Paper detail

Anomalous Hall Effect in Ferromagnetic Metals: Role of Phonons at Finite Temperature

The anomalous Hall effect in a multiband tight-binding model is numerically studied taking into account both elastic scattering by disorder and inelastic scattering by the electron-phonon interaction. The Hall conductivity is obtained as a function of temperature $T$, inelastic scattering rate $γ$, chemical potential $μ$, and impurity concentration $x_{\rm imp}$. We find that the new scaling law holds over a wide range of these parameters; $-σ_{xy}= (ασ_{xx0}^{-1} + βσ_{xx0}^{-2}) σ_{xx}^2 + b$, with $σ_{μν}$ ($σ_{μν0}$) being the conductivity tensor (with only elastic scattering), which corresponds to the recent experimental observation [Phys. Rev. Lett. {\bf 103} (2009) 087206]. The condition of this scaling is examined. Also, it is found that the intrinsic mechanism depends on temperature under a resonance condition.