Superexchange
This article may be too technical for most readers to understand.(October 2022) |
Superexchange or Kramers–Anderson superexchange interaction, is a prototypical indirect
Superexchange was theoretically proposed by
A set of semi-empirical rules were developed by John B. Goodenough and Junjiro Kanamori [ja] in the 1950s.[3][4][5] These rules, now referred to as the Goodenough–Kanamori rules, have proven highly successful in rationalizing the magnetic properties of a wide range of materials on a qualitative level. They are based on the symmetry relations and electron occupancy of the overlapping atomic orbitals (assuming the localized Heitler–London, or valence-bond, model is more representative of the chemical bonding than is the delocalized, or Hund–Mulliken–Bloch, model). Essentially, the Pauli exclusion principle dictates that between two magnetic ions with half-occupied orbitals, which couple through an intermediary non-magnetic ion (e.g. O2−), the superexchange will be strongly anti-ferromagnetic while the coupling between an ion with a filled orbital and one with a half-filled orbital will be ferromagnetic. The coupling between an ion with either a half-filled or filled orbital and one with a vacant orbital can be either antiferromagnetic or ferromagnetic, but generally favors ferromagnetic.[6] When multiple types of interactions are present simultaneously, the antiferromagnetic one is generally dominant, since it is independent of the intra-atomic exchange term.[7] For simple cases, the Goodenough–Kanamori rules readily allow the prediction of the net magnetic exchange expected for the coupling between ions. Complications begin to arise in various situations:
- when direct exchange and superexchange mechanisms compete with one another;
- when the cation–anion–cation bond angle deviates away from 180°;
- when the electron occupancy of the orbitals is non-static, or dynamical;
- and when spin–orbit coupling becomes important.
Manganese oxide
The p orbitals from oxygen and d orbitals from manganese can form a direct exchange. There is antiferromagnetic order because the singlet state is energetically favoured. This configuration allows a delocalization of the involved electrons due to a lowering of the kinetic energy.[citation needed]
Quantum-mechanical perturbation theory results in an antiferromagnetic interaction of the spins of neighboring Mn atoms with the energy operator (Hamiltonian)
where tMn,O is the so-called hopping energy between a Mn 3d and the oxygen p orbitals, while U is a so-called Hubbard energy for Mn. The expression is the
References
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- ISBN 9781119486831.
- PMID 11670054.
External links
- Erik Koch (2012). "Exchange Mechanisms" (PDF). In E. Pavarini; E. Koch; F. Anders; M. Jarrell (eds.). Correlated Electrons: From Models to Materials. Jülich. ISBN 978-3-89336-796-2.