Energy band calculations spin polarized

The zero-field moment of 7.63/iB permits a direct estimate of the conduction electron polarization as 0.63/xb, since the anisotropy-induced zero point motion is negligible for Gd. This increased estimate of the conduction electron polarization is of particular significance for energy band calculations. Harmon and Freeman s spin-polarized APW calculation (1974) requires little adjustment to concur with the experimental result. 

Figure 2. The structural energy difference (a) and the magnetic moment (b) as a function of the occupation of the canonical d-band n corresponding to the Fe-Co alloy. The same lines as in Fig. 1 are used for the different structures. In (b) the concentration dependence of the Stoner exchange integral Id used for the spin-polarized canonical d-band model calculations is shown as a thin dashed line with the solid circles. The value of Id for pure Fe and Co, calculated from LSDA and scaled to canonical units, are also shown in (b) as solid squares.

In a previous work we showed that we could reproduce qualitativlely the LMTO-CPA results for the Fe-Co system within a simple spin polarized canonical band model. The structural properties of the Fe-Co alloy can thus be explained from the filling of the d-band. In that work we presented the results in canonical units and we could of course not do any quantitative comparisons. To proceed that work we have here done calculations based on the virtual crystal approximation (VGA). In this approximation each atom in the alloy has the same surrounding neighbours, it is thus not possible to distinguish between random and ordered alloys, but one may analyze the energy difference between different crystal structures. 

For H at T in Ge, Pickett et al. (1979) carried out empirical-pseudopotential supercell calculations. Their band structures showed a H-induced deep donor state more than 6 eV below the valence-band maximum in a non-self-consistent calculation. This binding energy was substantially reduced in a self-consistent calculation. However, lack of convergence and the use of empirical pseudopotentials cast doubt on the quantitative accuracy. More recent calculations (Denteneer et al., 1989b) using ab initio norm-conserving pseudopotentials have shown that H at T in Ge induces a level just below the valence-band maximum, very similar to the situation in Si. The arguments by Pickett et al. that a spin-polarized treatment would be essential (which would introduce a shift in the defect level of up to 0.5 Ry), have already been refuted in Section II.2.d. 

In Fig. 7 the results of the model for the cohesive energy are given, and compared with the experimental values and with the results of band calculations. The agreement is satisfactory (at least of the same order as for similar models for d-transition metals). For americium, the simple model yields too low a value, and one needs spin-polarized full band calculations (dashed curve in Fig. 7) to have agreement with the experimental value. 

DV-Xa molecular orbital calculation is demonstrated to be very efficient for theoretical analysis of the photoelectron and x-ray spectroscopies. For photoelectron spectroscopy, Slater s transition state calculation is very effective to give an accurate peak energy, taking account of the orbital relaxation effect. The more careful analysis including the spin-polarized and the relativistic effects substantially improves the theoretical results for the core level spectrum. By consideration of the photoionization cross section, better theoretical spectrum can be obtained for the valence band structure than the ordinary DOS spectrum. The realistic model cluster reproduce very well the valence state spectrum in details. 

The calculation of the ground-state energy of the Wigner electron crystal necessitates the self-consistent solution of the Slater-Kohn-Sham equations for the Bloch orbitals of a single fully occupied energy band, since there is one electron per unit cell and one is concerned with the spin-polarized state [45], This was accomplished by standard computational routines for energy band-... 

The question of alternative structure can be answered by electronic-structure theory, and it turns out that a quantitative answer is slightly more complicated because different magnetic properties are calculated for the [NaCl] and [ZnS] types. Nonetheless, non-spin-polarized band-structure calculations are quite sufficient to supply us with a correct qualitative picture. This has been derived using the TB-LMTO-ASA method and the LDA functional, and they give the correct lattice parameters with lowest energies for both structure types [267], just as for the case of CaO. 

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