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Dirac matters provide a platform for exploring the interplay of theircarriers with other quantum phenomena. Sr$_{1-x}$Mn$_{1-y}$Sb$_2$ has beenproposed to be a magnetic Weyl semimetal and provides an excellent platform tostudy the coupling between Weyl fermions and magnons. Here, we reportcomprehensive inelastic neutron scattering (INS) measurements on singlecrystals of Sr$_{1-x}$Mn$_{1-y}$Sb$_2$, which have been well characterized bymagnetization and magnetotransport measurements, both of which demonstrate thatthe material is a topologically nontrivial semimetal. The INS spectra clearlyshow a spin gap of $\sim6$ meV. The dispersion in the magnetic Mn layer extendsup to about 76 meV, while that between the layers has a narrow band width of 6meV. We find that the linear spin-wave theory using a Heisenberg spinHamiltonian can reproduce the experimental spectra with the followingparameters: a nearest-neighbor ($SJ_1\sim28.0$ meV) and next-nearest-neighborin-plane exchange interaction ($SJ_2\sim9.3$ meV) , interlayer exchangecoupling ($SJ_c\sim-0.1$ meV), and spin anisotropy constant ($SD\sim-0.07$meV). Despite the coexistence of Weyl fermions and magnons, we find no clearevidence that the magnetic dynamics are influenced by the Weyl fermions inSr$_{1-x}$Mn$_{1-y}$Sb$_2$, possibly because that the Weyl fermions and magnonsreside in the Sb and Mn layers separately, and the interlayer coupling is weakdue to the quasi-two-dimensional nature of the material, as also evident fromthe small $SJ_c$ of -0.1 meV.

Spin dynamics of a magnetic Weyl semimetal Sr$_{1-x}$Mn$_{1-y}$Sb$_2$