The LCAO, or Bloch, or tight binding, approximation for solids is discussed as an interpolation method, to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants, so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made, and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given, including tables of matrix components of energy for simple cubic, face-centered and body-centered cubic, and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni, and Howarth on Cu, as illustrations of the fcc case. In discussing the bcc case, the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out, as well as a distribution of energy states for the case of no antiferromagnetism. For diamond, comparisons are made with the calculations of Herman, using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed, and it is shown that their properties fit in with the energy band picture.

Simplified LCAO Method for the Periodic Potential Problem

Character tables for the "group of the wave vector" at certain points of symmetry in the Brillouin zone are given. The additional degeneracies due to time reversal symmetry are indicated. The form of energy vs wave vector at these points of symmetry is derived. A possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure will be presented.

Spin-Orbit Coupling Effects in Zinc Blende Structures

A review is given of progress in the theoretical and experimental study of the Raman effect in crystals during the past ten years. Attention is given to the theory of those properties of long-wavelength lattice vibrations in both cubic and uniaxial crystals which can be studied by Raman scattering. In particular the phenomena observed in the Raman scattering from crystals which lack a centre of inversion are related to the theory. The angular variations of the scattering by any type of lattice vibration in a crystal having any symmetry can be easily calculated using a complete tabulation of the Raman tensor. Recent measurements of first-order lattice vibration spectra are listed. A discussion of Brillouin scattering is included. The relation of second-order Raman spectra to critical points in the lattice vibration density of states is discussed, and measurements of the second-order spectra of diamond and the alkali halides are reviewed. The theory and experimental results for Raman scattering by electroni...

The Raman effect in crystals

Using the full-potential screened Korringa-Kohn-Rostoker method we study the full-Heusler alloys based on Co, Fe, Rh, and Ru. We show that many of these compounds show a half-metallic behavior; however, in contrast to the half-Heusler alloys the energy gap in the minority band is extremely small due to states localized only at the Co (Fe, Rh, or Ru) sites which are not present in the half-Heusler compounds. The full-Heusler alloys show a Slater-Pauling behavior and the total spin magnetic moment per unit cell ${(M}_{t})$ scales with the total number of valence electrons ${(Z}_{t})$ following the rule ${M}_{t}{=Z}_{t}\ensuremath{-}24.$ We explain why the spin-down band contains exactly 12 electrons using arguments based on group theory and show that this rule holds also for compounds with less than 24 valence electrons. Finally we discuss the deviations from this rule and the differences compared to the half-Heusler alloys.

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Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys

Publisher Summary This chapter discusses that the subject of exchange in magnetic materials is divided into two parts, referring to insulators and to metals. This distinction is useful from the magnetic point of view because in insulators the spins and magnetic moments whose alignments lead to magnetic effects are certainly localizable so that phenomenologically is described by a spin Hamiltonian that contains spin operators and exchange terms of Heisenberg type. It discusses that there is relationship among the mechanisms important in metals, such as conduction electron polarization, and those in insulators. The chapter provides historical discussion of the subjects of antiferromagnetism and of exchange in insulators. It focuses on the Heisenberg Hamiltonian, with a brief derivation and a discussion of some of the statistical theories of magnetism based upon it, primarily molecular field theory, which is by far the most generally useful in the experimental measurement of exchange. The chapter also describes older theories and presents ideas about super-exchange, and gives a discussion and a diagrammatic classification of all the possible higher-order processes.

Theory of Magnetic Exchange Interactions:Exchange in Insulators and Semiconductors

It is well known that if the interaction between electrons 1 a metal is neglected, the energy spectrum has a zonal ructure. The problem of these “Brillouin zones” is eated here from the point of view of group theory. In is theory, a representation of the symmetry group ol ie underlying problem is associated with every energy slue.

R. Smoluchowski

Papers

Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals