  Band topology, or global wave-function structure that enforces novel
properties in the bulk and on the surface of crystalline materials, is
currently under intense investigations for both fundamental interest and its
technological promises. While band crossing of non-trivial topological nature
was first studied in three dimensions for electrons, the underlying physical
idea is not restricted to fermionic excitations. In fact, experiments have
confirmed the possibility to have topological band crossing of electromagnetic
waves in artificial structures. Fundamental bosonic excitations in real
crystals, however, have not been observed to exhibit the counterpart under
ambient pressure and magnetic field, where the difficulty is in part because
natural materials cannot be precisely engineered like artificial structures.
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. Beyond previous
understanding, we find that the material's spin lattice possesses a variety of
exchange interactions, with the interaction between the ninth-nearest
neighbours being as strong as that between the nearest neighbours. Although
theoretical analysis indicates that the presence of topological magnon band
crossing is independent of model details, Cu3TeO6 turns out to be highly
favourable for the experimental observation, as its optical magnons are
spectrally sharp and intense due to the highly interconnected spin network and
the large magnetic cell. The observed magnon band crossing generally has the
form of a special type of Z2-topological nodal lines that are yet to be found
in fermion systems, rendering magnon systems a fertile ground for exploring
novel band topology.
