Four-spin cyclic exchange in spin ladder cuprates

The four-spin cyclic exchange term J(ring) of three spin-ladder cuprates (SrCu2O3, Sr2Cu3O5, and CaCu2O3) has been calculated from ab initio quantum chemistry calculations. For the first two compounds, a non-negligible cyclic exchange is found, aproximately 20% of the magnetic coupling across the rungs, J(perpendicular to), and always larger than the value obtained for two-dimensional La2CuO4 system. In the case of CaCu2O3, the J(ring) value is quite small, due to the folding of the Cu-O-Cu rung angle, but the J(ring)/J(perpendicular to) ratio is also 0.2 as in the two other systems.