Application of the Bethe-Weiss Method to Ferrimagnetism

The Bethe-Weiss theory of ferromagnetism is extended and applied to systems containing two nonequivalent sets of sites, designated by $A$ and $B$, for the magnetic atoms. Each $B$ atom has $n_a$ nearest $A$ neighbors and each $A$ atom has $n_b$ nearest $B$ neighbors. In the theoretical development, the following restrictions are imposed: the spin per atom is ½ and only nearest neighbor $A-B$ interactions are considered ($\alpha =\beta =0\mathrm{}$, in Néel's notation). The $A-B$ interaction $J$ may be either positive or negative, however, so that the sublattice magnetizations below the Curie temperature may be either parallel or antiparallel, respectively. Expressions are derived for the Curie temperature and for the susceptibility above the Curie temperature. If the two sublattices are made equivalent, our results for positive $J$ reduce to Weiss' equations for the ferromagnetic case and our results for negative $J$ reduce to Li's equations for the antiferromagnetic case.