Magnetic Orbitals and Mechanisms of Exchange I. Direct Exchange

Summary.

The problem of direct exchange is examined in the simplest cases (formal coupling of two electrons initially isolated and hydrogen molecule). Then we consider the general case of a solid characterized by weak overlaps between the atomic orbitals of first-nearest neighbours so that the involved electrons are quasi-localized. We recall the physical origin of spin-orbit coupling. Its influence on direct exchange allows one to revisit Hund’s rules and to express phenomenological Hamiltonians describing anisotropic couplings as well as the antisymmetrical Dzialoshinski-Moriya coupling.