Order-from-disorder phenomena in Heisenberg antiferromagnets on a triangular lattice

We study the Heisenberg antiferromagnet on a triangular lattice with nearest- (J) and next-nearest- ({α}J) neighbor exchange interactions. For {α}>1/8, this system is known to have an accidental degeneracy at the classical level, which is lifted by quantum fluctuations (``order from disorder'' phenomena). We use large-S perturbation theory and confirm previous spin-wave and numerical observations that quantum fluctuations always select planar arrangement: There is thus no chiral symmetry breaking. When {α} increases, the conventional 120^∘{} N\'eel state first undergoes a first-order transition to a commensurate metamagnet at {α}{}1/8. This state then transforms by a continuous transition into an incommensurate state. We show that the fluctuation corrections do not diverge at the transition point. There is thus no disordered intermediate phase around the classical transition point.