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# Topological spin excitations in a three-dimensional antiferromagnet

## Abstract

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 potential1,2,3,4. While topological band crossing in three dimensions was first studied for electrons in semimetals4,5,6,7,8,9,10, the underlying physical idea is not restricted to fermions11,12,13,14,15 and similar band structures of electromagnetic waves have been observed in artificial structures16. 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+ ions17. Further to previous works on this system17,18, we find that the Cu2+ 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 details15, 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 Z2-monopole charges15,19, 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.

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## Acknowledgements

We wish to thank F. Wang, G. Chen, O. Janson, X. Zhang, E. Motoyama and L. Fu for discussions and comments. The INS experiments were performed at the MLF, J-PARC, Japan, under a user programme (proposal nos 2016B0116 and 2017I0001). Work at the Institute of Physics, Chinese Academy of Sciences is supported by the Ministry of Science and Technology of China (grant no. 2016YFA0302400) and the National Natural Science Foundation of China (grant no. 11674370). Work at Peking University is supported by the National Natural Science Foundation of China (grant no. 11522429) and the Ministry of Science and Technology of China (grant nos 2018YFA0305602 and 2015CB921302).

## Author information

Authors

### Contributions

Y.L. conceived the research. L.W., C.L., C.F. and Y.L. designed the experiment. W.Y., C.L., L.W. and Y.D. prepared the sample. W.Y., C.L., S.X., K.I., K.K. and Y.L. performed the INS experiments. W.Y. and Y.L. analysed the experimental data. C.L., K.L. and C.F. performed the theoretical analyses. W.Y., C.L., L.W., C.F. and Y.L. wrote the paper with input from all co-authors.

### Corresponding authors

Correspondence to Chen Fang or Yuan Li.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

11 Figures, 1 Table, 4 References

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Reprints and Permissions

Yao, W., Li, C., Wang, L. et al. Topological spin excitations in a three-dimensional antiferromagnet. Nature Phys 14, 1011–1015 (2018). https://doi.org/10.1038/s41567-018-0213-x

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