Light-Tunable Giant Anomalous Hall Effect in the Flat-Band Magnetic Weyl Semimetal $\mathrm{AlFe_2O_4}$
Achieving a giant anomalous Hall effect (AHE) and enabling its effective tuning are fundamental goals for topological spintronics. Magnetic Weyl semimetals hosting flat bands offer a promising route to maximize the AHE. However, while theoretical models are well-established, realistic material candidates remain scarce. Since the intrinsic anomalous Hall conductivity (AHC) is topologically dictated by the momentum separation ($\kappa$) between Weyl nodes, actively manipulating remains a key challenge. Here, through comprehensive first-principles calculations, we establish the inverse spinel $\mathrm{AlFe_2O_4}$ as a realistic ferromagnetic half-metallic platform integrating three-dimensional flat bands and Weyl physics. Spin-orbit coupling induces a single pair of Weyl nodes, yielding a giant intrinsic AHC of $398\ \mathrm{S}\cdot\mathrm{cm}^{-1}$. By constructing a symmetry-constrained tight-binding model, we uncover a deterministic relationship between microscopic electronic couplings and the macroscopic AHE. Exploiting this via Floquet engineering with circularly polarized light, we demonstrate that the effective couplings are dynamically suppressed. This optical modulation controllably enlarges $\kappa$, shortens the topological Fermi arcs, and drives a dramatic, quantitative suppression of the AHC, providing a practical blueprint for ultrafast, light-controlled topological transport.