Magnetic-Moment Distribution in NiFe and AuFe Alloys

We have determined the magnetic form factors and the corresponding magnetic-moment distributions for ordered ${\mathrm{Ni}}_3$Fe and for disordered NiFe and AuFe alloys in an attempt to establish the variation of the individual atomic-moment distributions with composition. The results confirm the individual moments previously determined for NiFe alloys by neutron-diffuse-scattering methods and provide an upper limit of $0.03{\mu }_B$ for the Au moment in a 25-at.% Fe in Au alloy. A small negative moment density between atoms was found for all of the alloys studied. The symmetry of the moment distributions was determined at the Ni and Fe sites in ordered ${\mathrm{Ni}}_3$Fe and for Fe in ${\mathrm{Au}}_{0.75}$ ${\mathrm{Fe}}_{0.25}$. The Fe moment distribution is nearly spherical in both cases (54% $T_{2g}$ in ${\mathrm{Ni}}_3$Fe and 56% $T_{2g}$ in the AuFe alloy) while the Ni moment distribution is strongly distorted. There seems to be little difference between the individual moment distributions in ordered and disordered ${\mathrm{Ni}}_3$Fe. In both, the effective $T_{2g}$ character decreases relative to pure Ni. The $\mathrm{Ni} d$-function populations in ordered ${\mathrm{Ni}}_3$Fe suggest that this decreasing $T_{2g}$ character is associated with the larger size of, and the stronger $d-d$ overlap with, the Fe atoms. The $\mathrm{Ni} d\left(\mathrm{xz}\right)\mathrm{}$ and $d\left(\mathrm{yz}\right)\mathrm{}$ functions that are directed toward nearest-neighbor Ni atoms have essentially the same population as in pure Ni while the $d\left(\mathrm{xy}\right)\mathrm{}$ function directed toward nearest-neighbor Fe atoms loses population to $d(x^2-y^2)$. Thus, there is a repulsion of spin-up electrons away from the regions of strong overlap.