Superexchange interaction in cuprates

Recent experiments have shown that the superexchange interaction J in one-d imensional (1D) cuprates is larger than that in two-dimensional (2D) ones. We investigate a microscopic origin of the difference of J in the 1D and 2D cuprates. The hopping matrix elements between Cu3d and O2p orbitals and be tween O2p orbitals are considerably influenced by the Madelung potential, w hich is a function of crystal structure, and these values in the 1D cuprate s are enhanced as compared with those for the 2D ones, resulting in larger values of J. The same mechanism is applied to hopping matrix elements in th e ladder cuprates. The elements between O2p orbitals are found to be respon sible for the anisotropic J's along leg and rung of the ladder; i.e., J(leg ) >J(rung). We find a unique dependence of the electronic structure of cupr ates on the dimensionality.