Effect of Electron-Phonon Scattering on the Anomalous Hall Conductivity of Fe${}_3$Sn: A Kagome Ferromagnetic Metal

We report on magnetic and magnetotransport studies of a Kagome ferromagnetic metal, Fe${}_3$Sn. Our studies reveal a large anomalous Hall conductivity (${\sigma }_{zx}$) in this system, mainly contributed by temperature independent intrinsic Hall conductivity (${\sigma }_{zx}^{int}$=485$\pm$60 S/cm) and temperature dependent extrinsic Hall conductivity (${\sigma }_{zx}^{ext}$) due to skew-scattering. Although ${\sigma }_{zx}^{ext}$ value is large and almost equivalent to the intrinsic Hall conductivity at low temperatures, it drastically decreases with increasing temperature, following the relation ${\sigma }_{zx}^{ext}=\frac{{\sigma }_{zx0}^{ext}}{(aT+1{)}^2}$, under the influence of electron-phonon scattering. The presence of electron-phonon scattering in this system is also confirmed by the linear dependence of longitudinal electrical resistivity at higher temperatures [$\rho (T)\propto T$]. We further find that Fe${}_3$Sn is a soft ferromagnet with an easy-axis of magnetization lying in the $ab$ plane of the crystal with magnetocrystalline anisotropy energy density as large as 1.02 $\times$ 10${}^6$