Anomalous Hall effect revisited

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  • 24 January 2001
Abstract
A model to calculate the anomalous Hall effect is developed. Based on the Dirac equation and on the Kubo formalism, this model allows to calculate simultaneously the skew-scattering and side-jump contributions to the anomalous Hall resistivity. The continuity and the consistency with the weak-relativistic limit described by the Pauli Hamiltonian is shown. For both approaches, Dirac and Pauli, the Feymann diagrams, which lead to the skew-scattering and the side-jump contributions, are underlined. In order to illustrate this method, we apply it to a particular case: a ferromagnetic bulk alloy in the limit of weak disorder and free-electrons approximation. Explicit expressions of the anomalous Hall conductivity for both skew-scattering and side-jump mechanisms are obtained.

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