Statistical Models of Ferrimagnetism

We study the temperature dependence of some idealized ferrimagnetic crystals. The whole lattice of the crystal discussed here can be divided into two sublattices. These sublattices are generally inequivalent to each other, and any lattice points of one sublattice Lt is nearest-neighbouring to some number of lattice points belonging to another sublattice L2 and vice versa. Every lattice point of Lt is occupined by a cettain kind of magnetic atom At and that of L 2 by another kind of magnetic atom .A2. In this configuration there exists an antiferromagnetic coupling between every pair of .At and .A2 nearest-neighbouring each other. Aratoms and .A2-atoms have their own magnetic moment generally different from each other. We compute without introdudng any approximation the spontaneous magnetization of such ferritnagnetic Ising model by making use of the well-known Onsager's theorytl and especially of the solution of the temprature dependence of the spontaneous magnetization of the plane square lattice obtained by Yang.2l Our exact results on the magnetic behaviour of the idealized simple model are quite similar in character to those of the actual ferrimagnetic crystal computed by Neel in the Weiss approximation. I. Introduction 69 C. N. Yang 2 > succeeded to derive the exact value of the spontaneous magnetization of the ferromagnetic plane square lattice. By making use of his result we can evaluate the