Unusual Exchange Couplings and Intermediate Temperature Weyl State in Co 3 Sn 2 S 2

Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. Here, we report the magnetic exchange couplings of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green's function methods. ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ exhibits highly anisotropic magnon dispersions and linewidths below ${T}_{C}$, and paramagnetic excitations above ${T}_{C}$. The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor ``across-hexagon'' ${J}_{d}$ model. Our density functional theory calculations reveal that both the symmetry-allowed 120\ifmmode^\circ\else\textdegree\fi{} antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.