Magnetic interaction localized approach

The intrinsic local nature of the interaction between two localized spin moments suggests the possibility to study the magnetic interactions in solids with a cluster model. In this approach, a small yet relevant piece is cut from the crystal and treated like a molecule. These bare clusters are only a reasonable choice in the case of molecular crystals, but otherwise nearly always too cmde a representation. Therefore it is necessary to account for the effect of the rest of the crystal especially when dealing with ionic or covalent lattices. Here, we will shortly review a few representative examples of the different approaches for improving the bare cluster model that find their basis in the theory of electron separability of McWeeny, the subsystem formulation of DFT of Cartona or the incremental scheme of Fulde and Stoll. 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

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