Impurity states and magnetic order in layered copper oxides (invited)

The influence of impurity potentials on vacancies in the t-J model is studied through the exact diagonalization of systems with 8 and 16 sites. For a wide range of model parameters, the ground state transforms according to the two-dimensional vector representation of C_4v and has S =1/2. The inclusion of symmetry breaking effects present for an isolated impurity in an infinite system yields an anisotropic ground state which may couple to local lattice distortions. Implications for magnetic order, spectroscopy, and the metal-insulator transition in the CuO₂ planes of the cuprate superconductors are discussed. The relationship to the behavior of free vacancies and the role of finite size effects are considered. A mean-field Hubbard model analysis is proposed as a supplementary approach.