Local spin polarization

Fourth, so far we have considered only spin-unpolarized systems, i.e., we have assumed that the local spin polarization... 

The muffin-tin potential around each atom in the unit cell has been calculated in the framework of the Local-Spin-Density-Approximation using the ASW method. The ASW method uses the atomic sphere approximation (ASA), i.e. for each atom a sphere radius is chosen such that the sum of the volumes of all the overlapping spheres equals the unit cell volume. The calculation yields the expected ferromagnetic coupling between Cr and Ni. From the self-consistent spin polarized DOS, partial and total magnetic moment per formula unit can be computed. The calculated total magnetic moment is 5.2 pg in agreement with the experimental value (5.3 0.1 e calculations presented here have been performed... 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

Using local spin density functional (LSDF) theory, we obtain 70 kcal/mole for the rotational barrier of the ethylene molecule (35). In these calculations, we use the equivalent of a double-zeta+polarization basis set, i.e. for C two 2s functions. 

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. 

In a similar fashion the bonding in H2 might be formally regarded as a complementary pair of one-electron donor-acceptor interactions, one in the ot (spin up ) and the other in the 3 (spin down ) spin set.8 In the long-range diradical or spin-polarized portion of the potential-energy curve, the electrons of ot and (3 spin are localized on opposite atoms (say, at on HA and 3 on HB), in accordance with the asymptotic dissociation into neutral atoms. However as R diminishes, the ot electron begins to delocalize into the vacant lsB(a) spin-orbital on HB, while (3 simultaneously delocalizes into Isa on HA, until the ot and (3 occupancies on each atom become equalized near R = 1.4 A, as shown in Fig. 3.3. These one-electron delocalizations are formally very similar to the two-electron ( dative ) delocalizations discussed in Chapter 2, and they culminate as before (cf. Fig. 2.9) in an ionic-covalent transition to a completely delocalized two-center spin distribution at... 

Von Barth, U. and Hedin, L. 1972. A local exchange-correlation potential for the spin polarized case I. J. Phys. C Solid State Phys. 5 1629-1642. 

Figure 8. Calculated spin polarization density map in a Co/Cr—O—Li plane in LiCri/gCoy/gOz from DFT calculations."pj-ie positions of the Cr, Co, Li, and O ions are indicated. Li(l) has a Cr ion as its second cation coordination shell, while Li(2) has a Cr + ion in its first cation coordination shell. The Li spectra of LiCr/ioi-/32 x= 0.05 and 0.1) are shown along with the assignments of resonances corresponding to Li(l) and Li(2) local environments.

Various reasons have been advanced for the relative accuracy of spin-polarized Kohn-Sham calculations based on local (spin) density approximations for E c- However, two very favourable aspects of this procedure are clearly operative. First, the Kohn-Sham orbitals control the physical class of density functions which are allowed (in contrast, for example, to simpler Thomas-Fermi theories). Second, local density approximations for are mild-mannered,... 

The interplay between the local Pb polarization and B-site ions may be described by a simple model. As discussed above the magnitude of the local off-centering of Pb " ions is always about 0.5 A, and does not depend on the environment. Thus it could be described as a pseudo-spin, and justifies the pseudo-spin model with the dipolar-dipolar interaction and the local anisotropy energy ... 

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. 

Brooks and Johansson , by calculating I and AE have been able to show that these curves are very much affected by the spin-polarization energy AE, which, in fact, appears as the most important contribution in cohesion for actinide elements in which the beginning of localization of 5 f orbitals occurs (at the half-filling of the 5 f" shell) and for which spin-polarization plays a major role (see Chaps. C and F). 

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