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First-principles investigation of magnetism and electronic structures of substitutional $3d$ transition-metal impurities in bcc Fe

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.