Abnormal scaling of the anomalous Hall effect in noncollinear antiferromagnetic metals from two-center scattering

The anomalous Hall effect is generally treated to originate from the Berry curvature of the band structure and scattering of the impurities, which is mainly attributed to the skew scattering and side jump for a single scattering source. In this Letter, using a first-principles-based scattering wave-function approach, we find an abnormal scaling law of the anomalous Hall effect in $L{1}₂$-type ${\mathrm{Mn}}₃X$ ($X=\text{Ir}$, Pt, Rh). Different from current conventional skew scattering, side jump, and Berry curvature contributions, this abnormal scaling law is demonstrated to come from a two-center scattering (TCS) contribution. Moreover, the corresponding anomalous Hall conductivity can be as large as ${\ensuremath{\sigma}}^{\mathrm{H}}\ensuremath{\simeq}5\ifmmode\times\else\texttimes\fi{}{10}⁴\phantom{\rule{0.28em}{0ex}}{(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$ in ${L1}₂$-type ${\mathrm{Mn}}₃\mathrm{Ir}$ at low temperature, which is two orders of magnitude larger than the current Berry curvature calculations, indicating that the TCS contribution dominates the anomalous Hall effect in noncollinear antiferromagnetic metals.