Theoretical Study of Magnetism and Superconductivity in 3d Transition-Metal- MgB₂ Alloys

We have studied the electronic structure of 3d transition-metal- MgB_{2} alloys, Mg_{0.97}TM_{0.03}B_{2}, (TM\equiv Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) using KKR-CPA method in the atomic-sphere approximation. For unpolarized calculations, our results for Mg_{0.97}TM_{0.03}B_{2} alloys are similar to that of 3d impurities in other s and s-p metals. In particular, the local densities of states (DOS) associated with the 3d impurities are similar to our earlier work on 3d impurities in bulk Al. For spin-polarized calculations, we find only the alloys of V, Cr, Mn, Fe and Co with MgB_{2} to be magnetic of all the 3d elements. We also find that Cr and Mn in MgB_{2} have a relatively large local magnetic moment of 2.43 \mu_{B} and 2.87 \mu_{B}, respectively. We have used the unpolarized, self-consistent potentials of Mg_{0.97}TM_{0.03}B_{2} alloys, obtained within the coherent- potential approximation, to calculate the electron-phonon coupling constant \lambda using the Gaspari-Georffy formalism and the superconducting transition temperature T_{c} using the Allen-Dynes equation. We find that the calculated T_{c} is the lowest for Mg_{0.97}Cr_{0.03}B_{2} and the highest for Mg_{0.97}Zn_{0.03}B_{2}, in qualitative agreement with experiment. The calculated trend in variation of T_{c} from Mn to Zn is also similar to the available experimental data. Our analysis of the variation in T_{c}, in terms of the DOS and the spectral function along \Gamma to A direction, shows the variation to be an interplay between the total DOS at the Fermi energy and the creation/removal of states along \Gamma to A direction [P. P. Singh, cond-mat/0201093].