Topological Nodal Line and Weyl Magnons in the Non-Coplanar Antiferromagnet MnTe$_2$

Abstract

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$_2$ hosts symmetry-protected topological nodal lines, Weyl points, and a three-fold degeneracy in its magnon band structure. The non-coplanar nature of the antiferromagnetic ordering protects the topological magnon nodal lines that transition into Weyl magnons upon the application of specific symmetry-breaking perturbations using an external magnetic field. Zero-field INS measurements confirm the existence of the topological magnon nodal lines through the pseudo-spin winding of the scattering intensity in angular scans near the nodal lines, indicating the non-trivial topology of the magnon wavefunctions. This work establishes a clear magnonic analog to Weyl electrons, allowing further exploration of topological behavior in bosonic systems, and highlighting the rich interplay between magnetic order and band topology in non-coplanar antiferromagnets.

Figures (5)

• Figure 1: a) Crystal Structure of MnTe$_2$: blue and gold spheres represent the Mn and Te ions, respectively. Each Mn ion is bonded to six Te ions forming tilted corner-sharing octahedra, colored in blue gray. b) The magnetic structure of MnTe$_2$ highlighting the different $J$ couplings used for the LSWT fitting. The dotted lines indicates the magnetic unit cell and the coincident nuclear unit cell c) Inelastic neutron scattering measurements of MnTe$_2$ at $5$ K along the principal directions in reciprocal space, with the different directions merged together. d) Temperature dependent Raman spectra above and below $T_N$, collected in both parallel (VV) and cross (VH) polarization configurations. The two magnons are labeled $M_1$ and $M_2$ while the four phonons are labeled A-D in increasing energy, with symmetries noted in parentheses.
• Figure 2: Probing magnon band structure of MnTe$_2$. a,c) An overlay of the LWST fitting of the magnonic spectra over the experimental INS data along (a) the high symmetry directions in the Brillouin zone and a (c) low symmetry direction $[K\; 0.2+1.3K\; 0]$. Refer to Supplementary Figs. 8-11 for more detailed comparison between LSWT simulations and INS measurements. b) Magneto-Raman data collected in the Faraday configuration with the field applied along [0 0.7 1] parallel to the light propagation direction. d) Magneto-Raman data collected in the Voigt configuration, with the field $B\parallel$ [0 1 0.63] and the light propagation along [1 0 0].
• Figure 3: Topological Weyl magnonic excitations in MnTe$_2$. a) Schematic representation of the magnon band structure of MnTe$_2$ upon symmetry reduction from parent $\mathcal{MSG}$$Pa \bar{3}$ into the subgroup $P\bar{1}$. The lower part manifests the explicit magnon band irreps calculated using the obtained spin Hamiltonian. b-c) Demonstration of the calculated Chern numbers of the upper two bands over high-symmetry planes upon symmetry breaking, consistent with the $\mathcal{SI}$ predictions, thus requiring non-trivial bands to occur. d) Weyl points in k-space upon the application of a $14\;T$ magnetic field along the $[0\; 1\; 6]$ direction.
• Figure 4: Magnon nodal lines in unperturbed MnTe$_2$. Zero-field INS energy scans on the $k_z=0$ plane covering the energy range of the nodal lines, whose energy-momentum structure is calculated using LSWT on the right panel. Lowest energy of the nodal lines start to appear from $\sim 3.6$ meV at the zone center, and shift away from the zone center towards the $M(1/2,1/2,0)$ (and its symmetry-equivalent) points as energy increases. A white arrow on INS scans refers to one of the symmetry-related crossing points. Above the highest energy part of the nodal lines at $\sim 11.76$ meV, the crossing points between the iso-energy contours start to gap out, as evident in the INS scans above $12$ meV.
• Figure 5: INS intensity winding associated with the magnon nodal lines. (a) Magnon dispersion along the [H $-0.429$$1$] line that intersects the nodal lines at the ($-1.50$$0.429$$0$) $k$-points. (b-d) INS intensity integrated over a finite energy range of $2$ meV above (red) and below (blue) the energy of the crossing at ($-1.50$$0.429$$0$) as a function of angle $\alpha$ around the crossing point. Data points are annotated with error bars that illustrate one standard deviation of the intensity. The solid lines are a refined sinusoidal fit to demonstrate the bimodal intensity pattern. $k_x$ vs. $k_y$ plots, at $k_z=0$, centered on the nodal crossing ($-1.50$$0.429$$0$) demonstrating the energy dependence below (c) and above (d) the nodal crossing. The overlaid circles demonstrate the region of integration for the plot in (b) with the colors matching the below and above designation in (b). The white line in (c) indicates the starting orientation of $\alpha=0$ and the direction in which $\alpha$ increases.