Chiral phase of the Heisenberg antiferromagnet with a triangular lattice

Abstract

In the presence of next-to-nearest-neighbor exchange interaction the classical ground state of the Heisenberg antiferromagnet with a triangular lattice in a wide domain of parameters has a four-sublattice structure. This ground state is highly degenerate: the only restriction for the spins on four sublattices is that their sum should be equal to zero. The accidental degeneracy is removed by fluctuations or nonbilinear interactions of spins. Fluctuations (quantum or thermodynamical) favor the collinear arrangement of spins, but a four-spin exchange interaction favors a nonplanar configuration that can be characterized by positive or negative chirality. In the presence of such an interaction the long-range order in chiralities will survive up to some finite temperature although the long-range order in spin variables will be destroyed by fluctuations at an arbitrarily low temperature.