Universal scaling law for chiral antiferromagnetism

The chiral antiferromagnetic (AFM) materials, which have been widely investigated due to their rich physics, such as non-zero Berry phase and topology, provide a platform for the development of antiferromagnetic spintronics. Here, we find two distinctive anomalous Hall effect (AHE) contributions in the chiral AFM Mn₃Pt, originating from a time-reversal symmetry breaking induced intrinsic mechanism and a skew scattering induced topological AHE due to an out-of-plane spin canting with respect to the Kagome plane. We propose a universal AHE scaling law to explain the AHE resistivity ( \({{\rho }}_{AH}\) ${\rho }_{AH}$ ) in this chiral magnet, with both a scalar spin chirality (SSC)-induced skew scattering topological AHE term, \({a}_{sk}\) $a_{sk}$ and non-collinear spin-texture induced intrinsic anomalous Hall term, \({{b}}_{{in}}\) $b_{in}$ . We found that \({{{a}}}_{{{sk}}}\) $a_{sk}$ and \({{{b}}}_{{{in}}}\) $b_{in}$ can be effectively modulated by the interfacial electron scattering, exhibiting a linear relation with the inverse film thickness. Moreover, the scaling law can explain the anomalous Hall effect in various chiral magnets and has far-reaching implications for chiral-based spintronics devices.