A tutorial lecture on magnetic exchange and order

Orateur : Steve BLUNDELL

The exchange interaction between magnetic moments arises from the effects of the Coulomb interaction (which corresponds to a large energy) and the exchange symmetry of ide ntical particles. I will consider particular incarnations of the exchange interactions : direct exchange, indirect exchange (superexchange and RKKY), and anisotropic exchange. The exchange interaction leads to the presence of magnetic order, and I will consider this in both localized and itinerant systems. In the latter case, the magnetization of the electron gas will be treated, including a discussion of Pauli susceptibility and the Stoner criterion. These ideas will be illustrated using the model system of a triangle of spins and I will solve the problem exactly, revealing the key symmetries. The Heisenberg model possesses rotational symmetry because the interaction Si.Sj has no preferred direction. However, magnetic moments in solids are sensitive the presence of the lattice. One consequence of this is magnetocrystalline anisotropy, which has an effect on the thickness of domain walls.

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