Quasi-2D magnetism and origin of the Dirac semimetallic behavior in nonstoichiometric Sr$_{1-y}$Mn$_{1-z}$Sb$_{2}$ (y, z~$<$0.1)

Nonstoichiometric Sr$_{1-y}$Mn$_{1-z}$Sb$_{2}$ (y, z~$<$0.1) is known to exhibit a coexistence of magnetic order and the nontrivial semimetallic behavior related to Dirac or Weyl fermions. Here, we report inelastic neutron scattering analyses of the spin dynamics and density functional theory studies on the electronic properties of Sr$_{1-y}$Mn$_{1-z}$Sb$_{2}$. We observe a relatively large spin excitation gap $\approx$ 8.5 meV at 5 K, and the interlayer magnetic exchange constant only 2.8 \% of the dominant intralayer magnetic interaction, providing evidence that Sr$_{1-y}$Mn$_{1-z}$Sb$_{2}$ exhibits a quasi-2D magnetism. Using density functional theory, we find a strong influence of magnetic orders on the electronic band structure and the Dirac dispersions near the Fermi level along the Y-S direction in the presence of a ferromagnetic ordering. Our study unveils novel interplay between the magnetic order, magnetic transition, and electronic property in Sr$_{1-y}$Mn$_{1-z}$Sb$_{2}$, and opens new pathways to control the relativistic band structure through magnetism in ternary compounds.