Ionic crystals magnetic interactions

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 systems would be particularly interesting to study if single crystals were available, since lower-dimensional materials are rare in 5f systems. All the experiments so far, have been performed on polycrystalline samples. Reorientations of the moments are relatively rare in actinide magnetic structures. This is because the anisotropy is usually enormous (see sect. 4.7 below), especially in intermetallics, and in all cases determines the easy-moment direction. In ionic systems, in which the hybridization between f and plane-wave (conduction-electron) state is absent, the moment directions are determined by an interplay between the exchange and crystal-field interactions, as is found in lanthanide systems. Clearly this is the case in the above trihalides. 

As for the valence band, the picture is relatively complicated. Considering a single hole near the top of the Fg valence band (for zinc blende crystal structure) and the magnetic ion with five d orbitals occupied by N electrons, the Hamiltonian that is applicable would have ionic, crystal, and hybridization components. The p-d hybridization mediated kinetic exchange depends on the filling of only the orbitals, not all the one-electron d-orbitals of the magnetic ion. The spin-dependent part of the exchange Hamiltonian for interaction between the Fg valence band p-like electrons and all the three d-orbitals occupied by one electron can be described as... 

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