Employing a combination of first-principles calculations and an ab initio derived model Hamiltonian study, we investigate the electronic and magnetic properties of the rare-earth antimonides ${\mathrm{LaCrSb}}_3, {\mathrm{CeCrSb}}_3$, and ${\mathrm{NdCrSb}}_3$. Our findings indicate that the long-range ferromagnetic order in these metallic compounds originates from a kinetic energy-driven double exchange mechanism, first proposed in the context of double perovskite compound ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$. The calculated magnetic transition temperatures are in reasonable agreement with the measured values. The spin-orbit coupled band structure of the studied compounds reveals nontrivial topology, hosting multiple Weyl point crossings. The number of these crossings increases in moving from ${\mathrm{LaCrSb}}_3$ to ${\mathrm{CeCrSb}}_3$ to ${\mathrm{NdCrSb}}_3$, assisted by the lowering of the $5d$ states in nonzero $f$ rare-earth compounds. The calculated anomalous Hall conductivity captures experimentally observed large anomalous Hall conductivity in these compounds, and the trend between ${\mathrm{LaCrSb}}_3, {\mathrm{CeCrSb}}_3$, and ${\mathrm{NdCrSb}}_3$. Our study provides a microscopic understanding of the trend.

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• Anomalous Hall effect
• Berry curvature
• Magnetic interactions
• Topological materials
• Rare-earth alloys
• Rare-earth magnetic materials
• Density functional calculations