Determination of moment distributions and hyperfine fields at and surrounding transition-element solute atoms in Fe

A new method is developed which uses the hyperfine spectra of the Fe atoms in dilute Fe alloys to obtain (i) the moment on a transition-metal-solute atom in Fe, (ii) the moment perturbations in the Fe matrix, and (iii) the hyperfine-field shifts at the Fe atoms in the four-nearest-neighbor shells to the solute atom. We find that this method has much more sensitivitiy than the comparable technique using elastic diffuse neutron scattering. A moment perturbation varying as $\frac{1}{r^3}$ is found to best fit the spectra. For Co and Ni solute atoms we obtain moments of (1.9 ± 0.1)${\mathrm{\mu }}_{\mathit{B}}$ and (1.4 ± 0.1)${\mathrm{\mu }}_{\mathit{B}}$, respectively. These agree with the neutron-scattering results but are much more accurately determined. The moments at Rh and Pd in Fe are found to be (1.1 ± 0.2)${\mathrm{\mu }}_{\mathit{B}}$ and (0.7 ± 0.2)${\mathrm{\mu }}_{\mathit{B}}$, in agreement with neutron-scattering results on more concentrated alloys. The hyperfine-field shifts are obtained in a much more fundamental way than the previous analyses of FeCo spectra. This results in very different hyperfine-field shifts than the previous determination. The average-moment and moment-perturbation behavior is discussed from the point of view that the magnetic behavior of the $3d$ transition series is determined by the coupling via exchange and interband mixing of mainly localized moments through a small fraction of itinerant $d$ electrons. This is in contrast to a charge-perturbation-type model where the moment behavior is attributed to arise from the different screening of the spin-up and spin-down $d$ electrons. The latter is not believed to be significant in determining the moment behavior. Using the results of this analysis we derive from only hyperfine-field data the value of the core-polarization hyperfine field in Fe. We find indications that this term may be larger than the values previously obtained by band calculations. From the derived moments of Rh and Pd we can obtain a value for the hyperfine field per ${\mathrm{\mu }}_{\mathit{B}}$ due to core polarization for the $4d$ transition series. We find reasonable agreement with the calculated value. Earlier derivations of the moments of $4d$ and $5d$ solute atoms in Fe, as obtained from their measured hyperfine fields, omitted the large self-polarization conduction-electron term. This is considered here and corrected moment values are obtained.