Ferromagnetic and Antiferromagnetic Curie Temperatures

Abstract

The methods of calculating Curie temperatures used by Opechowski and Weiss are extended to higher spin values. Using the former, Curie temperatures are found for the face-centered, body-centered, and simple cubic and the hexagonal and quadratic layer lattices for spin ½ to 3. Weiss' method is applied to the body-centered and simple cubics for spin ½ to 2 and to the quadratic layer lattice for spin ½ and 1. Numerical results show good agreement between the two methods for three-dimensional ferromagnetic lattices. However, the Opechowski method fails to locate the antiferromagnetic transition and predicts a transition for the two-dimensional lattices while the Weiss method does not. A classical-spin approximation is investigated and is found to give Curie temperatures within a few percent of the quantum-mechanical results for spin 1 or greater.