Field-tunable Weyl points and large anomalous Hall effects in degenerate magnetic semiconductor EuMg$_2$Bi$_2$

Magnets, with topologically-nontrivial Dirac/Weyl points, have recently attracted significant attention owing to the unconventional physical properties, such as large anomalous Hall effects. However, they typically have a high carrier density and complicated band structure near the Fermi energy. In this study, we report degenerate magnetic semiconductor EuMg$_2$Bi$_2$, which exhibits a single valley at the $\Gamma$ point, where the field-tunable Weyl points form via the magnetic exchange interaction with the local Eu spins. By the high-field measurements on high-quality single crystals, we observed the quantum oscillations in resistivity, elastic constant, and surface impedance, which enabled us to determine the position of the Fermi energy. In combination with the first-principles calculation, we revealed that the Weyl points are located in the vicinity of the Fermi energy when the Eu spins are fully polarized. Furthermore, we observed large anomalous Hall effect (Hall angle $\Theta_{\mathrm{AH}}\sim0.07$) in the forced ferromagnetic phase, which is consistent with this field variation of band structure.