Green Functions in the Theory of Antiferromagnetism

A Green function method has been used to treat the statistics of a general antiferromagnetic structure with arbitrary spin value per site and with Heisenberg exchange interactions between any or all pairs of spins in the system. The only restrictions placed upon the type of order are that there shall be a single direction of spin alignment and that each of the two ferromagnetic sublattices shall be translationally invariant. Expressions are given for the sublattice magnetization and N\'eel temperature and, as a particular application of the results, the N\'eel temperatures for certain face-centered cubic orders are calculated explicitly. The behavior of a general antiferromagnetic structure in the presence of an external magnetic field is also examined. Expressions are derived for the parallel and perpendicular magnetic susceptibilities, and are discussed in detail at low and high temperatures and also at the N\'eel point.