Application of the Cluster-Variation Method to the Uniaxial Antiferromagnet FeF2

Abstract

Low-temperature nuclear-magnetic-resonance measurements together with antiferromagnetic-resonance observations in Fe${\mathrm{F}}_{2}$ furnish a reliable set of values of first- and second-neighbor exchange integrals as well as a uniaxial anisotropy energy. It is the purpose of this paper to see to what extent one can understand the high-temperature properties, such as the N\'eel temperature and the anisotropic susceptibilities, in terms of the known parameters obtained at low temperatures. To achieve this, the cluster-variation method is used, taking into account spin correlations between the nearest and next-nearest neighbors. The anisotropy energy in Fe${\mathrm{F}}_{2}$ is larger than the exchange integrals, and consequently cannot be treated as a small perturbation. After explicit diagonalization of effective two-spin Hamiltonians, we calculate the N\'eel temperature and the anisotropic susceptibilities for spin $S=2$. The effect of the anisotropy energy on the N\'eel temperature is shown to be much less pronounced in the cluster approximation than in the Weiss molecular-field approximation. In the neighborhood of the critical temperature, we find that the anisotropic susceptibilities are considerably improved in the cluster approach as compared to the Weiss-theory predictions.