Ab-initio description of the magnetic shape anisotropy due to the Breit interaction

Abstract

A quantum-mechanical description of the magnetic shape anisotropy, that is usually ascribed to the classical magnetic dipole-dipole interaction, has been developed. This is achieved by including the Breit-interaction, that can be seen as an electronic current-current interaction in addition to the conventional Coulomb interaction, within fully relativistic band structure calculations. The major sources of the magnetic anisotropy, spin-orbit coupling and the Breit-interaction, are treated coherently this way. This seems to be especially important for layered systems for which often both sources contribute with opposite sign to the magnetic anisotropy energy. Applications to layered transition metal systems are presented to demonstrate the implications of this new approach in treating the magnetic shape anisotropy.PACS numbers: 31.15. 71.15.Rf, 75.30.Gw, Magnetic anisotropy is among the most important properties of magnetic materials in particular concerning their application in devices. When discussing the magnetic anisotropy energy of a material, denoting the difference in energy for two orientations of the magnetisation, an incoherent approach is used so far [1,2]. On the one hand side, the dependency of the electronic structure and the associated total energy on the orientation of the magnetisation, that is induced by spin-orbit coupling (SOC), is accounted for by corresponding relativistic band structure calculations. On the other hand, the additional shape anisotropy is ascribed to the anisotropy of the magnetic dipole-dipole coupling, that is treated in a classical way. This hybrid approach is used in particular when dealing with layered transition metal systems. The pioneering and successful theoretical work on magnetic surface films by Gay and Richter [3] was followed later on by many more investigations that benefited from the extension of standard band structure schemes to account simultaneously for the presence of spin-orbit coupling and spin-polarisation, i.e. magnetisation, in a numerically reliable way. Especially interesting in this context are investigations on systems showing a competition of the SOC and shape induced contributions to the magnetic anisotropy energy. This situation is frequently encountered for magnetic multi-layer or surface layer systems for which a flip of the magnetic easy axis from outof-plane to in-plane may be observed when the thickness of the magnetic layer is increased starting from a single mono-layer. In fact corresponding experimental findings could be reproduced by calculations based on the above mentioned hybrid scheme in the case of magnetic multilayers [4] as well as surface layer systems [5].In spite of the successful applications of this hybrid scheme in dealing with the magnetic anisotropy, one has to keep in mind that there is no real justification for its use. Furthermore, as there have been no coherent quantum mechanical investigations performed so far, there is no experience on the range of its applicability. It seems that the first steps towards a coheren...

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