Magnon Topology in Chiral Crystals: Multifold Crossings and Nodal Planes

We investigate the topology of magnon excitations in magnets with chiral space groups. The presence of (magnetic) screw rotations leads to symmetry enforced Weyl points and nodal planes in the magnon band structure. In addition, there are multifold crossings pinned at high-symmetry points.We systematically analyze the band topology of these crossings and calculate their topological charges. In particular, we find that the magnon nodal planes carry a quantized topological charge similar to magnon Weyl points. Analogous to the protected spin currents on the surface of topological insulators, the topologically nontrivial magnon crossings result in protected surface modes of heat quanta. We propose several candidate materials and calculate their magnon band structures, topological invariants,and topologically protected surface modes. Further, we investigate the excitations of a quantum paramagnet on a one-dimensional ladder, and show that by applying an external magnetic field a topological phase transition is enforced. Because the triplon excitations of the ladder are gapped, fewer scattering channels are available and the topological exciations are potentially more robust than their spinwave counterparts.