Energy Bands in Ferromagnetic Nickel

The energy bands in ferromagnetic nickel have been calculated within the framework of the unrestricted Hartree-Fock scheme, in which the exchange terms were approximated by a local potential. The augmented-plane-wave method was used to find the eigenvalues of the approximate Hamiltonian, and self-consistency was achieved after several iterations of this method. It was found that the use of the averaged free-electron exchange potential, i.e., ${{\overline{V}}_x}^{\mathrm{}\left(s\right)\mathrm{}}=-6\mathrm{}{\left(\frac{6{\rho }_s}{8\pi }\right)}^{\frac{1}{3}}$, gave results in qualitative disagreement with experiment. Reducing the exchange potential by a factor of $\frac{2}{3}$ gave more realistic results. Comparisons with the experimental data are presented which show that the unrestricted Hartree-Fock scheme may be an acceptable model for the ground state of a ferromagnetic solid.