Electronic structure of ferromagnetic hcp cobalt. III. Magnetic hyperfine field

Abstract

Using the energy bands and wave functions of ferromagnetic cobalt from a self-consistent hybridized tight-binding---orthogonalized-plane-wave ferromagnetic band calculation, we have obtained the core and the band contributions to the hyperfine field at the cobalt nucleus to be, respectively, -380.1 and -42.7 kOe. The core contribution of -380.1 kOe, in the moment-perturbation (MP) approach, is composed of contributions from $1s$, $2s$, and $3s$ cores, respectively, of -0.07, -272.4, and -107.7 kOe. These values have been transformed to derive the results that would be expected from a unrestricted-Hartree-Fock (UHF) theory, for the core states and give the individual contributions, in order, from $1s$, $2s$, and $3s$ states as -19.0, -528.1, and +154.6 kOe which add up to about the same total core contribution. The most important effect, causing the individual core contributions to differ substantially in the two methods, is shown to result from exclusion-principle-violating (EPV) diagrams. The small difference of the total core contributions from the MP and the UHF approaches arises from EPV diagrams in which the band electrons are involved. The negative band contribution to the hyperfine field is found to arise from the paired $3d$-like and free-like band states, which overwhelm the positive contribution from the unpaired-spin electrons in the majority-spin band. Arguments are proposed to show that the difference between the theoretical value -422.9 kOe for the hyperfine field and the experimental value of -223.0 could arise from the influence of correlation effect on the $3d$-like band electron wave functions, particularly those at the Fermi surface.