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 $\mu \mathrm{\Omega }$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 $R_{\mathrm{s}}$ is 6.7$\times {10}^{-9}$ $\mathrm{\Omega }$cm/G at 300 K, which is three orders of magnitude larger than that of pure Fe. $R_{\mathrm{s}}$ obeys an unconventional scaling to the longitudinal resistivity, ${\rho }_{xx}$, of $R_{\mathrm{s}}\propto {\rho }_{xx}^{3.3}$. 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.