Magnetic interaction in insulating cuprates

We examine two-spin (2S) and cyclic four-spin (4S) magnetic interactions in insulating ladder and two-dimensional (2D) cuprates. By a comparison of ei genstates between d-p and Heisenberg models, we evaluate magnitudes of thes e interactions. We find that the 4S interaction is similar to 10 % of neare st neighboring 2S interaction, and a diagonal 2S interaction is considerabl y small. The 4S interaction for a ladder cuprate is larger than that for 2D one, and plays an important role in the low-energy excitation. The Heisenb erg ladder with the obtained 2S and 4S interactions reproduces very well th e experimental result of the temperature dependence of the magnetic suscept ibility.