Magnetic anisotropy description

Although the Heisenberg and Ising models have been intensively used in theoretical works, the description of real materials often requires more complicated Hamiltonians. For example when single-ion anisotropy is relevant, a finite magnetic anisotropy has to be considered. In this case, the corresponding Hamiltonian can be written ... 

A satisfactory description of the magnetic anisotropy in R2Fe14B requires a Hamiltonian which consists of crystal-field terms as well as of exchange terms. For a given rare earth atom this Hamiltonian may be expressed as... 

The influence of the internal rock structure on the magnetic properties creates magnetic anisotropy. A detailed description of the magnetic anisotropy of rocks was published by Tarling and Hrouda (1993). Siegesmtmd et al. (1993) have studied the fabric-controlled anisotropy of KTB (German Continental Deep Drilling Project) core samples. 

After an introduction to methods of electronic structure calculations, we review how recent trends translate into the description of magnetic nanostructures. Among the considered structures are nanowires, small particles, surfaces and interfaces, and multilayers, and emphasis is on magnetic properties such as moment and magnetization, interatomic exchange, and anisotropy. 

The description of nanomagnets requires new approaches. First, nanostructures are not periodic and tend to have large surface-to-volume ratios. Because of this the magnetization is not uniform across the nanostructure, local magnetic moments differ from site to site, exchange coupling varies throughout the nanostructure, and the anisotropy can be quite different from bulk or surface anisotropies. Second, it is hard to define properties in the similar fashion as in the bulk or as in case of molecules. 

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