Broken discrete symmetries in a frustrated honeycomb antiferromagnet

We study the magnetic phase diagram of the J sub(1)-J sub(2) Heisenberg antiferromagnet on a honeycomb lattice at the strongly frustrated point J sub(2)/J sub(1) = 1/2 using large-scale Monte Carlo simulations. At low temperatures we find three different field regimes, each characterized by different broken discrete symmetries. In low magnetic fields up to hc1/J sub(1) [approximate] 2.9 the Z sub(3) rotational lattice symmetry is spontaneously broken while a 1/2-magnetization plateau is stabilized around hc2/J sub(1) = 4. The collinear plateau state and the coplanar state in higher fields break the Z sub(4) translational symmetry and correspond to triple-q magnetic structures. The intermediate phase hc1 < h < hc2 has an interesting symmetry structure, breaking simultaneously the Z sub(3) and Z sub(4) symmetries. At much lower temperatures the spatial broken discrete symmetries coexist with the quasi-long-range order of the transverse spin components.