Ground state of a spin system with two- and four-spin exchange interactions on the triangular lattice

We study a spin system with both two- and four-spin exchange interactions on the triangular lattice as a possible model for the nuclear magnetism of solid He-3 layers adsorbed on grafoil, The ground state is analyzed by the use of the mean-field approximation, It is shown that the four-sublattice state is favored by introduction of the four-spin exchange interaction. A possible phase transition at a finite temperature into a phase with the scalar chirality is predicted. Application of a magnetic field is shown to cause a variety of phase transitions.