Statistical Models of Ferrimagnetism

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Abstract
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 L1 is nearest-neighbouring to some number of lattice points belonging to another sublattice L2 and vice versa. Every lattice point of L1 is occupined by a certain kind of magnetic atom A1 and that of L2 by another kind of magnetic atom A2. In this configuration there exists an antiferromagnetic coupling between every pair of A1 and A2 nearest-neighbouring each other. A1-atoms and A2-atoms have their own magnetic moment generally different from each other. We compute without introducing any approximation the spontaneous magnetization of such ferrimagnetic Ising model by making use of the well-known Onsager’s theory and especially of the solution of the temperature dependence of the spontaneous magnetization of the plane square lattice obtained by Yang. 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 Néel in the Weiss approximation.

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