Magnetocrystalline Energy, Electronic Charge Distribution, and Fermi Surface of Iron from a Tight-Binding Calculation

By introducing the spin-orbit coupling, the first constant $K_1$ of the magnetocrystalline energy of bcc Fe has been evaluated, using 284 nonequivalent points of the Brillouin zone. Previous results obtained with the tight-binding approximation are used. $K_1$ is found to be positive, in agreement with the experimental data on the directions of easy magnetization, but its value is lower than expected. The $3d$-electron charge distributions for the $t_{2g}$ and $e_g$ symmetries are given as a function of energy. Both the charge and spin densities show the same kind of deviation from spherical symmetry as the ones deduced, respectively, by x-ray and neutron-diffraction experimental results. Finally, the shape of Fermi surface in paramagnetic and ferromagnetic bcc Fe is suggested.