A Simple Procedure for Computing Density of States Spectra in Solid State Physics

Abstract

The histogram method for computing density of states spectra is simplified considerably for the cubic lattices. As an example we treat the fcc lattice by randomly sampling a cube in k space (composed of octants from two adjacent Wigner-Seitz cells of the reciprocal lattice). Graphical results for the magnitude of the group velocity are used to locate the critical points that cause the singularities in the density of states. Illustrations are given that show how this can be used to improve the resolution of singularities that are not clearly resolved by the histogram method. A utility dispersion relation has been used for the examples, and it can be applied to spin waves as well as to electrons in the tight-binding approximation. Students can gain much insight into solid state research from this method since it helps to bridge the gap between the standard textbook treatments and the highly technical discussions of the research literature. The authors have used this method in a detailed study of the spectra of fcc lattices that will be presented elsewhere.

Extended Theory of Magnon Sideband Shapes. I. Impure Three-dimensional Ferromagnets

“…This is repeated until sufficient smoothness of the curve is obtained, the error being proportional to N-~ for N points generated in the cube. As also pointed out by Buchheit and Loly (1972) an estimate of the energy at which van Hove singularities occur in the density of states may be made from evaluating the mInimum of the group velocity at the energy of each cell. The group velocity is given by (AI)…”

“…A good description of the method is given by Buchheit and Loly (1972). Other Monte Carlo calculations using various types of interpolation with improved accuracy for a given computing time have been described by Mueller et al (1971), Gilat and Raubenheimer (1966) and Cooke and Wood (1972).…”

“…It was therefore considered desirable to find an alternative means of evaluating R(A). The method used follows from considering the Monte Carlo calculation of Buchheit and Loly (1972) with the Fourier series calculation of Mahanty (1966). The pure crystal density of states go(A) is evaluated using the Monte Carlo method to the desired accuracy.…”