# Scattering-Free Nature of Intrinsic Anomalous Hall Current

## Abstract

First, we investigate the intrinsic AHE which is related with Berry-phase. In contrast to the extrinsic mechanisms, an intrinsic AHE induced by the Berry phase is, in principle, not affected by the scattering. Experimentally, the relation that \(\rho _{yx} \propto \rho _{xx}^{\ 2}\) (namely, Hall conductivity \(\sigma _{xy} = \rho _{yx}/\rho _{xx}^{\ 2}\) is independent of \(\rho _{xx}\)) is identified in some materials and is thought to be the evidence of the dissipationless nature of anomalous Hall current (C. Kooi, Phys. Rev. **95**, 843 (1954), W-L. Lee, S. Watauchi, V.L. Miller, R.J. Cava, and N.P. Ong, Science **303**, 1647 (2004)). Nevertheless, the same \(\rho _{xx}\) dependence of \(\rho _{yx}\) is also expected for the side jump mechanism. In addition, the Hall conductivity may show the nontrivial \(T\)- or doping-dependence because of its high sensitivity to the position of the chemical potential in the electronic band structure. Another way to examine the origin and nature of the AHE is thus highly desired. Here, we take the approach to this problem in terms of the comparative study on the charge and heat anomalous Hall currents. Since the Lorenz ratio for the anomalous Hall current (\(L_{xy}^{A}\)) is sensitive to the inelastic scattering, the scattering-free (dissipationless) nature of the intrinsic anomalous Hall current manifests in the temperature dependence of \(L_{xy}^{A}\). Moreover, we investigate in the second section to what extent the scattering-free nature is robust against the scattering strength by changing the doping concentration in Ni, Fe, or Co.

## Keywords

Anomalous Hall effect Berry phase of electrons Spin-orbit interaction Dissipationless electronic current Itinerant ferromagnet## References

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