Effects of cyclic four-spin exchange on the magnetic properties of the CuO2 plane

For the CuO2 square lattice, as a parent system of high-Tc superconductors, a numerical study has suggested that the effective-spin model contains a large cyclic four-spin exchange interaction Jc. This paper investigates the effects of Jc upon magnetic Raman scattering and upon properties of the ground state by an exact numerical method mainly for a 16-site cluster. It is found that the main Raman peak with the B1g symmetry is shifted by 20% to the lower-energy side with a realistic magnitude for Jc, which is about one fourth the size of the nearest-neighbor exchange J. Accordingly a value of J extracted from analyses of experimental data becomes larger by 10% than that estimated with the use of the Heisenberg model. Furthermore the four-spin exchange enhances a shoulder due to multimagnon states at an energy of about 4J, and this result compares favorably with the experimental line shape. Detailed discussion is given on the effect of the four-spin exchange upon the ground-state properties such as the staggered magnetization, the ground-state energy, weight of various spin configurations, and the spin-spin correlation function.