Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet with cyclic-exchange interaction

We study the effect of four-spin cyclic-exchange interactions on the magnetic properties of the spin-1/2 Heisenberg antiferromagnetic on a two-dimensional square lattice with the two-spin interactions between nearest and next-nearest neighbors. We found that the four-spin exchange competes with the effects of frustration and this competition leads to a very rich phase diagram. We use the standard spin-wave formalism, the perturbative expansions around various dimerized states and finite-cluster calculations to study the locations of different phases of the model. The phase diagram in the frustration-cyclic exchange plane involves two collinear phases [(,) and (0,)], three canted states, and two different dimerized configurations.