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. Co_{3}Sn_{2}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 Co_{3}Sn_{2}S_{2} using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green's function methods. Co_{3}Sn_{2}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° 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 Co_{3}Sn_{2}S_{2} can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.