Local electronic structure and magnetism of 3d transition-metal impurities (Cr, Mn, Fe, Co, and Ni) in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$

Local-density-functional calculations have been performed to study the electronic structure and magnetism of 3d transition-metal ions (Cr, Mn, Fe, Co, and Ni) substituting for the Cu ion in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$. These systems are simulated by small clusters which are surrounded by over 5000 point charges. It is found that all the substituting ions possess local magnetic moments. Through a systematic comparison we find that the Cu-O system has the smallest p-d separation and the largest p-d hybridization. The Cu-O system has the smallest local magnetic moment, which can be reduced to zero by hole doping. We also find that removing an electron from these systems further increases the p-d hybridization. The crystal-field splittings of these transition-metal oxide systems are found to remain nearly constant at about 0.1 Ry, while the Jahn-Teller splittings vary considerably, depending on the manner in which single-particle levels are filled. Hyperfine fields have been calculated for the Fe ion at both trivalent and divalent states. These calculations are compared with available experimental measurements.