Systematic Study of Magnetic Interactions in Insulating Cuprates

The magnetic interactions in one-dimensional, two-dimensional (2D) and ladder cuprates are evaluated systematically by using small Cu-O clusters. We find that the superexchange interaction J between nearest neighbor Cu spins strongly depends on Cu-O structure through the Madelung potential, and in 2D and ladder cuprates there is a four-spin interaction Jcyc, with magnitude of 10% of J. We show that Jcyc has a strong influence on the magnetic excitation in the high-energy region of 2D cuprates.