Light-Tunable Giant Anomalous Hall Effect in the Flat-Band Magnetic Weyl Semimetal $\mathrm{AlFe_2O_4}$

Abstract

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 ($κ$) 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 $κ$, shortens the topological Fermi arcs, and drives a dramatic, quantitative suppression of the AHC, providing a practical blueprint for ultrafast, light-controlled topological transport.

Figures (4)

• Figure 1: Crystal structure and spin-polarized electronic properties of the inverse spinel $\mathrm{AlFe_2O_4}$. (a) Schematic of the $\mathrm{AlFe_2O_4}$ crystal lattice, with Al, Fe, and O atoms represented by purple, dark yellow, and red spheres, respectively. (b) Bulk Brillouin zone (BZ) and its projection onto the (010) surface, with high-symmetry points labeled. (c) First-principles electronic band structure (left panel) and the corresponding density of states (DOS, right panel) calculated without spin-orbit coupling (SOC). The spin-up and spin-down channels are denoted by red and blue curves, respectively. The system exhibits a half-metallic nature with fully spin-polarized quasi-flat bands near the Fermi level, which give rise to a sharp peak in the DOS.
• Figure 2: Topological electronic structure and anomalous Hall effect in $\mathrm{AlFe_2O_4}$ with SOC included. (a) Comparison of the band structure obtained from density functional theory (DFT, yellow solid curves) and the maximally localized Wannier function (MLWF) tight-binding model (blue dashed curves). The right panel shows the total DOS. (b) Magnified band dispersion along the $-K \leftrightarrow \Gamma \leftrightarrow K$ path, revealing the SOC-induced gap opening and the emergence of a single pair of Weyl nodes. The blue and yellow dots denote the Weyl nodes with chiral charges of $-1$ and $+1$, respectively. (c) Local density of states on the semi-infinite (010) surface. The bright red/yellow lines highlight the topological surface states connecting the projected Weyl nodes. (d) Constant-energy contour showing the Fermi arcs connecting the projected Weyl nodes of opposite chiralities on the (010) surface. (e) Calculated intrinsic anomalous Hall conductivity (AHC) as a function of energy. The solid red line represents the non-zero transverse component $\sigma_{xy}$, exhibiting a giant peak near the Fermi level, while the dashed black ($\sigma_{yz}$) and dotted blue ($\sigma_{zx}$) lines vanish due to symmetry constraints.
• Figure 3: Minimal tight-binding model and the microscopic origin of the tunable AHC. (a) Schematic of the symmetry-allowed effective lattice model on the pyrochlore sublattice (space group $Fd\bar{3}m$). The arrows indicate the considered hopping pathways, where $t_1$ represents the spin-independent nearest-neighbor (NN) hopping, and $t_2$, $t_3$, $t_4$ denote the SOC-induced spin-dependent hoppings. (b) Calculated bulk band structure of the effective model. The inset provides a magnified view of the band crossing along the $-K \leftrightarrow \Gamma \leftrightarrow K$ path, capturing the single pair of Weyl nodes. (c) Projected surface states derived from the minimal model, with the Weyl nodes marked by yellow ($+1$) and blue ($-1$) dots. (d) Evolution of the momentum separation $\kappa$ (in units of $2\pi/a$) between the Weyl nodes as a function of the NN hopping parameter $t_1$. (e) Dependence of the macroscopic AHC spectrum on $t_1$. Different colored curves correspond to varying magnitudes of $t_1$ (from $-0.24$ to $-0.16$), demonstrating that the AHC peak can be deterministically tuned by modulating the microscopic NN coupling.
• Figure 4: Floquet engineering of the macroscopic topological transport via circularly polarized light (CPL). (a) Schematic of the high-frequency CPL propagating along the $z$-axis (with vector potential $\boldsymbol{A}(t)$), which dynamically renormalizes the effective electronic couplings. (b) Momentum separation $\kappa$ (in units of $2\pi/a$) between Weyl nodes as a function of the dimensionless light intensity parameter $eA_0/\hbar$ (denoted as $A$ in the unit of $\text{\AA}^{-1}$). (c) Dynamic suppression of the AHC spectrum under varying light intensities. The different colored curves correspond to light intensities ranging from $A = 0.00$ to $0.10\ \text{\AA}^{-1}$. The two insets provide magnified views of the AHC evolution near the Fermi level ($E=0$) and at the primary peak ($E \approx 0.07\ \mathrm{eV}$), clearly illustrating the quantitative and controllable optical modulation of the macroscopic topological transport.