Noncoplanar magnetic order in low-carrier-density semiconductors provides a platform on which spin-charge coupling can reshape the electronic structure and induce nontrivial topological phases. Motivated by the recent discovery of the four-sublattice triple-$q$ order in the magnetic semiconductor GdGaI, we study an effective theory that couples a Ga $4p$ hole pocket at the $\mathrm{\Gamma }$ point to three Gd $5d$ electron pockets at the $M$ points through four exchange channels. For the antiferromagnetic umbrella state with zero net magnetization, the model hosts trivial ($C=0$) and $C=\pm 4$ Chern insulator phases separated by metallic regions; by deriving an analytical low-energy theory at the $\mathrm{\Gamma }$ point, we show that the topological phase boundary is described by two degenerate double-Weyl semimetals, naturally explaining the $\mathrm{\Delta }C=4$ jump in the Chern number. In addition, a nodal-line-like state pinned near the Fermi level emerges in the absence of the $p\text{−}d$ exchange coupling, which separates the $C=\pm 4$ phases for $\theta =arccos\left(\frac{1}{3}\right)$ into two. Tuning the canting angle by an external magnetic field drives an insulator-to-metal transition out of the Chern insulator phase while leaving the trivial insulator largely intact, and stabilizes an additional $C=\pm 2$ Chern insulator phase when the uniform-magnetization exchange couplings become appreciable. These results identify GdGaI and its sister compounds as highly tunable platforms for realizing topological phases and field-induced metal-insulator transitions in clean magnetic semiconductors.

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• Chern insulators
• Metal-insulator transition
• Weyl fermions
• Chiral magnets
• Triangular lattice