Spin-polarized electron gas

Coupling-Constant Average for the Spin-Polarized Electron Gas. [Erratum Phys. Rev. B, 56,... 

In analogy to the coordinate scaling of Eqs. (59) - (61), this property is often called spin-scaling , and it can be used to construct an SDFT exchange functional from a given DFT exchange functional. In the context of the LSDA, von Barth and Hedin [89] wrote the exchange functional in terms of an interpolation between the unpolarized and fully polarized electron gas which by construction satisfies Eq. (99). Alternative interpolation procedures... 

The correlation energy of a uniform electron gas has been determined by Monte Carlo methods for a number of different densities. In order to use these results in DFT calculations, it is desirable to have a suitable analytic interpolation formula. This has been constructed by Vosko, Wilk and Nusair (VWN) and is in general considered to be a very accurate fit. It interpolates between die unpolarized ( = 0) and spin polarized (C = 1) limits by the following functional. 

Table II The essentialiy-exact PW92 exchange-correlation energy per electron (in hartree) in a spin-polarized = 1) uniform electron gas of density parameter Tj(in bohr), and the deviation (in hartree) of other approximations from PW92. (1 hartree = 27.21 eV = 627.5 kcal/mol.]...

Just as for the simple, spin compensated situation where pa(r) = pp(r) = j p(r), there are related expressions for the exchange and correlation energies per particle of the uniform electron gas characterized by p (r) pp(r), the so-called spin polarized case. The degree of spin polarization is often measured through the spin-polarization parameter... 

Let us first discuss a system which is traditional for optical pumping in the Kastler sense [106, 224, 226], namely an optically oriented alkali atom A (see Fig. 1.1) in a noble gas X buffer surrounding. It is important to take into account the fact that in alkali atoms, owing to hyperfine interaction, nuclear spins are also oriented. However, in a mixture of alkali vapor with a noble gas alkali dimers A2 which are in the 1SJ electronic ground state are always present. There exist two basic collisional mechanisms which lead to orientation transfer from the optically oriented (spin-polarized) atom A to the dimer A2 (a) creation and destruction of molecules in triple collisions A + A + X <—> A2 + X (6) exchange atom-dimer reaction... 

The spin transistor as represented in Fig. 34 is a vertical spin transistor. Figure 35 is a schematic picture of a lateral spin transistor as originally proposed by Datta and Das [179]. In this case, a iron emitter injects spins into a 2D electron gas. A Schottky gate can rotate the spin polarization by the Rashba effect, and another iron analyzer detects transmitted spin polarized current. 

The LDA or its spin-polarized generalization, the local spin density (LSD) approximation provides a means of folding exchange and correlation effects, calculated on the basis of the local behavior of a uniform electron gas, into a set of self-consistent Hartree-like equations which contain only local operators for the potential. This procedure is represented schematically in Fig. 1. 

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