Magnetic and Thermal Properties of Dysprosium Aluminum Garnet. II. Characteristic Parameters of an Ising Antiferromagnet

Abstract

Extensive earlier work has indicated that dysprosium aluminum garnet (DAG) in a magnetic field along a (111) axis should approximate to a two-sublattice Ising-model antiferromagnet, and in this paper we examine this correspondence critically. Quantitative estimates are derived for the differences between the ideal model and the real material, and it is shown that they are in fact very small and that appropriate corrections can be applied to allow for most of the deviations. General expressions based on the Ising model are derived for the magnetization, differential susceptibility, and specific heat in field and temperature regions where exact asymptotic expansions are valid, and these are fitted to available experimental data on DAG. The results of the analysis can be expressed in terms of two sets of parameters which describe, respectively, the single-ion properties and combinations of the spin-spin interactions. The relation of these parameters to the microscopic Hamiltonian is deferred to a later paper, but a number of empirical cross checks indicate excellent consistency in the results. In addition, a number of parameters describing the cooperative behavior are extracted from the experimental data and there is a discussion of some of the general problems of analyzing critical-point data. The significance of most of these parameters must await further theoretical work on Ising models with competing and long-range interactions.