Half-magnetization plateau in a Heisenberg antiferromagnet on a triangular lattice

Abstract: We present the phase diagram in a magnetic field of a 2D isotropic Heisenberg antiferromagnet on a triangular lattice. We consider spin-$S$ model with nearest-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) interactions. We focus on the range of $1/8<J_2/J_1<1$, where the ordered states are different from those in the model with only nearest neighbor exchange. A classical ground state in this range has four sublattices and is infinitely degenerate in any field. The actual order is then determined by quantum fluctuations via "order from disorder" phenomenon. We argue that the phase diagram is rich due to competition between competing four-sublattice quantum states which break either $\mathbb{Z}_3$ orientational symmetry or $\mathbb{Z}_4$ sublattice symmetry. At small and high fields, the ground state is a $\mathbb{Z}_3$-breaking canted stripe state, but at intermediate fields the ordered states break $\mathbb{Z}_4$ sublattice symmetry. The most noticeable of such states is "three up, one down" state in which spins in three sublattices are directed along the field and in one sublattice opposite to the field. Such a state breaks no continuous symmetry and has gapped excitations. As the consequence, magnetization has a plateau at exactly one half of the saturation value. We identify gapless states, which border the "three up, one down" state and discuss the transitions between these states and the canted stripe state.