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Anomalous Hall transport in Mn$_{3}$Sn$_{0.5}$X$_{0.5}$C (X = Ge and Zn)

Mn-based antiperovskites that exhibit topological surface states show potential applications in spintronics, magnetoelectronics, and quantum devices owing to the interplay between magnetism and topology. In this family of compounds, Mn$3$SnC exhibits a concurrent ferromagnetic and antiferromagnetic ground state below $T \sim 285$ K, along with a Berry curvature driven anomalous Hall effect. Here, we report the anomalous Hall effect in Ge- and Zn-doped Mn$3$SnC compounds, namely Mn$3$Sn${0.5}$Ge${0.5}$C (MSGC) and Mn$3$Sn${0.5}$Zn${0.5}$C (MSZC). MSGC undergoes a paramagnetic to concurrent antiferromagnetic and ferromagnetic transition at $T_C \sim 300$ K, whereas MSZC exhibits a paramagnetic to ferromagnetic transition at $T_C \sim 240$ K, followed by a ferromagnetic to ferrimagnetic transition at $T_N \sim 170$ K. The electronic transport in these compounds is governed by electron-phonon and electron-magnon scattering and shows anomalous Hall resistivity $ρ^A_{xy}$. Our analysis indicates that the anomalous Hall effect arises from contributions of skew scattering and intrinsic Berry curvature mechanisms, with electron-phonon and electron-magnon scattering playing an important role in skew scattering at high temperatures. Ge and Zn doping in Mn$_3$SnC significantly enhances the anomalous Hall conductivity.