Exchange Interactions

1 9.1 Many-Electron Wave Functions

The existence of ordered states at high temperatures cannot be explained by classical physics using the dipolar magnetic interaction, as this interaction is at least 100 times weaker than required. Quantum mechanics has to be invoked to understand the origin of the exchange interactions that give rise to them.

The exchange interaction in a solid has the same quantum origin as the interaction between electrons within one atom (chap. 7): the correlations between two electrons lead to a difference in energy between configurations in which the spins are parallel and antiparallel. This originates in the Pauli principle, which stipulates that two electrons cannot occupy the same quantum state. One of the consequences of this principle is that many-electron wavefunctions must be antisymmetric with respect to the exchange of two electrons. We will treat here the case of a two-electron wave function ψ(1, 2), where 1 and 2 describe both the spatial coordinates...