From Néel long-range order to spin liquids in the multiple-spin exchange model

The phase diagram of the multiple-spin exchange model on the triangular lattice is studied using exact diagonalizations. The two-spin (J₂) and four-spin (J₄) exchanges have been taken into account for 12-, 16-, 19-, 21-, 24-, and 27-site samples in the parameter region J₄=0--0.25 (for a fixed J₂=1). It is found that the three-sublattice N\'eel-ordered state built up by the pure two-spin exchange can be destroyed by the four-spin exchange, forming a spin-liquid state. The different data suggest that the phase diagram in this range of parameters exhibits two phases. The pure J₂ phase is a three-sublattice N\'eel-ordered phase; a small J₄ drives it into a spin-liquid state with a spin gap filled of a large number of singlets. This spin-liquid phase is not of the same generic kind as the phase studied by Misguich et al. [Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples that the spin-liquid phase, as the N\'eel-ordered phase, exhibits a magnetization plateau at $m=1/3,$ and for J₄>0.15 a second plateau at $m=1/2.$ These two plateaus are associated, respectively, with the semiclassical orderings uud and uuud.