Spin polarized band calculation

In Fig. 6, it is seen that the americium metallic volume at T = 0, p = 0, is well reproduced by spin-polarized band calculations. The same band-calculations predict the pressure p in which the transition from localized to itinerant behaviour occurs for americium. Here, we want to present the simplified Friedel-type model (Skriver, Anderson and Johansson ) by which the spin-polarized americium system is described and both transitions, i and ii, predicted. One word of caution the model, as well as the band calculations, do not account for the change in structure accompanying the transition, and which is an important fact in actinide metals, which will be discussed in the following... 

In order to calculate the magnetic moment it is necessary to perform spin polarized band calculations. The extension of the local density approximation to cover the spin polarized case has been made by von Barth and Hedin and Guimarsson and Lund-qvist ... 

In this section we will illustrate the gap concept by some explicit applications. We exclude applications to small molecules as well as spin-polarized band calculations, which fall outside the scope of this article. Several of the examples to be discussed are related to the concepts of Mott and Peierls gaps,21 28 but we will not discuss these very interesting aspects here. A number of—direct or indirect—applications on polyenes have been carried out these have been treated in another paper.29... 

The main motivation of the spin polarized band calculation was to study the spatial distribution or form factor of the conduction electron spin. This will be discussed more thoroughly in ch. 7, section 4. 

A cluster density of states of Niia, literally (not just formally) broadened by 0.2 eV, is presented in Figure 2a for the icosahedral geometry near the equilibrium structure. The general features are roughly similar to that derived from a spin-polarized band structure calculation of bulk nickel. Near the Fermi level a very high density of states of the minority spin is found, the d band of the... 

Finally, in Sect. E the optical and magnetic properties are considered. It is found experimentally that some Zintl phases are colored and in ternary systems the color changes continuously as a function of the composition. This change can be correlated to a shift in a maximum of the imaginary part 2 of the dielectric constant e, and 2 can be interpreted by electronic interband transitions ) The magnetic susceptibility and Knight shift are discussed on the basis of spin polarized band structure calculations . Spin and orbital contributions are also considered. 

In the present work electronic properties and the nature of chemical bonding in intermetallic B 32-type Zintl phases are discussed on the basis of relativistic and non-relativistic as well as spin polarized band structure calculations. 

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. 

Fig. 3. 18 Non-spin-polarized band structure (a), DOS (b) and Fe-Fe COHP curves (c) of a-Fe based on a TB-LMTO-ASA calculation and the LDA. The shaded region and dashed line in the DOS curve corresponds to the projected DOS of the Fe 4s orbitals and its integration, respectively. The Brillouin zone is also given.

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.

We observe that for the Fe-Co system a sim le spin polarized canonical model is able to reproduce qualitatively the results obtained by LMTO-CPA calculations. Despite the simplicity of this model the structural properties of the Fe-Co alloy are explained from simple band-filling arguments. 

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. 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

The charge density in a (110) plane for neutral H at the bond-center site in Si, as obtained from pseudopotential-density-functional calculations by Van de Walle et al. (1989), is shown in Fig. 7a. In the bond region most of the H-related charge is derived from levels buried in the valence band. It is also interesting to examine the spin density that results from a spin-polarized calculation, as described in Section II.2.d. The difference between spin-up and spin-down densities is displayed in Fig. 7b. It is clear... 

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. 

A last remark the LDA approach disregards spin-polarization phenomena. Taking into account this effect (already indicated by Koelling as the future direction of development for band calculations) has turned out to be of paramoimt importance at the centre of the actinide series. We shall examine it in the next section. 

One important point is whether narrow bands would display permanent magnetic moments and undergo magnetic collective phenomena. This depends clearly upon their bandwidth and will lead again to the problem localization vs itineracy. In band calculations, new ways have to be looked for, since the set of hypotheses examined previously, which hold for non-magnetic solids, must be corrected for spin-polarization. 

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. 

In americium, the occupation number is n = 6 (actually, n = 6.4 from band calculations ). If we assume full spin-polarization for this metal, then the 5 f bonding partial pressure is very small, and we may be reconducted to the lanthanide case for this metal also. 

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