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By V. E Cosslett
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Extra info for Introduction to Electron Optics: the production, propagation and focusing of electron beams
Sample text
In both bulk and thin film calculations this sum is an integral of an energy density over the k-space volume enclosed by the Fermi surface. The spin-orbit operator, because it is traceless, introduces a fundamental computational difficulty into this integration. To see the nature of the difficulty consider the simplest approach to the full-relativistic problem in which one starts with a solution of the scalar-relativistic problem and adds the spin-orbit interaction as a perturbation. This full problem is not solved by perturbation theory in practice but variationally in the basis of the eigenstates of the scalar problem.
The calculations do not agree on the subtle question of whether the majority surface state at M is occupied; Wimmer et al. find it just occupied in agreement with experiment, whereas the others find it just empty. However, it is clear that the calculations have essentially produced the same electronic structure for Ni {100}. 40, 41]. This provokes the speculation that a ferromagnetic overlayer on a relatively inert substrate might also exhibit a greatly enhanced moment. This was confirmed by Richter et al.
O. J. H. 64]. An indication as to the origin of this phenomenon has been found through measurements of the anisotropy energy density, K, as a function of the thickness of the Co layers, t. The anisotropy energy density varies approximately with the inverse of the Co layer thickness and can be expressed by the relation Kt ^ 2Ks + Ky t. 64], perpendicular magnetic anisotropy (PMA) will only occur if the interface anisotropy energy density Ks is positive and sufficiently large. Various explanations for the origin of the interface anisotropy have been put forward.