Showing papers in "Advances in Physics in 1974"

Experiments on simple magnetic model systems

Abstract: “…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...

Electron transport phenomena in small-gap semiconductors

Abstract: Electron transport phenomena in small-gap III–V, II–VI and IV–VI semiconducting compounds are reviewed. We emphasize peculiarities due to nonparabolic energy-momentum dependence in the conduction band and the structure of Bloch wavefunctions, when electron energy becomes comparable to that of the gap. General theoretical framework is compared with real conduction bands in the materials of interest. Thermodynamic properties of electron gas are derived for arbitrary nonparabolic and nonspherical energy bands. We develop a theory of d.c. transport phenomena and free-carrier optics based on a linear Boltzmann equation solved for an ellipsoidal band of arbitrary nonparabolicity. Elastic electron scattering is considered taking into account true Bloch eigenstates of the conduction electrons. We give a unified description of electron mobility, thermoelectric power, thermomagnetic phenomena and free-carrier optical effects illustrating the theoretical methods with experimental results of various authors....

Elastic interaction and phase transition in coherent metal-hydrogen alloys

Abstract: We study the statistical mechanics of hydrogen dissolved in metals. The underlying model is based on the assumption that the dominant attractive interaction between the protons in the metal is of an elastic nature. In the first part of the paper we review some general properties of the elastic interaction. We then discuss the importance of boundary conditions for the form of the elastic interaction, which turns out to be of the Curie-Weiss type with macroscopic range. In the second part we investigate the a-a' (‘gas-liquid’) phase transition in the hydrogen lattice fluid. The long-range part of the elastic interaction is treated in mean field approximation. In the canonical ensemble as opposed to the grand canonical ensemble one finds no co-existing phases near the critical point. Instead there is a continuous transition which changes into a first-order transition at tricritical points. In the temperature-density region which normally corresponds to the two-phase co-existence region the hydrogen ...

Experimental evidence for many-body effects in dilute alloys

Abstract: The macroscopic and local properties of 3d transition metal impurities in normal metals are reviewed and compared with the theoretical situation in this field. The parameters of the Anderson and s-d exchange models are derived from direct and indirect experimental data using as a guide the Hartree-Fock approximation of the non-degenerate Anderson model. The basic observations about the magnetic-non-magnetic transition, and the behaviour of the magnetic, thermal and transport properties when going through the transition region are demonstrated for specific examples. A detailed comparison between the present status of theory and experiment is performed by inspecting the large body of experimental data of two typical alloys, which served as testing materials for the development of the existing theories. CuFe is often regarded as a typical ‘yes moment’ system, and the experiments are therefore compared with the predictions based on the s-d exchange model; in the case of AlMn, the spin-fluctuation con...

Deviations from Matthiessen's rule at low temperatures: An experimental comparison between various metallic alloy systems

Abstract: The low temperature electrical resistivity data on Al, Cu, Au, Ag, Pt, Mg, Sn, Zn, In and Ga are reviewed with particular emphasis on the variation of the phonon contribution with the magnitude of the impurity resistivity. A comparison is made within the various alloys having the same base metals, and also between the different solvents, by developing a phenomenological fitting formula for the deviations from Matthiessen's rule. The derived phenomenological parameters show a strong similarity for all metals. The limits imposed on this type of comparison by the uncertainty of data obtained on different samples and in different laboratories are discussed. An updating of the references given in an earlier review in this journal by Bass (1972) is also included.

Electronic transport and localization in low mobility solids and liquids

Abstract: This article is concerned with the electronic transport properties of the large group of solids (and also some liquids) which possess carrier mobilities from 10 cm2V-1sec-1 to many orders below that value. Its main aim is to trace the close relation between transport and localization. To this end the physical basis of three important localization models is discussed and the predicted transport mechanisms are reviewed in the light of the experimental information. After a brief summary of the experimental methods, the first subject is the localization arising from strong electron-phonon interaction. Here we consider in some detail the formation of a small polaron in a molecular crystal and its transport by phonon-assisted intermolecular hopping. The second part of the paper deals with the localization of an electron in a so-called electronic bubble, which occurs for example in simple liquids such as Ne or He. The stability and transport of this entity is discussed. The third section is devoted to n...

Monte Carlo computer experiments on critical phenomena and metastable states

Abstract: Ising and Heisenberg models are studied by the Monte Carlo method. Several hundred up to 60 000 spins located at two- and three-dimensional lattices are treated and various boundary conditions used to elucidate various aspects of phase transitions. Using free boundaries the finite size scaling theory is tested and surface properties are derived, while the periodic boundary condition or the effective field-like ‘self-consistent’ boundary condition are used to derive bulk critical properties. Since Monte Carlo averages can be interpreted as time averages of a stochastic model, ‘critical slowing down of convergence’ occurs. The critical dynamics is investigated in the case of the single spin-flip kinetic Ising model. Also non-equilibrium relaxation processes are treated, e.g. switching on small negative fields the magnetization reversal and nucleation processes are studied. The metastable states found can be understood in terms of a scaling theory and the droplet model. Using a spin exchange model t...

Functional integral methods in the theory of the Anderson model

Abstract: The use of the functional integration technique applied to the problem of local moment formation in the Anderson model is reviewed in this paper. The different approximations are discussed, in order to clarify both their internal consistency and relations among them. Connection with the ordinary diagrammatic approach is made by summarizing and extending previous treatments done on this subject; and the difference between the one-field and the two-field approaches is explained in terms of the ‘unphysical diagrams’ generated by the first. The results for the magnetic susceptibility are presented for each approximation discussed in the paper, both in the strong magnetic and in the non-magnetic regime; while it is shown that no reliable approximation has been developed for the intermediate coupling situation. Finally the Kondo effect is discussed within the functional integration scheme and application of the method to the study of superconducting magnetic alloys is reviewed.

Group theory in solid-state physics is not dead yet alias some recent developments in the use of group theory in solid-state physics

Abstract: In this article a review is given of the principal applications of group theory in solid-state physics. Some of these applications are well established, such as the simplification of the forms of tensors representing physical properties of crystals, the labelling of electronic energy band structures, and the study of the splitting of atomic or ionic energy levels in crystals. The general principles involved in these applications are discussed. However, no attempt is made to give a comprehensive review of all the work which has been done in these areas; for further details references are given to the existing literature. The main intention of the article is to show that apart from the well-established applications, which are adequately described in the existing literature, there have been many new developments in recent years. Group theory has come to be applied to many other types of problems in solid-state physics and these applications have not been discussed extensively in the existing review ...

Galvanomagnetic effects in anisotropic metals

Abstract: The aim of this article is to present an introductory review of those aspects of the isothermal galvanomagnetic effects in metals (which here means the electrical resistance, magnetoresistance and Hall effect) which are peculiar to the existence of an anisotropic electrical conductivity. This anisotropy may be intrinsic to the solid, such as that arising from a non-cubic crystal structure, or it may be induced by the application of the external magnetic field. Such induced anisotropy can itself be divided into two classes : that arising directly from the effect of the Lorentz force upon the itinerant electrons, and that in which the external field is merely an agent which makes evident on a macroscopic scale an anisotropy which exists microscopically, even in the field-free case. The article traces the usual phenomenological formulation of the galvanomagnetic effects, and then particularizes this to the commonly-encountered experimental situations used to study the consequences of both induced an...

On the application of group theory to spinwaves in collinear magnetic structures

Abstract: The application of group theory to spinwaves in collinear magnetic structures is discussed in close analogy with similar applications made in the case of lattice vibrations. Some of the basic features pertaining to magnetic space groups are first recalled and the spinwave equations for collinear magnetic systems are set up. The details of applying group theory are then described using the multiplier-representation approach, and finally the methodology is illustrated by working through in detail the classification of spinwaves in Fe3O4. The relationship of the present results to those given earlier by Brinkman and Elliott for the same crystal is also pointed out.

The elastic dielectric

Abstract: Macroscopic field equations, boundary conditions and equations of state are derived for the non-linear, macroscopic elastic and dielectric response of an insulator. A centrosymmetric polynomial representation of order four is introduced for the energy density; the equations of state for the electric field and stress tensor are then deduced as polynomials of degree three in the displacement gradients and electric displacement field. The results are applied to the special case of m3m material symmetry. A finite, point-charge model of a centrosymmetric ionic crystal is introduced and used to determine 0°K microscopic expressions for the electric field and stress tensor equation of state coefficients introduced in the macroscopic analysis. The results are used to calculate the full set of second and third-order non-linear coefficients for NaI, based on a Born-Mayer potential and the 4·2°K elastic stiffness data of Claytor and Marshall.