Calculations, band theory spin densities

The observation of the CT gap should be contrasted with the predictions of band theory. Local-density-approximation (LDA) calculations performed for a number of undoped materials predict these systems to be metals since die Cu 3d and O 2p orbitals form a conduction band which is half-filled (for a review see Pickett 1989). The spin-polarized version of this band theory is not sufficiently accurate to yield an antiferromagnetic state of the insulating compound (Pickett et al. 1992). Thus LDA calculations fail to account for the two principal features of undoped materials the insulating gap and antiferromagnetic ordering. However, despite these serious problems these calculations do yield accurate values for the Fermi surface crossings as observed by angle-resolved photoemission (for a review see Pickett et al. 1992 see also ch. 201 of this Handbook). 

Magnetization can be calculated from first principles by band theory. Calculation methods are usually separated into (i) scalar-relativistic calculations and (ii) full-relativistic calculations. The scalar-relativistic calculations can predict the occurrence of ferromagnetism, the value of the spin moment, and several nonmagnetic properties. The fuU-relativistic calculations are additionally able to determine the magnetocrystalline anisotropy and the induced orbital moment. The most common approach uses the formalism of local density approximation (LDA) to the density functional theory (DFT) [10]. 

Earlier it was mentioned that the relativistic theory of electronic states in solids in many respects is identical to that of atoms. Since this is well described elsewhere, this section will only deal with some features of specific implementations of the theory in actual calculation methods used for solids, and the importance of relativistic effects — apart from those already discussed — will be illustrated by examples. Although Section 3 did refer to results of LMTO calculations, we did not describe how these included relativity. This section will deal with these items in the form of an overview, and the basic band structure calculations described relate to the density-functional theory [62,63]. Since magnetism is one of the most important solid state physics fields we shall discuss the simultaneous inclusion of spin-polarization and relativistic effects, in particular the spin-orbit coupling. In that context it appears that several of the materials where such effects are particularly large and interesting are those where electron... 

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