High-throughput Discovery of Topological Magnon Materials: Realization of Topological Weyl Magnons in MnTe₂.

To make reliable and systematic predictions about material realization of topological magnons has been a major challenge so far, due to the lack of neutron scattering data for most materials. In this work, we significantly advance the symmetry-based approach for identifying topological magnons through developing a fully automated algorithm, utilizing the theory of symmetry indicators, that enables a highly efficient and large-scale search for candidate materials hosting field-induced topological magnons without requiring input from their spin models. This progress not only streamlines the discovery process but also expands the scope of materials exploration beyond previous manual or traditional methods, offering a powerful tool for uncovering novel topological phases in magnetic systems. Performing a large-scale search over all 1649 magnetic materials in Bilbao Crystallographic Server with a commensurate magnetic order, we discover 387 candidate materials for topological magnons, significantly expanding the pool of topological magnon materials. We benchmark our findings on the noncollinear magnet MnTe₂, highlighting recent progress on the existence of topological magnons supported by magneto-Raman and inelastic neutron scattering measurements. Additionally, we discuss signatures of non-trivial bulk transport revealed by thermal Hall measurements.