Energy Bands in Ferromagnetic Iron

Abstract

Results of a self-consistent tight-binding calculation of the band structure of body-centered-cubic iron are reported. The basis set consisted of atomic wave functions for the $1s$, $2s$, $3s$, $4s$, $2p$, $3p$, and $4p$ states, expressed as linear combinations of Gaussian-type orbitals (GTO), and five individual GTO for each $3d$ state. The Coulomb part of the crystal potential in the first iteration was constructed from a superposition of overlapping neutral-atom charge densities; the atoms being in the $3d^{7}4s^1$ configuration. Exchange potentials for both spins were calculated utilizing the $X\alpha$ method. Self-consistent band structures were obtained for different values of the exchange parameter $\alpha$. Best results appear to be obtained for $\alpha =0.64\mathrm{}$. In this case, 140 points in $\frac{1}{48}$ of the Brillouin zone (BZ) were used to determine the charge density. The resulting self-consistent potentials were then utilized to compute energy levels at 819 regularly spaced points in $\frac{1}{48}$ of the BZ. The results thus obtained are discussed and compared with other reported band-structure results for the same metal. The Fermi surface is analyzed in detail. The density of states has been computed. Magnetic and x-ray form factors are presented. The results are found to be in reasonably good agreement with experiment.