Tight-binding parameters and exchange integrals of Ba₂Cu₃O₄Cl₂

Band structure calculations for Ba_2Cu_3O_4Cl_2 within the local density approximation (LDA) are presented. The investigated compound is similar to the antiferromagnetic parent compounds of cuprate superconductors but contains additional Cu_B atoms in the planes. Within the LDA, metallic behavior is found with two bands crossing the Fermi surface (FS). These bands are built mainly from Cu 3d_{x^2-y^2} and O 2p_{x,y} orbitals, and a corresponding tight-binding (TB) model has been parameterized. All orbitals can be subdivided in two sets corresponding to the A- and B-subsystems, respectively, the coupling between which is found to be small. To describe the experimentally observed antiferromagnetic insulating state, we propose an extended Hubbard model with the derived TB parameters and local correlation terms characteristic for cuprates. Using the derived parameter set we calculate the exchange integrals for the Cu_3O_4 plane. The results are in quite reasonable agreement with the experimental values for the isostructural compound Sr_2Cu_3O_4Cl_2.