Magnets, with topologically nontrivial Dirac/Weyl points, have recently attracted significant attention owing to their unconventional physical properties, such as a large anomalous Hall effect. However, they typically have a high carrier density and a complicated band structure near the Fermi energy. In this Letter, we report a degenerate magnetic semiconductor ${\mathrm{EuMg}}_2{\mathrm{Bi}}_2$, which exhibits a single valley at the $\mathrm{\Gamma }$ point, where field-tunable Weyl points form via a magnetic exchange interaction with the local Eu spins. By the high-field measurements on high-quality single crystals, we observed quantum oscillations in the resistivity, elastic constant, and surface impedance, which enabled us to determine the position of the Fermi energy $E_F$. In combination with a first-principles calculation, we revealed that the Weyl points are located in the vicinity of $E_F$ when the Eu spins are fully polarized, leading to a peak of energy-dependent anomalous Hall conductivity due to the Berry curvature. Accordingly, in the forced ferromagnetic phase, we observed a large anomalous Hall effect (Hall angle ${\mathrm{\Theta }}_{\mathrm{AH}}\sim 0.07$) qualitatively consistent with the calculation, which demonstrates a marked impact of the Weyl points in the simple band structure.

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• Anomalous Hall effect
• Electrical conductivity
• Fermi surface
• First-principles calculations
• Hall effect
• Magnetic interactions
• Magnetic order
• Magnetoresistance
• Magnetotransport
• Shubnikov-de Haas effect
• Spin-orbit coupling
• Topological Hall effect
• Topological materials
• Transport phenomena
• de Haas-van Alphen effect