Band model exchange interaction

As already mentioned, the phenomenon of magnetic circular dichroism in photoemission originates from spin-orbit and exchange interactions in combination with the dipole selection rules. In the atomic model picture, the splitting of the 3p level (into sublevels with orbital momentum m) is caused by the electrostatic interaction of the core level with the magnetically polarized valence electrons [57]. The observed intensity differences and the respective asymmetry values in photoemission from the Fe 3p levels are small (typically 3%) compared to the large MCDAD and MLDAD asymmetries (up to about 12%) observed in valence band photoemission [27]. 

In the mixed-valent compound SmB6 the exchange interactions between the impurity and the host 4f electrons contribute the main part to the g-shift. The ESR linewidths show a remarkable temperature dependence. As the temperature increases the linewidth of the Gd " -absorption line remains nearly constant below 4K, increases rapidly between 4 and 10 K, followed by a more gradual increase above lOK. This broadening is less developed in the case of Eu. This temperature behavior of the linewidths can be explained by a band-structure model of Kasuya (1976), assuming that the localized 4f electrons and the delocalized 5d orbitals are strongly mixed and form a hybridization gap. 

In the spin-fluctuation model the tendency towards magnetism is determined by the strength of the effective exchange interaction between electrons in a narrow band. The presence of this exchange interaction leads to an enhanced susceptibility over the Pauli value, predicted for a free-electron gas. At T = 0 K this enhaneement factor, known as the Stoner factor, is given by... 

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