Density-of-States Spectra for the fcc Lattice with Variable Second-Neighbor Interactions

Publisher Website
Google Scholar
Abstract
Using an analytic dispersion relation we have computed density-of-states spectra on an fcc lattice. The transition from the spectrum of the nearest-neighbor fcc case has been studied in detail as the strength of second-neighbor interactions increases and eventually produces the spectrum of the nearest-neighbor sc case. Graphical results for the magnitude of the group velocity have been used to improve the resolution of the singularities of the spectra enabling the changes in number, order, and degeneracies of these singularities to be followed as the second-neighbor interaction is varied. A simple algebraic analysis of the critical points of the dispersion relation gives a complete explanation of all features found in the spectra and reveals a singularity not previously found in three-dimensional spectra. The results can be applied to spin waves in ferromagnetic insulators as well as to electronic-energy bands in the tight-binding approximation and have relevance to a large number of phenomena in solid-state physics.