Anomalous Hall Response Induced by Correlated Disorder in the Breathing Kagome Lattice Mn$_{3}$Sn

Macroscopic transport tensors are generally constrained by the average crystallographic and magnetic symmetries of a material. In the kagome antiferromagnetic Weyl semimetals Mn$_{3+δ}X$ ($X=$~Sn or Ge), previous studies showed that the anomalous Hall conductivity $σ_{yx}$ is forbidden by the average \hexsg{} structure and coplanar inverse-triangular magnetic order. Here we report that nearly stoichiometric Mn$_3$Sn nevertheless exhibits a finite $σ_{yx}$ with large hysteresis, together with enhanced $σ_{zx}$ and $σ_{yz}$, in the inverse-triangular phase below $T_{\mathrm{N1}}\approx 440~\mathrm{K}$, whereas all AHE components vanish in the amplitude-modulated conical phase below $T_{\mathrm{N2}}\approx 280~\mathrm{K}$. Total scattering and magnetic pair distribution function analysis reveal correlated orthorhombic distortions and noncoplanar Mn moments. First-principles calculations show that this coupled lattice-spin distortion activates the average symmetry forbidden $σ_{yx}$ within the inverse-triangular phase. Its disappearance below $T_{\mathrm{N2}}$ indicates that the correlated disorder must cooperate with a long-range inverse-triangular antiferromagnetic order capable of supporting Berry curvature. Our results establish correlated disorder as an active symmetry-breaking degree of freedom that enables topological transport inaccessible from the Bragg-average structure alone.