Topological spin excitations in a three-dimensional antiferromagnet

Band topology, namely the global wavefunction structure that gives rise to the properties observed in the bulk and on the surface of crystalline materials, is currently a topic under intense investigation for both fundamental interest and its technological potential(1-4). While topological band crossing in three dimensions was first studied for electrons in semimetals(4-10), the underlying physical idea is not restricted to fermions(11-15) and similar band structures of electromagnetic waves have been observed in artificial structures(16). Fundamental bosonic excitations in real crystals, however, have not been observed to exhibit any counterparts. Here we use inelastic neutron scattering to reveal the presence of topological spin excitations (magnons) in a three-dimensional antiferromagnet, Cu3TeO6, which features a unique lattice of magnetic spin-1/2 Cu2+ ions(17). Further to previous works on this system(17,18), we find that the Cu(2+ )spins interact over a variety of distances, with the ninth-nearest-neighbour interaction being particularly strong. While the presence of topological magnon band crossing is independent of model details's, the far-reaching interactions suppress quantum fluctuations and make the magnon signals sharp and intense. Using accurate measurement and calculation, we visualize two magnon bands that cross at Dirac points protected by (approximate) U(1) spin-rotation symmetry. As a limiting case of topological nodal lines with Z(2)-monopole charges(15,19), these Dirac points are new to the family of experimentally confirmed topological band structures. Our results render magnon systems a fertile ground for exploring novel band topology with neutron scattering, along with distinct observables in other related experiments.