Electronic band structure spin-polarized

It is important to recognize the solid-state counterpart of the above observations. Consider a one-dimensional (ID) chain with one electron and one orbital per site (Fig. 26.5a). If electron-electron repulsion is neglected, the levels of the bottom half of the band are each doubly filled, thereby leading to a metallic state (Fig. 26.5b). Non-spin-polarized electronic band structure calculations predict that a system with a half-filled... 

Electronic structures of crystalline solids are mostly calculated on the basis of DFT. In this approach an open-shell system is described by spin polarized electronic band structures, in which the up-spin and down-spin bands are allowed to have different orbital... 

There are three main effects of relativity on the electronic (band) structure (i) scalar-relativistic shift of bands, frequently connected with a considerable change of the band width in comparison with the related non-relativistic calculation (ii) spin-orbit (s-o) splitting of degenerate band states, most notably in the vicinity of high-symmetry points in fe-space (iii) in combination with spin polarization that breaks the time-inversion symmetry, s-o coupling may reduce the crystal symmetry. 

Fig. 8. Electronic band structure of spin polarized fee Ni obtained by assuming a reduced velocity of light, c = 68.5 a.u., in the RFPLO method. The magnetic moment points along (001). All symmetry-determined degeneracies are lifted by spin-orbit interaction.

Fig. 9. Electronic band structure of spin polarized fee Ni. The majority spin character is indicated by the thickness of the lines. The calculation was carried out with RFPLO in LSDA, Perdew-Wang 92 [25].

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 electronic state calculations of transition metal clusters have been carried out to study the basic electronic properties of these elements by the use of DV-Xa molecular orbital method. It is found that the covalent bonding between neighboring atoms, namely the short range chemical interaction is very important to determine the valence band structure of transition element. The spin polarization in the transition metal cluster has been investigated and the mechanism of the magnetic interaction between the atomic spins has been interpreted by means of the spin polarized molecular orbital description. For heavy elements like 5d transition metals, the relativistic effects are found to be very important even in the valence electronic state. 

Since many experimental studies of 7-Fe were performed for 7-Fe particles in a Cu matrix (or Cu alloy, including Cu-Al) [113], [114], it is important to probe the electronic structure of the particle-matrix systems. Embedded-cluster methods are ideally taylored to treat small particles of a metal in a host matrix, a system that would require a very large supercell in band-structure calculations. DV calculations were performed for the 14-atom Fe particle in copper shown in Fig. 21 [118]. Spin-density contour maps were obtained to assess the polarization of the Cu matrix by the coherent magnetic 7-Fe particle. Examples are given in Figs. 22 and 23 for a Fe particle in Cu and 7-Fe in Cu with two substitutional Al. If the matrix is a Cu-Al alloy, this element is known to penetrate the Fe particle [114]. 

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. 

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