  Co$_{3}$Sn$_{2}$S$_{2}$ is a newly discovered magnetic Weyl semimetal with a
kagome lattice of cobalt ions that exhibits tunable magnetic orderings coupled
to quantum transport properties. Determination of the magnetic interactions in
the ground state is crucial to understanding the physical properties. Here, we
report the magnetic excitations and exchange couplings of
Co$_{3}$Sn$_{2}$S$_{2}$ determined using inelastic neutron scattering in
conjunction with 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 revealed that both the symmetry-allowed different
120$^\circ$ antiferromagnetic orders support Weyl points in the higher
temperature region, with distinct number and the location 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.
