Origin of the Hyperfine Fields in Pure Fe and at Solute Atoms in Fe

Abstract

The measured spin-density oscillations in Fe (preceding paper) are interpreted as due to $4s$-like conduction-electron polarization and compared with improved Ruderman-Kittel-Kasuya-Yosida-type calculations. The hyperfine field shifts due to a solute atom are shown to be due to moment perturbations rather than charge perturbations, and agreement with the improved RKKY-type calculations is considered to be quite good. We find ${J}_{\mathrm{int}}(q=0)\ensuremath{\sim}+0.5$ eV. There is some indication that the exchange interaction and interband mixing cause comparable polarizations in the region of the nearest-neighbor shell. We find the net integrated $4s$-like polarization in pure Fe to be about +(5-8)%. Using the latest Fe band calculations, we are able to obtain identifications and magnitudes for the terms contributing to the hyperfine field of Fe. With this model we are able to explain the well-known variations of hyperfine fields at solute atoms in Fe. There is shown to be a positive hyperfine field contribution from the polarization induced in the $\mathrm{ns}$-like electron density near the solute atom. This positive polarization is proportional to the volume overlap of the solute atom with the Fe matrix.