Abstract
The magnetic interaction between local magnetic moments in an insulator or a semiconductor host is theoretically studied. For a dilute concentration of magnetic ions, the dominant mechanism for magnetic interaction could be the exchange polarization of the valence-band electrons of the host lattice. Its properties are investigated with two models, one representing insulator and the other semiconductor energy bands. As anticipated, the polarization effect in an insulator is found to be unimportant. On the other hand, for narrow-gap semiconductors with small electron and hole effective masses, the range of the magnetic interaction can be relatively long, extending over several lattice constants. The sign of the interaction is ferromagnetic for semiconductors with a direct energy gap, but may oscillate with interspin distances for an indirect-gap semiconductor.
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