A simple interpolation scheme for paramagnetic fcc transition and noble metals has been developed and extended to the ferromagnetic state of Ni. It is based on the representation of $d$ and conduction bands by linear combinations of atomic orbitals and orthogonalized plane waves, respectively, and includes hybridization effects through the use of k-dependent matrix elements. The energy bands of augmented-plane-wave calculations from first principles for Cu and paramagnetic Ni are fitted with an rms deviation of about 0.12 eV. The density of states of paramagnetic Ni is calculated and shown to be significantly influenced by hybridization. A self-consistent calculation of the ferromagnetic band structure of Ni is carried out by the incorporation of correlation effects through the use of an intra-atomic Coulomb interaction patterned along the lines suggested by Gutzwiller, Hubbard, and Kanamori. Experimental information relating to the magnetization, ferromagnetic Kerr effect, Fermi surfaces, neutron magnetic form factor, electronic specific heat, and high-field susceptibility is used to determine the parameters characteristic of the ferromagnetic state and to check the predictions of the resulting band structure. The k-dependent splitting of the bands averages 0.37 eV in the vicinity of the Fermi level. The wave functions resulting from these calculations are shown to be sufficiently realistic to permit the calculation of the total charge density in Cu and the magnetic form factor of Ni. The use of approximate spin-polarized wave functions appropriate to the solid demonstrates the importance of both unpaired and paired electrons to the magnetic form factor. The net conduction-electron polarization is found to be small and positive. The effective $s-d$ exchange energy changes sign between the central and outer parts of the Brillouin zone. The inclusion of spin-orbit effects is discussed, and the reduction of the density of states at the Fermi level due to this interaction is calculated. The effect is too small to explain the presence of ferromagnetism in Ni and its absence in Pd and Pt.

• Received 17 June 1966

DOI:https://doi.org/10.1103/PhysRev.152.505