Statistical Theory of Ferro- and Antiferromagnetism

Abstract

The method of the constant coupling approximation is applied to investigate the effect of the second nearest neighbor interactions. Ferromagnetic, antiferromagnetic, and screw spin arrangements are discussed as functions of a ratio of the magnitude of the nearest neighbor and the second nearest neighbor interactions. The critical value where the spin arrangement changes is obtained for the antiferromagnetic body centered cubic lattice. The condition for screw arrangement of spins to occur in rutile type structure is same as that in the simple molecular field approximation but the transition temperature is different due to the short range order effect. We further improve the constant coupling approximation by taking account of three spin or four spin system. One of the important results is two-dimensional triangular lattice cannot be ferromagnetic, on the contrary to the results obtained by the constant coupling approximation.