Magnetic interactions and excitations in SrMnSb$_2$

The magnetic interactions in the antiferromagnetic (AFM) Dirac semimetal candidate SrMnSb$_2$ are investigated using \textit{ab initio} linear response theory and inelastic neutron scattering (INS). Our calculations reveal that the first two nearest in-plane couplings ($J_1$ and $J_2$) are both AFM in nature, indicating a significant degree of spin frustration, which aligns with experimental observations. The orbital resolution of exchange interactions shows that $J_1$ and $J_2$ are dominated by direct and superexchange, respectively. In a broader context, a rigid-band model suggests that electron doping fills the minority spin channel and results in a decrease in the AFM coupling strength for both $J_1$ and $J_2$. To better compare with INS measurements, we calculate the spin wave spectra within a linear spin wave theory, utilizing the computed exchange parameters. Although the calculated spin wave spectra somewhat overestimate the magnon bandwidth, they exhibit overall good agreement with measurements from INS experiments.