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

Abstract

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 N\'eel 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.