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Giant anomalous Hall resistivity of the room temperature ferromagnet Fe3Sn2 - a frustrated metal with the kagome-bilayer structure

We have investigated magnetic and transport properties of the {\it kagomé-bilayer} ferromagnet Fe$_{3}$Sn$_{2}$. A soft ferromagnetism and a large anomalous Hall effect are observed. The saturated Hall resistivity of Fe$_{3}$Sn$_{2}$ is 3.2 $μΩ$cm at 300 K, which is almost 20 times higher than that of typical itinerant-ferromagnets such as Fe and Ni. The anomalous Hall coefficient $R_{\rm s}$ is 6.7$\times10^{-9}$ $Ω$cm/G at 300 K, which is three orders of magnitude larger than that of pure Fe. $R_{\rm s}$ obeys an unconventional scaling to the longitudinal resistivity, $ρ_{xx}$, of $R_{\rm s} \propto ρ_{xx}^{3.3}$. Such a relationship cannot be explained by the skew and/or side-jump mechanisms and indicates that the origin of the anomalous Hall effect in the frustrated magnet Fe$_{3}$Sn$_{2}$ is indeed extraordinary.