Sensitivity of Curie temperature to single-ion anisotropy

Existing numerical estimates of the sensitivity of Heisenberg Curie temperature TC to crystal-field anisotropy have been obtained (primarily by Green's-function techniques) only for simple easy-axis anisotropy and low values of spin quantum number. In this paper we demonstrate the usefulness of the correlated-effective-field (CEF) theory in this context, showing that with modest computational effort numerical results for both easy-axis and easy-plane anisotropies can be obtained for any spin quantum number of physical relevance. Moreover, for cases where a comparison can be made with the existing literature, we show that the CEF results are more accurate than those obtainable from first-order equation-of-motion Green's-function techniques. Numerical calculations in the correlated-effective-field approximation are given for all three cubic lattices subject to the Hamiltonian $H={{Σ}}ᵢD{S}iz²{-}{{Σ}}ᵢ{{Σ}}ᵢJ{{{→}}{S}}ᵢ·{}{{{→}}{S}}ⱼ$, where $J$ is a nearest-neighbor exchange parameter. Results are given for the complete range ${-}{∞}{≤}D/J{≤}{∞}$ (where negative values refer to an easy-axis situation and positive values to a preferred easy plane) and for spin quantum numbers $S=1 to 7/2$ inclusive. For integer spin values and an easy-plane anisotropy we encounter the problem of singlet-ground-state ferromagnetism for which ${T}C{→}0$ at a finite value of $D/J$.