# Analyse:Ym/Fragment 016 23

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 Typus KomplettPlagiat Bearbeiter Hindemith Gesichtet
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Quelle: Kurz 2000
Seite(n): 12, Zeilen: 9 ff.
2.2 Spin Density Functional Theory

In order to describe magnetic effects the density functional theory has to be extended to the case of spin polarized electrons. This is important for systems that posses non-zero ground state magnetization, which is the case for most atoms, magnetic solids and surfaces and electronic systems exposed to an external magnetic field. The necessary extension to the Hohenberg-Kohn theory can be formulated replacing the electron density by the electron density plus the magnetization density as fundamental variables. In this case, the variational principle becomes

$E[n(\mathbf{r}),\mathbf{m}(\mathbf{r})]\geq E[n_0(\mathbf{r}),\mathbf{m}_0(\mathbf{r})]$. (2.16)

An alternative, but completely equivalent, formulation can be obtained using a four component density matrix ραβ instead of n(r) and m(r) [117].

[117] U. von Barth and L. Hedin. A local exchange-correlation potential for the spin polarized case: I. J. Phys. C, 5:1629, 1972.

2.3 Spin Density Functional Theory

In order to describe magnetic effects the density functional theory has to be extended to the case of spin polarized electrons. This is important for systems that posses non-zero ground state magnetization, which is the case for most atoms, magnetic solids and surfaces and electronic systems exposed to an external magnetic field. The necessary extension to the Hohenberg-Kohn theory can be formulated replacing the electron density by the electron density plus the magnetization density as fundamental variables. In this case, the variational principle becomes

$E[n(\mathbf{r}),\mathbf{m}(\mathbf{r})]\geq E[n_0(\mathbf{r}),\mathbf{m}_0(\mathbf{r})]$. (2.15)

An alternative, but completely equivalent, formulation can be obtained using a four component density matrix ραβ instead of n(r) and m(r) [vBH72, Küb95].

[vBH72] U. von Barth and L. Hedin. A local exchange-correlation potential for the spin polarized case: I. J. Phys. C., 5:1629, 1972.

[Küb95] J. Kübler. Derivation of the single-particle schrödinger equation: Density and spin-density functional theory and the magnetic susceptibility, noncollinear ground States, towards the curie temperature. 1995. Lecture Notes from: Workshop on Condensed Matter Physics.

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