Superexchange interaction in cuprates

Recent experiments have shown that the superexchange interaction J in one-dimensional (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 between O2p orbitals are considerably influenced by the Madelung potential, which is a function of crystal structure, and these values in the 1D cuprates 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 the ladder cuprates. The elements between O2p orbitals are found to be responsible 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 cuprates on the dimensionality.