Magnetic Interaction in 1D, 2D and Ladder Cuprates

In this paper, the magnetic interactions for one-dimensional (1D), two-dimensional (2D) and ladder cuprates are systematically examined. By a comparison of eigenstates between Cu-O clusters and the corresponding Heisenberg models, we evaluate magnitudes of these interactions. As a result, it is found that (1) superexchange interaction J between nearest neighbor Cu spins for 1D cuprate is larger than that of 2D one, (2) for ladder an anisotropy of J between leg and rung is small, and (3) a cyclic four-spin interaction J cyc in a plaquette exists with magnitude of ~10% of J for ladder and 2D cuprates. The effect of J cyc on the magnetic properties of ladder and 2D cuprates is briefly discussed.