S,p-d exchange interaction

Ando, K. (2003) Magneto-optical studies of s, p-d exchange interactions in GaN Mn with room-temperature ferromagnetism. Applied Physics Letters, 82, 100. 

Here, denotes the energy of the orbital a (a = s, p, d) at atomic site i and hiao are the corresponding occupation-number operators. The are the hopping integrals describing electronic transitions between atoms i and j. The third term in Eq. (1) approximates the electron-electron interactions [30, 31]. The prime in the sum indicates that the terms with a = P and a = a are to be excluded. is the effective on-site interaction between electrons with spin a and a in the orbitals a and P of atom i. In Eq. (1) only the Coulomb and exchange intra-atomic integrals Uafi = otP /r 2 otP) and J fi = otP lr 2 Pot) are... 

The advantages of INDO over CNDO involve situations where the spin state and other aspects of electron spin are particularly important. For example, in the diatomic molecule NH, the last two electrons go into a degenerate p-orbital centered solely on the Nitrogen. Two well-defined spectroscopic states, S" and D, result. Since the p-orbital is strictly one-center, CNDO results in these two states having exactly the same energy. The INDO method correctly makes the triplet state lower in energy in association with the exchange interaction included in INDO. 

Litowski, J. R., Semchuk, P. D., Mant, C. T., and Hodges, R. S., Hydrophilic interaction/cation-exchange chromatography for the purification of synthetic peptides from closely related impurities Serine side-chain acetylated peptides, /. Peptide Res., 54, 1, 1999. 

The discussion of the preceding two sections relied on the presumption that localized (atomic-like) moments were present. However, valence s and p electrons are always best described by Bloch fimctions, while 4/electrons are localized and 5/are intermediate. Valence d electrons, depending on the intemuclear distance, are also intermediate -neither free nor atomic-Uke. In such cases, the dilemma is that the Heisenberg exchange interaction of Eq. 8.43, which is the physical basis for the Weiss field, is not strictly applicable in the case of delocalized electrons in metallic systems, in spite of the success of the Weiss model. 

M. A. Korotin, I. S. Elfimov, V. I. Anisimov, M. Troyer, and D. I. Khomskii (1998) Exchange interactions and magnetic properties of the layered vanadates CaV205, MgV205, CaVsOr, and CaV40g. Phys. Rev. Lett. 83, p. 1387... 

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