Ground-state properties of the S=1/2 Heisenberg antiferromagnet on a triangular lattice

We study the S=1/2 Heisenberg antiferromagnet on a triangular lattice with both nearest-neighbor (${\mathit{J}}_1$) and next-to-nearest-neighbor (${\mathit{J}}_2$) couplings. We have performed a spin-wave analysis around the classical ground state. At large (${\mathit{J}}_2$/${\mathit{J}}_1$) the Néel state is destabilized and the system exhibits the ‘‘order from disorder’’ phenomenon with a threefold-degenerate ground state that spontaneously breaks the lattice rotational invariance. These results are in agreement with a Lanczos study of a 12-site lattice. For even larger values of ${\mathit{J}}_2$/${\mathit{J}}_1$ the spin-wave calculation shows the existence of a second transition to an incommensurate spiral. Thus, the previously suggested existence of chiral order in this model should be reanalyzed.