First-Order Green's-Function Theory of the Heisenberg Ferromagnet

Calculation of the magnetization, specific heat, and susceptibility of a Heisenberg ferromagnet with simple, face-centered, and body-centered cubic lattices have been made by terminating the first-order Green's-function equation in a manner similar to that suggested by Callen, who used a termination function $\alpha =\frac{〈S^z〉}{2S^2}$, based on certain physical criteria. We are led to the value $\alpha =\frac{{〈S^z〉}^3}{2S^4}$. For $\alpha =\frac{{〈S^z〉}^x}{2S^{x+1\mathrm{}}}$ there is no Curie point if $x<\mathrm{}1\mathrm{}$, and the magnetization $M$ is double valued if $1<x<\mathrm{}3\mathrm{}$. The value $x=3\mathrm{}$ was chosen because it leads to the best agreement with high-temperature solutions for the Heisenberg ferromagnet and experimental data for europium oxide and nickel. Computer results for general temperatures as well as series expansions in the neighborhood of the Curie temperature are presented and compared with experimental data for nickel, iron, and europium oxide. It appears that the general magnetic behavior of these materials is explained by the Heisenberg model.