POTENTIAL AND KINETIC EXCHANGE INTERACTIONS
It is well known that the direct dipole-dipole interaction between magnetic moments is much too weak to explain the typical magnitudes of spin dependent interactions between electrons. It is convenient to single out two spin exchange mechanisms accounting for the magnetic properties of solids, discussed in detail in the context of in a number of reviews, particularly in the context of diluted magnetic semiconductors [1–3].
The driving force behind the potential exchange is the Pauli exclusion principle which precludes two electrons with the same spin to appear simultaneously in the same location. Accordingly, the magnitude of the Coulomb potential energy is lower for such a pair, comparing to the case of two electrons with anti parallel spins. The potential exchange is ferromagnetic and accounts for the Hund’s rule, intra-atomic s-d exchange interaction, and exchange interactions between spins of carriers occupying the same band.
The kinetic exchange occurs between two electrons residing at different sites. One of these electrons can visit the site occupied by the other provided that its spin has the orientation matching a relevant empty level. Such a quantum hopping, or in other words hybridisation of states, enlarges the localisation radius and, hence, lowers the electron kinetic energy. The kinetic exchange leads usually, but not always, to an antiferromagnetic interaction between the spin pair in question. In compounds containing transition metals, the p-d kinetic exchange couples the spins of carriers occupying anion p-like bands with the spins of electrons residing in open d shells of magnetic cations. Typically, in the considered TM compounds the kinetic exchange – if symmetry allowed – is much stronger than the potential exchange. The opposite situation occurs in the case of rare earth doped materials, where the spd-f hybridisation is usually weak.
The driving force behind the potential exchange is the Pauli exclusion principle which precludes two electrons with the same spin to appear simultaneously in the same location. Accordingly, the magnitude of the Coulomb potential energy is lower for such a pair, comparing to the case of two electrons with anti parallel spins. The potential exchange is ferromagnetic and accounts for the Hund’s rule, intra-atomic s-d exchange interaction, and exchange interactions between spins of carriers occupying the same band.
The kinetic exchange occurs between two electrons residing at different sites. One of these electrons can visit the site occupied by the other provided that its spin has the orientation matching a relevant empty level. Such a quantum hopping, or in other words hybridisation of states, enlarges the localisation radius and, hence, lowers the electron kinetic energy. The kinetic exchange leads usually, but not always, to an antiferromagnetic interaction between the spin pair in question. In compounds containing transition metals, the p-d kinetic exchange couples the spins of carriers occupying anion p-like bands with the spins of electrons residing in open d shells of magnetic cations. Typically, in the considered TM compounds the kinetic exchange – if symmetry allowed – is much stronger than the potential exchange. The opposite situation occurs in the case of rare earth doped materials, where the spd-f hybridisation is usually weak.
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