A specific model for the origin of ferromagnetism in Fe, Co, and Ni is given, which attributes the origin of the ferromagnetism to the indirect coupling of the predominately localized $d$-like electrons through a small number of itinerant $d$-like electrons. The model suggests that about 5% of the $3d$ electrons are in itinerant bands and 95% are in $d$ bands which are sufficiently narrow that they can be considered localized. Band-structure calculations and Fermi-surface measurements for Fe strongly support this model. Many other features of the $3d$ transition series are discussed and seen to be consistent with this model. Using this model we give the scaling rules for the three contributions to the hyperfine fields: $H_{\mathrm{cp}}$, the core polarization; $H_{\mathrm{ce}}$, the $4s$-like conduction-electron polarization; and $H_v$, the volume overlap polarization. We also update the treatment of the volume overlap term and show that the change in sign of the hyperfine field at Sn in Ni as compared with that in Fe and Co results from the competition of the comparable-sized $H_{\mathrm{ce}}$ and $H_v$ terms for Sn.

• Received 29 January 1973

DOI:https://doi.org/10.1103/PhysRevB.8.4383