The Critical Field Curve in an Antiferromagnetic Crystal

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Abstract
Van Vleck's theoretical model for the antiferromagnetic state is extended to describe the effect of applying magnetic fields so large that the Zeeman splitting is of the same order of magnitude as the exchange interaction. The intensity of magnetization, entropy, and Gibbs free energy are calculated. It is concluded that, when the field is applied parallel to the direction of the antiferromagnetic chains, the antiferromagnetic configuration (that in which there are two sublattices in the crystal possessing unequal magnetizations) is energetically favored for all values of H and T at which it is mathematically permissible. The boundary of the antiferromagnetic solution is a certain critical field curve in the H, T plane, ending at the Curie temperature TC on the T axis, and at a critical field HC on the H axis, related to TC by μHC/kTC=1. The case of perpendicular field, and the influence of next‐to‐nearest neighbor interaction, are also discussed. Comparison is made between the predictions of the theory and the results of recent experiments by the writer on critical field phenomena in cobalt ammonium sulfate at temperatures below 1°K. This theoretical treatment of exchange antiferromagnetism is contrasted with the theory of Sauer and Temperley on dipole‐dipole interaction cooperative effects, which also predicts the existence of a critical curve. The possibility of observing critical field effects in other materials at much higher or much lower temperatures is also discussed.

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