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Owing to the geometrical frustration, Mn$_3 $Sn exhibits a 120$^{\circ}$in-plane triangular antiferromagnetic (AFM) order with a large anomalous Halleffect (AHE). Here, we present a combined theoretical and experimental study todemonstrate that the in-plane AFM structure in Mn$_3 $Sn can be significantlymodified to a tunable noncoplanar magnetic state by suitable electron doping.With the help of Density Functional Theory calculations we show that thepresence of higher-order exchange interactions in the system leads to thestabilization of the noncoplanar magnetic ground state, which is furtherestablished by neutron diffraction study in the Fe-doped Mn$_3 $Sn sample.Interestingly, we find a large scalar spin chirality (SSC) induced topologicalAHE that can be significantly tuned with the degree of non-coplanarity. Wecarry out 60~T magnetic and Hall resistivity measurements to demonstrate thecontribution of SSC to the observed AHE. We also illustrate a simultaneousmanipulation of dual order in the system, where the AHE arising from thein-plane 120$^{\circ}$ triangular AFM order can switch its sign withoutaffecting the AHE generated by the SSC. The present study opens up a newdirection to explore novel quantum phenomena associated with the coexistence ofmultiple orders.

Higher order exchange driven noncoplanar magnetic state and large anomalous Hall effects in electron doped kagome magnet Mn$_3$Sn