Towards the First Realization of Weyl Magnons in the Non-Coplanar Antiferromagnet MnTe$_2$
Using a combination of band representation analysis, inelastic neutron scattering (INS), magneto-Raman spectroscopy measurements, and linear spin wave theory, we establish that the non-coplanar antiferromagnet MnTe$_2$ is a tunable Weyl magnon material, hosting symmetry-protected topological nodal lines in its magnon band structure, protected by the the non-coplanar nature of the antiferromagnetic ordering, that transition into Weyl magnons upon the application of symmetry-breaking perturbations using an external magnetic field. By constructing a spin model that reproduces the observed INS magnon spectra and field-dependence of the Raman $Γ$-magnons, we directly probe the topological magnon nodal lines and observe their associated signature of non-trivial topology through the pseudo-spin winding of the scattering intensity in angular scans near the nodal lines. Finally, we discuss the emergence of Weyl magnons in the spectrum through an external magnetic field, and analyze the associated magnon thermal Hall effect allowed by the cubic-symmetry breaking and the associated magnon surface modes, shedding light on future in-field INS and thermal Hall experiments. This work establishes a clear magnonic analog to Weyl electrons, enabling further exploration of topological behavior in bosonic systems and highlighting the interplay between magnetic order and band topology in non-coplanar antiferromagnets.