Table of contents

High-precision measurements of the specific heat C_p of MnF₂ near its Neel temperature, T_N have been performed. It is shown for 10^-2<or= mod 1-T/T_N mod <or=4*10^-1 that magnetic specific heat obeys a power-law singularity with exponents characteristic of the three-dimensional Heisenberg model, that is, alpha = alpha '=-0.103. As one approaches T_N, a crossover to dipolar-dominated Ising nature can be clearly observed. Asymmetric behaviour of the critical divergence in the vicinity of T_N can be also well explained by the existing numerical values of the magnetic anisotropy.

Analysis of single-crystal reflectivity data of spinel MgAl₂O₄ shows that a six-oscillator least-square fit reproduces the reflectivity data well. The transverse optic frequencies are found to be 306, 363, 491, 581, 674, and 812 cm^-1 whereas the corresponding longitudinal optic frequencies are 310, 365, 580, 609, 806 and 864 cm^-1. This would tend to support the suggestion by Grimes (1972) that some members of the spinel family belong to space group F43m as opposed to Fd3m.

By measuring the changes in frequency of an oscillator loaded with a capacitor cell containing a crystal of CoSiF₆ 6H₂O, the thermal expansions of the crystal have been measured near its transition temperature. The value for the rate of change of transition temperature with pressure has been calculated.

The causes of streaking often observed in RHEED intensity distributions are discussed. A theoretical study of electron scattering is presented and it is shown that the occurrence of streaks is a consequence of thermal diffuse scattering.

The density of states in the gap of heavily doped closely compensated semiconductors is calculated taking into account the high-temperature correlation in the impurity distribution. It is shown that at small energies the density of states varies as exp(-5 epsilon ³2//8E_B¹2/kT₀) where E_B is the effective Bohr energy and T₀ is the temperature at which the impurity diffusion has been frozen out. At large energies the density of states is Gaussian. Numerical results are given for n-type GaAs.

Without adequate filtering of light from a grating spectrometer, the second-order spectrum of the intrinsic oscillatory photoconductivity of GaAs(Cr) overlaps the much weaker first-order extrinsic spectrum of deep traps. The intrinsic oscillations have a period of 41.8 meV and extrapolate to a threshold of 1.511 eV. In a recently published paper by Stocker (J. Appl. Phys., vol.48, p.3283 (1977)) this intrinsic spectrum, appearing in second order, has been incorrectly assigned to photo-excitation of a deep trap accompanied by a local mode effect.

The absorption coefficient in the n=1 Gamma (3/2) and n=1 Gamma (1/2) exciton region of solid Kr has been determined from transmission spectra of samples of different thickness.

The band structure and electron-phonon interaction of a system where localised and free electronic states are mixed is calculated. The mixing produces on enhancement in the average strength of the electron-phonon interaction A, which is proportional to the superconducting T_c. This idea is tested on a simple model for Ge ion-implanted in Al where it reproduces qualitatively the enhancement observed experimentally.

Measurements of the frequency dependence of the low-field susceptibility of insulating cobalt and manganese aluminosilicate spin glasses are reported. The results are discussed in terms of the superparamagnetic domain model, which attributes to low-temperature properties of spin glasses to the blocking of groups of correlated spins by local anisotropy fields.

Many-body perturbation theory is used to calculate the correction to the nuclear quadrupole crystal field screening parameter gamma _infinity in Pr³⁺, which arises because excited states are not eigenstates of the Hartree-Fock potential. This correction increases the magnitude of the previously calculated value of gamma _infinity by more than 100%.

Mishra and Ramakrishnan have recently claimed (ibid., vol.10, p.L667 (1977)) that in a spin-conserving approximation no T² ln T terms exist in the spin susceptibility of nearly ferromagnetic Fermi systems. It is shown that the approximation used by them is in fact not spin-conserving and if a proper correction is made the T² ln T term is recovered.

The bound state of one magnon with one photon is predicted to occur for the first time in a ferromagnet with the magnetic vector of the electromagnetic wave parallel to the direction of magnetisation. The binding energy is calculated as a function of the sample size and the possibility of observing the one-magnon one-photon bound state, in a well controlled parallel pumping experiment, is suggested.

It is shown that the Ginzburg-Landau free energy used in a recent paper by Da Silva and Rivier (ibid., vol.10, p.L719, 1977) to describe mixed magnets or spin glasses does not have an inhomogeneous solution as its absolute minimum.

It is shown that the conventional Brillouin scattering mechanism involving the elasto-optic effect provides a poor theoretical description of the measured spectra of liquid mercury and gallium. An alternative contribution to the cross-section from reflection by surface ripples is shown to be dominant and to provide a good qualitative fit to the experimental spectra.

A direct calculation of the shear viscosity coefficient for models of liquid rubidium and liquid argon is presented by by neglecting the cross-terms in the auto-correlation function in a fluid. For liquid argon this is found to yield a long decaying tail for the correlation function in qualitative agreement with the computer calculation of Levesque et al. (1973). For liquid rubidium there appears a small oscillatory behaviour at large time in addition to the long tail. However, the numerical values of the shear viscosity coefficients are smaller than the experimentally determined values by about 30% for liquid rubidium and 25% for liquid argon.

An attempt to observe inelastic neutron scattering from short; wavelength charge fluctuation modes in molten potassium bromide is described. Measurements were made using a triple axis crystal spectrometer with fixed scattered neutron energy (19 THz, or 78.6 meV) and scans were recorded at scattering angles between 2 degrees and 7 degrees . An analysis of the results indicates weak shoulders on each side of the elastic peak, corresponding to energy transfers about 4 THz. A calculation of the expected scattering, based on the computer simulation results of Hansen and McDonald (1975) is described, and the neutron scattering results are discussed in the light of this calculation.

The spectral functions corresponding to number and charge density fluctuations are evaluated in model molten NaCl over the range of wavevector (0.751<or=q<or=7.506), and the results are compared with the molecular dynamics data of Hansen and McDonald (1975). For the density fluctuation spectrum results are in very good agreement for all the momentum transfers. In the case of charge fluctuations, our formalism predicts an optic-mode peak only for q=0.751 and is unable to account for the three peak structure exhibited due to the cross-correlation of random forces of second order is important only for small wavevectors.

The contribution of long-range dipole-dipole forces to the energy of the internal modes in a series of molecular crystals has been evaluated using the Weald-Kornfeld summation method. Comparison with experimental infrared observations such as LO-TO and Davydov splittings, gas to crystal frequency shifts, band shapes, transition dipole moments, phonon bandwidths, is discussed.

Using the equation of motion method one- and two-phonon Green functions for the internal modes of a molecular crystal are calculated taking into account the internal anharmonicity of the single molecule. The equations thus derived, formally equivalent to those for a lattice with an impurity, are explicitly solved. These renormalised functions exhibit, if the anharmonicity is strong enough, extra poles, outside the two-phonon continuum, which can be interpreted as bound-states.

For pt.I see ibid., vol.11, p.1283 (1978). Using the Green function obtained in pt.I, the author obtains explicit expression for the two-phonon absorption coefficient of internal modes of molecular crystals. This expression is compared with the IR transmission spectra of CO₂, N₂O and OCS crystals and excellent agreement is found, in terms of two-phonon bound-states and resonances, for both shape and intensity of the bands under consideration.

An extensive study of a large, compact, disordered ensemble of plastic spheres of constant diameter, a fraction p of which has been metallically coated is reported. An initial discussion deals with the compactness and average connectivity z of the system. The electrical conductance for completely conducting samples (p=1) has been studied as a function of pressure applied uniaxially to the ends of a cylindrical container, and compared to that of individual contacts in test samples. Although the variation of conductivity with p is consistent with expectations for a site percolation problem, the idea of a simultaneous bond percolation must be introduced to take into account variations in the quality of the different contacts.

The Niemeyer-van Leeuwen formulation of the renormalisation group is used to describe a quenched dilute Ising model on a triangular lattice in two dimensions. The two- and three-cluster approximations are applied to calculate the probability dependence of the critical temperature T_c(p) and the critical exponents near the percolation threshold phi =1 is found to be in agreement with previous epsilon expansion results.

The temperature dependence of the second harmonic intensity SH(T) at a wavelength of 0.532 mu m has been measured across the weakly discontinuous phase transition of NH₄Cl. It is shown that the tensor component d₁₄ of the non-linear quadratic susceptibility, which is proportional to square root SH(T), can be taken as an order parameter eta for the phase transition. The experimental data are well described by equations derived from the Landau free energy expansion of the form: F=F₀+¹/₂A₂ eta ²+¹/₆A₆ eta ⁶+¹/₈A₈ eta ⁸, recently proposed by Benguigui (1976) for tetracritical systems. It is further shown, that the theoretical order parameter data, calculated from the Landau equations using the best fitting parameters of the experimental data, can themselves be fitted very precisely to a 'critical' power law. In this way the low values for the 'critical' exponent beta of the order parameter, reported in literature for NH₄Cl, can be explained.

Textures of superfluid ³He with point or line singularities are studied by looking for local minima of the free energy in the A, B and A₁ phases. It is found that whereas disgyrations occur in all three phases, 'hedgehogs' occur only in the B phase, in bulk superfluid.

The velocity, v, of positive ions in normal ³He in strong electric fields, E, is calculated using the theory of Fetter and Kurkijarvi (1977). A model for the recoil function, F(k,t), has been proposed by the author, which leads to the prediction that the mobility increases linearly with ln(1/T), where T is the temperature. Measurements of the v-E characteristic will test this model of F(k,t). It is found that the model predicts that v^-1=( mu E)^-1+C for fields greater than 10³ V m^-1, a result which has already been observed.

It is generally agreed that electron wavefunctions are localised in disordered one-dimensional systems, and it has been shown rigorously that wavefunctions grow exponentially inside semi-infinite random systems with a probability one. This has often been taken as evidence for localisation. An application of these exponential growth arguments is applied to the Anderson model for the case of long but finite random chains. It is shown that, except for statistical uncertainty, electron states are quite strongly localised on the long finite system. The statistical uncertainty makes it impossible to prove localisation in the limit of the infinite system using the methods described here.

Photocapacity spectra have been obtained for Schottky barriers on natural semiconducting diamond using photon energies between 0.8 and 4.0 eV. The results indicate the presence of a deep level approximately 1.4 eV above the valence band. In reaching this conclusion independent evidence regarding the donor nature of this level has been used, and it has been assumed that electrons are excited from the valence band to ionised donors in the depletion layer in a two-step process via ionised acceptors. This is the reverse process to donor-acceptor pair recombination.

The random-phase model (RPM) due to Mott (1967) and Cohen (1970), which is expected to be valid for a strongly disordered metallic system, is extended to derive an expression of the electrical conductivity for a case with off-diagonal or bond-type disorder where transfer integrals and hence current matrix elements (in the site representation) are random variables. The RPM expression of the electrical conductivity for such a system is not written simply in terms only of the density of states, in contrast to the Mott-Hindley-Friedman formula for the case with only diagonal disorder. Some simple model systems with the bond-type disorder are studied numerically by applying the RPM formula derived here.

Transient current responses I to a range of step voltages V applied to samples of various thickness L over a range of temperatures T have been previously described. From these responses, the authors plot families of characteristics such as I(V), I(T) and I(L) with two of the remaining three parameters constant while the third is changed by steps. The resulting characteristics are discussed in terms of the same ideas advanced previously for the transient responses. These are that the current is both bulk and contact controlled. Transport in the bulk is in both localised and extended states, and space charge and polarisation effects are important. The contacts are blocking at low fields and low temperatures, and become more injecting as either or both are increased.

An approximate treatment of quenched bond- and site-disordered Ising ferromagnet is presented. It represents an extension of the cluster-variational method considered by Oguchi (1976). Various thermodynamic properties (magnetisation, nearest neighbour correlation, susceptibility and entropy) are obtained from the approximate free energy of the system with binary distribution of bonds. The ferromagnetism disappears in bond-disordered system when the concentration of bond with negative exchange interaction exceeds a critical value. The transition temperature and magnetisation of quenched bond-disordered system exhibit a behaviour very similar to that of the corresponding annealed case. For site disordered case, the transition temperature and magnetisation are determined. Results are in good agreement with those of other theories.

Extending a recent work (ibid., vol.11, p.497 (1978)) on ferromagnets, a diluted Heisenberg antiferromagnet is studied which possesses both nearest and next-nearest neighbour exchange interactions. As in that work, the coherent potential approximation (CPA) is used and for generality the possibility that exchange bonds between any pair of interacting magnetic atoms may also be random is included. By examining the frequency moment conservation behaviour and the dependence of the Neel temperature on randomness, it is shown that the present CPA is exactly analogous to that given in the previous work for the ferromagnet and, moreover, possesses the same level of accuracy, i.e. to two leading orders in 1/z (where z is of the order of the coordination number). For a variety of cases, numerical results are presented for the coherent exchange integrals, the Neel temperature, the density of states and the magnetic response functions.

The sf model for ferromagnetic semiconductors-Coulomb interaction included, but with simplified f-f exchange-has been exactly solved in the limit W to 0 (W=band width) using a Green function technique. It turns out that the original s level is split by the sf interaction into six quasiparticle levels for each electron spin direction. Starting from the atomic limit, a calculation has been performed for a conduction band of finite width under the assumption that it contains only one electron. The temperature behaviour of the quasiparticles energies and their spectral weights (reduced densities of states) is discussed. It is shown that especially very near to the ferromagnetic saturation, the dependence of the spectral weights on the magnetisation of the localised f system gives rise to a spectacular redistribution of the density of states. Furthermore, for sf coupling constants g up to 1 eV, a small variation of g leads already to very strong shifts in weight between the different quasiparticle subbands. It turns out that the usual assumption that the conduction band is split into two spin-polarised subbands is only reasonable, if at all, for very small g values.

The compound URh₃ (cubic AuCu₃ structure, a=3.988 AA) has an almost temperature independent magnetic susceptibility with a value of 1.10*10^-3 emu/mol^-1 at 5K. Both resistivity and de Haas-van Alphen effect measurements suggest a strong interaction between the uranium and rhodium outer-shell electrons. The spatial distribution of the induced magnetisation with a polarised-beam diffractometer has been measured. In an applied field of 48 kOe at 5K the total induced moment is 0.0107 mu _B. Eleven reflections of the form (hhl) were measured out to sin theta / lambda =0.5 AA^-1. Important corrections have to be made for extinction effects, because the one crystal available is almost perfect. To determine the extinction parameters the integrated intensities at lambda =1.05, 0.757 and 0.527 AA with unpolarised neutrons have been measured. An excellent fit is obtained with a simple two-parameter model and this allows a reliable estimate of the extinction in the polarised-beam experiment.

Neutron scattering measurements have been undertaken of the temperature dependence of the critical scattering from a disordered antiferromagnet. The sample-Mn/ZnF₂-was a single crystal of MnF₂ in which 32% of the (magnetic) manganese ions were randomly replaced by (nonmagnetic) zinc ions. The transition temperature of the mixed crystal was T_N=38.7K or about 58% of that of pure MnF₂. The experimental results for the inverse correlation length and susceptibility in Mn/ZnF₂ cannot be equated with simple power-law fits in the reduced temperature. However, if it is assumed that there is a 1% concentration variation throughout the sample, the resulting exponents are consistent with those found in pure MnF₂ and with theoretical predictions. Unfortunately, without independent corroboration of a concentration gradient, it is at present impossible to distinguish the system from one in which it is the actual disorder which smears the transition.

The critical behaviour of solid solutions of quenched paramagnetic impurities which are exchange coupled in a non-magnetic substrate is studied by renormalisation group techniques. A new renormalisation group treatment is proposed to calculate the free energy of these non-equilibrium systems and its consequences to their critical behaviour within the epsilon -expansion are discussed. Critical exponents are calculated to first order in epsilon . The results are compared with experimental data.

Measurements are reported of the optical absorption in phosphorus doped silicon in the wavelength range 25 mu m to 700 mu m, together with the concentration dependence of refractive index. Sample doping levels varied from N_d=5*10¹⁵ Pcm^-3, where the donors are virtually isolated, to N_d=2.7*10¹⁸ Pcm^-3 where they are strongly interacting and just on the insulator side of the metal-insulator transition (critical concentration N_c=3*10¹⁸ Pcm^-3). Specimens doped to 6*10¹⁶ Pcm^-3 exhibited two new absorption lines at 294 cm^-1 and 250 cm^-1, and it is proposed that these lines lead to the formation of an absorption edge which moves towards smaller wavenumber as N_d to N_c. The absorption line at 294 cm^-1 is identified as being the lower limit of a D₂^- band, and its position is in good agreement with Norton's measurement of a band edge using the temperature dependence of a photoexcitation technique.