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

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

X-Ray Analysis of Oxygen-induced Perpendicular Magnetic Anisotropy in Pt/Co/AlOx trilayer

X-ray spectroscopy measurements have been performed on a series of Pt/Co/AlOx trilayers to investigate the role of Co oxidation in the perpendicular magnetic anisotropy of the Co/AlOx interface. It is observed that high temperature annealing modifies the magnetic properties of the Co layer, inducing an enhancement of the perpendicular magnetic anisotropy. The microscopic structural properties are analyzed via X-ray Absorption Spectroscopy, X-ray Magnetic Circular Dichroism and X-ray Photoelectron Spectroscopy measurements. It is shown that annealing enhances the amount of interfacial oxide, which may be at the origin of a strong perpendicular magnetic anisotropy