Molecular Field Treatment of Ferromagnetism and Antiferromagnetism

Abstract

A modified Weiss treatment of magnetism in crystals which considers both first and second nearest neighbor interactions with all four combinations of signs has been carried out. The usual results for ferromagnetism are obtained for both interactions positive. For the other cases, various types of magnetic ordering below the Curie temperature are predicted, the exact kind depending on the signs and magnitudes of ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$, the Weiss field coefficients for first and second nearest neighbor interactions, respectively. Explicit results are given for the kind of ordering as functions of $\frac{\ensuremath{\theta}}{{T}_{c}}$ for bcc and fcc lattices. Expressions are derived for the susceptibility of an antiferromagnet above and below the Curie temperature, the latter calculation being given for only a single axis of spontaneous magnetization only. The theory gives a good qualitative description of the behavior of an antiferromagnet for all temperatures, although some of the detailed results are in disagreement with experiment.