upon anisotropy and relatively small effect on the linewidth is observed. The behaviour is explained in a broadly satisfactory manner in terms of a ion theory of the anisotropy and the longitudinal relaxation model, assuming a simple form for the ground doublet energy levels of the Co²⁺ ion on octahedral sites. Only about one third of the cobalt ions substituted into the magnesium host contribute to the anisotropy energy, whereas all the ions do so in the other host. The relatively weak effect upon the linewidth is interpreted to show that the Co²⁺ ion populations relax between the doublet states in approximately=10^-13s.