  The magnetic and electronic structures of $3d$ impurity atoms from Sc to Zn
in ferromagnetic body-centered cubic iron are investigated using the
all-electron full-potential linearized augmented plane-wave method based on the
generalized gradient approximation (GGA). We found that in general, the GGA
results are closer to the experimental values than those of the local spin
density approximation. The calculated formation enthalpy data indicate the
importance of a systematic study on the ternary Fe-C-$X$ systems rather than
the binary Fe-$X$ systems, in steel design. The lattice parameters are
optimized and the conditions for spin polarization at the impurity sites are
discussed in terms of the local Stoner model. Our calculations, which are
consistent with previous work, imply that the local spin-polarizations at Sc,
Ti, V, Cu, and Zn are induced by the host Fe atoms. The early transition-metal
atoms couple antiferromagnetically, while the late transition-metal atoms
couple ferromagnetically, to the host Fe atoms. The calculated total
magnetization ($M$) of bcc Fe is reduced by impurity elements from Sc to Cr as
a result of the antiferromagnetic interaction, with the opposite effect for
solutes which couple ferromagnetically. The changes in $M$ are attributed to
nearest neighbor interactions, mostly between the impurity and host atoms. The
atom averaged magnetic moment is shown to follow generally the well-known
Slater-Pauling curve, but our results do not follow the linearity of the
Slater-Pauling curve. We attribute this discrepancy to the weak ferromagnetic
nature of bcc Fe. The calculated Fermi contact hyperfine fields follow the
trend of the local magnetic moments. The effect of spin-orbit coupling is found
not to be significant although it comes into prominence at locations far from
the impurity sites.
