Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation

Details Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation

2001-01-24

arxiv.org/abs/cond-mat/0101376v3

Phys. Rev. B 64, 014416 (2001)

Physics

Condensed Matter

Scientific paper

10.1103/PhysRevB.64.014416

A model to treat the anomalous Hall effect is developed. Based on the Kubo formalism and on the Dirac equation, this model allows the simultaneous calculation of the skew-scattering and side-jump contributions to the anomalous Hall conductivity. The continuity and the consistency with the weak-relativistic limit described by the Pauli Hamiltonian is shown. For both approaches, Dirac and Pauli, the Feynman 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 compound in the limit of weak-scattering and free-electrons approximation. Explicit expressions for the anomalous Hall conductivity for both skew-scattering and side-jump mechanisms are obtained. Within this model, the recently predicted ''spin Hall effect'' appears naturally.

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