Spin bags, polarons, and impurity potentials in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ from first principles

A full-potential version of a recently proposed generalization of the local-density method (LDA+U) is used to study the influence of impurities, lattice, and magnetic relaxation in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$. The carriers form mean-field analogs of Zhang-Rice singlets, which are only slightly affected by impurity and in-plane lattice relaxation effects. On the other hand, an ‘‘anti-Jahn-Teller’’ polaron, characterized by a 0.26 Å shorter Cu to apical-oxygen bond length and triplet spin, is nearly stable. Although the impurity potentials are similar, the self-localization effects are much stronger in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{NiO}}_4$.