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Understanding the magnetism and its possible correlations to the topologicalproperties has emerged as a forefront and difficult topic in studying magneticWeyl semimetals. Co$_{3}$Sn$_{2}$S$_{2}$ is a newly discovered magnetic Weylsemimetal with a kagome lattice of cobalt ions and has triggered intenseinterest for rich fantastic phenomena. Here, we report the magnetic exchangecouplings of Co$_{3}$Sn$_{2}$S$_{2}$ using inelastic neutron scattering and twodensity functional theory (DFT) based methods: constrained magnetism andmultiple-scattering Green's function methods. Co$_{3}$Sn$_{2}$S$_{2}$ exhibitshighly anisotropic magnon dispersions and linewidths below $T_{C}$, andparamagnetic excitations above $T_{C}$. The spin-wave spectra in theferromagnetic ground state is well described by the dominant third-neighbor"across-hexagon" $J_{d}$ model. Our density functional theory calculationsreveal that both the symmetry-allowed 120$^\circ$ antiferromagnetic orderssupport Weyl points in the intermediate temperature region, with distinctnumbers and the locations of Weyl points. Our study highlights the importantrole Co$_{3}$Sn$_{2}$S$_{2}$ can play in advancing our understanding of kagomephysics and exploring the interplay between magnetism and band topology.

Unusual exchange couplings and intermediate temperature Weyl state in Co3Sn2S2