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 kagom\'{e}-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 $\mu\Omega$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$\times10^{-9}$ $\Omega$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, $\rho_{xx}$, of $R_{{\rm s}} \propto \rho_{xx}^{3.3}$. 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.