Table of contents

Magnetic anisotropy effects have been studied in ³He B with transverse NMR on liquid confined into 0.4 mm wide slits between flat parallel foils. The results have been fitted to recent theories on orientational effects in dynamic magnetism.

The authors show that recent inelastic neutron scattering measurements on the low temperature magnetic excitations in the planar Heisenberg random antiferromagnet Rb₂Mn_0.5Ni_0.5F₄ may be well understood by using a numerical technique involving the time integration of the equations of motion for the system.

Previous work (see abstr. A25442 of 1975) concerning the attenuation of transverse waves in the (1,0,0) direction is extended to an investigation of the (1,1,0) direction in cubic crystals. In order to compare the strength of Landau and Rumer processes of temperature dependence T⁴ with near collinear energetically disallowed processes of expected temperature dependence T⁷ or T⁹, finite thermal phonon lifetimes have been used throughout the calculations. This has been done by numerical techniques and full account of crystal anisotropy and the three-phonon anharmonic coupling has been taken. An extensive comparison is made with experimental data, good agreement being obtained in most cases. It is found that in the case of the slow transverse mode in germanium and silicon, the experimentally observed temperature-dependent attenuation of approximately T² can be explained in terms of interactions with fast transverse thermal phonons. The crystal calcium fluoride is treated in some detail and it is found that sixty per cent of the attenuation of the slow transverse mode is due to 'same branch' energetically allowed interactions with slow transverse thermal phonons in the temperature range 30-40K.

A study is made of the phase transitions for the one-dimensional Landau-Ginzburg system in the limit of zero degrees of freedom found by Balian and Toulouse (see abstr. A30922 of 1974). It is shown that they correspond to a rather simple property of a polymer in one dimension. The phase transitions are exhibited for a discrete model as well as for the Landau-Ginzburg model. The properties of an electron in a one-dimensional random potential can be found by an analytic continuation of this theory, but the phase transitions lie away from the physical region of this system. An explicit expression is derived for the localization length for the electron in a white-noise potential, and it is indicated how the conductivity could be calculated.

A 10000 particle molecular-dynamics computer model, using the PPPM method, has been used to study a system of classical electrons confined to move in a plane. This is a realistic model of electrons at low densities bound in external surface states on liquid helium. A lambda-type phase transition has been observed at a temperature T_t, and density, n, for which Gamma ₀= phi ¹2/n¹2/e²/kT_t=95+or-2. The transition has an associated internal energy change of 1.1 k/electron and is between a poly-microcrystalline solid phase and a liquid phase. On the low temperature side, the gradual rise of specific heat (C_v approximately (- epsilon )^-0.08. epsilon =(T-T₁)/T₁) is associated with a gradual decrease of crystallite size. On the high temperature side there is a sharp drop in specific heat, following roughly C_v approximately ( epsilon )^-0.14, to a state with a distribution function characteristic of a liquid.

Estimates of the longitudinal and shear viscosities of liquid rubidium have been made on the basis of the memory-function approach coupled with the frequency-moment sum rules. The basic ingredients used were the potential of Price et al. (1970) and the molecular dynamics data of Rahman (1974) for the pair correlation function consistent with this potential. The theoretical results for the viscosities have been found to be in good agreement with the available experimental result. An estimate of the longitudinal viscosity from mean-field theory has also been found to be of the right order of magnitude.

The well known sum rules for the density-density correlation function of a homogeneous charged Fermi system are extended to arbitrary inhomogeneous systems. The result is applied to a metallic half-space.

The reasons for the discrepancies between the expressions for the Righi-Leduc effect derived by Putley (1960) and by Honig and Harman (1963) are discussed. To obtain a correct result, the lattice thermal conductivity must be properly included in the calculations. Differences, attributed to sign convections, between the two formulations are discussed. Expressions for the principal transverse galvano- and thermo-magnetic coefficients for an isotropic multi-band conductor are tabulated.

The method of solving the Boltzmann equation used by Fletcher and Butcher (see abstr. A16080 of 1972) to calculate the mobility of Gamma _1c electrons due to polar optical scattering has been extended to the case of non-parabolic bands and, in particular, the Kane band form. Values of polar optical mobility have been calculated as a function of Fermi energy and reduced temperature for the compounds InP, InAs, InSb, GaAs and GaSb and the results compared with values obtained by using the relaxation-time approximation. Values have also been determined for the Hall scattering factor as a function of reduced temperature and magnetic field.

A new method of calculating image potentials including dynamic corrections for a quantum-mechanical particle is proposed. The motivation for this work is the investigation of dynamic effects for a light particle bound by its image potential in a surface state; for example, a positron trapped at a metal surface or void. Previous quantum-me- chanical treatments of image potentials have assumed the incident particle wavefunction to approximate a plane wave, which is clearly invalid for a surface state. The method used here involves an expansion of the self-energy operator, calculated in the RPA, in powers of the momentum operator. It has the additional advantage that self-energy insertions may be incorporated self-consistently in the particle propagator which enters the self-energy diagram in the RPA. By this method, a quantum-mechanical version of the Harris-Jones treatment of dynamic corrections to the image potential may be derived.

Evidence for the validity of the superposition model as applied to the n=4 Gd³⁺ spin-Hamiltonian parameters is examined. This model is shown to give a consistent interpretation of all available experimental data, provided that the possibility of the single ligand parameter b₄ varying over a wide range of both positive and negative values is accepted. The variation of this parameter is shown to be correlated with the ligand ionicity and provides a measure of the extreme variations in the ionicity of oxygen atoms in crystals.

In order to understand the transferred hyperfine structure of the trigonal centres of Yb³⁺ in CaF₂ it is essential to know their ground state wavefunctions accurately. For this purpose an estimate of the crystal field parameters must be made. The authors calculations of the crystal field parameters and the ground state wavefunctions are discussed. The limited data available from optical and EPR studies make it necessary to construct models of the crystal fields of these centres by comparison with one another and with the well known cubic centre. The most suitable model for each centre has been selected using a least squares fit to the available data, followed by chi ² tests of significance. A good model of the T₂ centre has been found giving accurate ground state wavefunctions. For the T₁ and T₃ centres the models are not so good, but give adequate accuracy. The estimates of the crystal fields have allowed us to make predictions of the positions of all the energy levels of the Yb³⁺ (4f¹³) configuration in these centres.

Like the hexahydrated perchlorates of Fe²⁺ and Ni²⁺, the isomorphous Co²⁺ salt is observed to show thermally-reversible anomalous magnetic properties at T_c=(166+or-1)K. Mossbauer studies of this salt diluted with Fe²⁺ ions, however, show an anomaly in the quadrupole splitting ( Delta E_Q) in the range from 140K to 160K. This difference in the temperature of the anomaly is probably due to dilution. Again similar to the Fe²⁺ salt, the authors find in Co(ClO₄)₂6H₂O a change in sign from positive to negative and an increase in magnitude of about 50% of the axial field parameter Delta below the transition temperature. As in the other isomorphous perchlorates of this group, it is observed for Co(ClO₄)6H₂O that K/sub ///>K_{perpendicular to} above T_c and K_{perpendicular to} <K/sub /// below T_c. The experimental data in the region of transition can be satisfactorily fitted with theory only by reducing the values of Delta , keeping the other parameters more or less constant. This peculiar phase change in Co²⁺ perchlorate is also associated with the appearance of anisotropy in the ab plane accompanied by a change of asymmetric field from trigonal (above T_c) to tetragonal (below T_c) symmetry.

Calculations are made of the magnetic excitations in the random systems Rb₂NiF₄/Rb₂MnF₄ and K₂MnF₄/K₂ZnF₄ using various approximations based upon the single-site coherent potential approximation. For the former system, three different ways were used to treat the transverse part of the exchange interaction; the most successful was to reduce the disorder in the transverse exchange interactions by appropriate scaling of the single-site Green functions. The calculations then gave good agreement with recent measurements. In the calculations for the latter system, two approximations have been used for treating the transverse part of the interactions and two ways of keeping the magnetic excitations off the non-magnetic zinc ions. The results predict considerable structure which is absent in theories which average the single-site energies.

An effective-field calculation for diluted Ising ferromagnetic thin films is proposed. The critical concentration below which the ferromagnetism disappears is shown to decrease with increasing film thickness.

Detailed investigations of the spin-lattice relaxation of single Cu²⁺ ions and Cu²⁺-Cu²⁺ pairs in zinc (II) bis(di- ethyl-dithiocarbamate) single crystals are reported. The measurements were made in the temperature range 1.5<T<35K at v=28.8 and 9.0 GHz using the pulse saturation and the spin-echo method, respectively. At T<5K the single-ion relaxation is defined by direct processes; at higher temperatures two-phonon Raman processes were observed. In the range 4<T<12K the data can be fitted by an Orbach-Aminov process. A calculation of the single-ion relaxation rate for the direct process has been made. Also the pair relaxation rate in the same range was calculated considering the rate equations of the populations of the triplet state. From the temperature dependence of the Orbach-Aminov process the isotropic exchange integral was derived. Low-temperature EPR measurements provided the signs of the D-tensor and of the exchange integral. From the temperature dependence of the single-ion Raman relaxation rate the Debye temperature of the host crystal was estimated. For exchange coupled pairs the anomalous frequency dependence of T₁^-1 was observed.

Neutron irradiated CaO has an EPR spectrum at 77K with g-values g/sub /// (100)=2.0694, g_{perpendicular to} =2.0021, due to a V^- centre which differentiates it from the previously reported values, suggesting a distinction between the V^- centres produced in this way from those produced thermally. On examination of the behaviour of this spectrum with increasing temperature it shows the features of motional averaging. At 195K a broad isotropic line g(iso)=2.0475-approximately ¹/₃(g/sub ///+2g_{perpendicular to} -is observed, confirming that this is indeed an intrinsic V^- centre. Further centres have been discovered which are tentatively identified as interstitial O₂^- along (110) axes and a weaker spectrum of similar centres with the axes tilted by about 14.5 degrees from (110) lying the corresponding (001) plane. Discussion is given of the interpretation of these results.

An inhomogeneous polarization distribution is shown to arise in KDP from space charge due to contact with metal. The first moment of the polarization distribution is determined by excitation of acoustic flexure resonances.

A theory is presented for the temperature dependence of one-magnon light scattering in antiferromagnets. The Hamiltonian describing the interaction of light with the magnetic system is taken to include terms linear and quadratic in the spin operators, and these terms may be related respectively to the linear and quadratic complex magnetooptical effects. This represents an extension of earlier work in which only linear spin terms (linear magneto-optical coupling) were considered in calculating the scattered intensity for antiferromagnets. The theory is applied to FeF₂, for which it is shown that the quadratic spin coupling may be important, and improved agreement with experimental data is obtained.

The methods of linear response theory are used to determine the power spectra of the electric-field and vibrational-amplitude fluctuations associated with the polaritons which exist at the plane surface between two isotropic dielectric media. A general form of the cross section for inelastic scattering of light in reflection at such a surface is derived and applied to the scattering by surface polaritons. The special case of a crystal which possesses a single lattice resonance is considered and numerical estimates for GaP are obtained.

The thermal fluctuations in electric field and vibrational amplitude associated with optical surface phonons in dielectric spheres are derived and compared with the corresponding bulk-phonon fluctuations. Expressions for the Raman scattering efficiencies of bulk and surface phonons in very small spherical crystals are obtained, and numerical results for the case of GaP are presented.

The reflectivity of the ternary compound Ga_(1-x)Al_xSb has been measured on single-crystalline layers from 2 to 5.5 eV for 0<or=x<or=0.73. The variation of the energies E₁, E₁+ Delta ₁, E'₀, E'₀+ Delta '₀ and E₂ with the composition x is reported. A parabolic variation is found for E₁, E₁- Delta ₁ and Delta ₁, whereas the E₂ transition varies linearly with x. As for the variation of E₁, the experimental bowing is compared to that calculated by the dielectric two-band method in the virtual crystal approximation, to which a term due to the effects of aperiodicity is added.

New high-resolution X-ray fluorescence measurements of the Nb L₃ emission band and Nb and NbN are presented. The Nb L₃ emission of Nb, NbC and NbN are compared with available density-of-states calculations. It is shown that only the NbC band can be described satisfactorily by an APW model. A complex satellite structure appears on the high-energy side of the parent Nb L alpha _1,2 emission lines, and it is interpreted as due to L₃M-M_4,5M double-vacancy distribution. No Nb L alpha _1,2 line shift is observed, in agreement with earlier results on NbC.