This study examines the anomalous Hall effect (AHE) in the Heusler series ${\mathrm{Mn}}_{3}Z$ ($Z$=Ga, Ge, Sn), with a particular emphasis on the manipulation of noncollinear antiferromagnetic structures to enhance the AHE. By employing density-functional theory and first-principles calculations, we demonstrate that the anomalous Hall conductivity is markedly responsive to electron filling. By strategically doping Ga into ${\mathrm{Mn}}_3\mathrm{Sn}$ and ${\mathrm{Mn}}_3\mathrm{Ge}$ in order to modulate the electron density, a significant increase in anomalous Hall conductivity (AHC) is achieved. It is noteworthy that a Ga:Sn ratio of 1:5 yields peak AHC values exceeding $700{\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$, while 3:7 Ga-Ge ratios can result in AHC values surpassing $600{\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$. A comparison between the virtual crystal approximation and supercell construction methods for doping has revealed consistent trends. The results of this study pave the way for optimizing the AHE in noncollinear antiferromagnetic materials.

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• Anomalous Hall effect
• Antiferromagnetism
• Berry curvature
• Spintronics
• Noncollinear magnets
• Weyl semimetal
• Density functional theory