Giant Full-Space Anomalous Hall Effect Induced by Non-Coplanar Spin State in Mn-Rich Mn3Sn

Antiferromagnets are promising candidates for next-generation spintronic devices owing to their negligible stray fields and ultrafast spin dynamics. The noncollinear antiferromagnet $\mathrm{Mn}_{3}\mathrm{Sn}$ exhibits a large anomalous Hall effect (AHE). However, its specific noncollinear spin configuration leads to the forbiddance of the anomalous Hall conductivity from the (0001) basal plane, $\sigma_{(0001)}$, limiting practical applications. Here, using first-principles density functional theory, we demonstrate that Mn enrichment in $\mathrm{Mn}_{3}\mathrm{Sn}$ drives a magnetic transition from the coplanar $120^\circ$ spin configuration to a non-coplanar state with moments tilted toward the $c$-axis. This transition is primarily mediated by four-spin ring exchange interaction in the local triangular lattice, which breaks the time-reversal symmetry and generates a giant intrinsic anomalous Hall conductivity over the full three-dimensional space in $\mathrm{Mn}_{3}\mathrm{Sn}$. We predict that $\sigma_{(0001)}$ reaches as high as $\sim\!-468~\Omega^{-1}\cdot\mathrm{cm}^{-1}$, and an enhanced $\sigma_{(01\bar{1}0)}$ of $\sim\!-229~\Omega^{-1}\cdot\mathrm{cm}^{-1}$ is expected in light Mn self-doping of $\mathrm{Mn}_{3}\mathrm{Sn}$ ($\mathrm{Mn}_{3.125}\mathrm{Sn}_{0.875}$). Unlike previously reported mechanisms relying on external magnetic fields or strain, our approach exploits intrinsic compositional tuning to stabilize a non-coplanar magnetic ground state for realizing a strong full-space AHE in antiferromagnets, providing another viable pathway toward high-performance, low-power spintronic devices.