Origins of Magnetic Interactions

There are several origins for the interactions between the magnetic moments that lead to a long-range ordering of the unpaired spins.^1,2 The Pauli exclusion principle requires that no two electrons can have the same quantum numbers. When acting together with the electrostatic repulsion between like charges, unpaired electrons that are in orthogonal orbitals (orbitals with different orbital quantum numbers) in the same space have parallel spin alignment. Hund’s rule is the application of this guideline for atoms and molecules. An example of the application of Hund’s rule for intramolecular highspin species is Mn^II, which has five unpaired electrons that align to give spin S = 5/2 in the 3d level. Similarly, O₂ molecules form S = 1 states (triplet oxygen). The overlap of the wave functions of electrons centered on different atoms, ions, or molecules leads to an exchange interaction, which also is based on the Pauli exclusion principle and the Coulomb repulsion of like charges. Direct exchange occurs when there is direct overlap of the wave functions of electrons associated with nearest-neighbor sites that contain spin. Often the sites with unpaired electrons are too far apart for there to be sufficient direct overlap of the unpaired electron wave functions for substantial direct exchange. Super-exchange occurs when there is an indirect overlap of nearby sites that have unpaired spin by coupling through energy levels associated with intermediate sites that are without spin. RKKY (Ruderman-Kittel-Kasuya-Yosida) exchange couples localized magnetic spin through delocalized metallic electrons. In some situations, the magnitude of these exchange interactions may be estimated through configuration interaction computations. Another means of coupling among spins is through space interaction by means of dipole magnetic fields associated with the magnetic moment of each spin. Although generally a very weak effect, in some organic-based magnets this dipole–dipole interaction can dominate the magnetic phenomena.³

1. J.S. Miller and A.J. Epstein, Journal of the American Chemical Society 109, 3850 (1987).
2. J.S. Miller, A.J. Epstein, and W.M. Reiff, Science 240, 40 (1988).
3. C.M. Wynn, M. Girtu, W.B. Brinkerhoff, K.-I. Sugiura, J.S. Miller, and A.J. Epstein, Chemistry of Materials 9, 2156 (1997).

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