Goodenough-Kanamori rule

Dr. John B. Goodenough, Mechanical Engineering, University of Texas at Austin, USA

The Goodenough-Kanamori rule, first formulated by Goodenough in 1955 (Goodenough 1958; Goodenough 1995) and subsequently provided more rigorous mathematical underpinning by Kanamori (1959), applies to interatomic spin-spin interactions between two atoms, each carrying a net spin, that are mediated by virtual electron transfers between the atoms (superexchange)and/or between a shared anion and the two atoms (semicovalent exchange). A virtual electron transfer occurs between overlapping orbitals of electronic states that are separated by an energy ∆E; and a spin-spin interaction mediated by an electron transfer, virtual (or real as in ferromagneticdouble exchange), is a kinetic exchange. Orthogonal orbitals do not overlap, so there is no electron transfer and the exchange interaction between spins in orthogonal orbitals is a ferromagnetic potential exchange; it is responsible for the Hund highest-spin rule for the free atom or ion.

The Goodenough-Kanamori rule states that superexchange interactions are antiferromagnetic where the virtual electron transfer is between overlapping orbitals that are each half-filled, but they are ferromagnetic where the virtual electron transfer is from a half-filled to an empty orbital or from a filled to a half-filled orbital. The Goodenough-Kanamori rule is the same for both superexchange and semicovalent exchange.

Where the two cation orbitals overlap the same p orbital of a shared anion as in a 180° cation-anion-cation bridge, it is customary to introduce the virtual electron transfer from the shared anion to the interacting cations first as the covalent component of the cation orbital. The net spin of the cation orbital is not changed by addition of a covalent component, but the covalent component extends the cation wavefunction out over the anions to give an orbital overlap for the superexchange electron transfer. However, a pure semicovalent antiferromagnetic exchange can occur between two empty orbitals provided each cation carries a net spin and the empty orbitals share the same anion p orbital.

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