Topological magnon bands in antiferromagnetic systems with honeycomb lattice

We present the topological property of magnon bands in the collinear magnetic orders for the antiferromagnetic honeycomb lattice. We investigated the linear spin waves of zigzag and stripy phases. Berry curvature and symmetry constraints on magnon band structure are identified. For both zigzag and stripy phases, we found that spatial mirror symmetry protects gapless points in the magnon bands, which can be removed by additional Dzyaloshinskii-Moriya (DM) term. In the zigzag phase, a non-symmorphic symmetry gives rise to two-(four-)degeneracy at the zone boundary with (without) spin anisotropy, preventing the disentanglement of the magnon bands. In contrast, the magnon bands of the stripy phase can be disentangled with a finite DM term, leaving each band with a non-zero Chern number. We have also studied the spin Nernst property. Our study establishes the existence of the non-trivial magnon band topology for all observed collinear antiferromagnetic honeycomb lattice in the presence of the DM term.