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

2001; American Physical Society; Volume: 64; Issue: 1 Linguagem: Inglês

10.1103/physrevb.64.014416

1095-3795

Adeline Crépieux, P. Bruno,

Magnetic properties of thin films

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.