Ferromagnetic Curie Temperatures of the Heisenberg Model with Next-Nearest-Neighbor Interactions

Abstract

The Curie temperatures of the Heisenberg ferromagnet with nearest-neighbor interactions $-2\mathrm{}{J}_1{\mathrm{S}}_i·{\mathrm{S}}_j$ and next-nearest-neighbor interactions $-2\mathrm{}{J}_2{\mathrm{S}}_k·{\mathrm{S}}_l$ are calculated for the bcc, sc, and fcc lattices on the basis of exact high-temperatures series expansions of the zero-field susceptibility ${\chi }_0$. The dependence of $T_c(\alpha ,S)$ ($\alpha =\frac{J_2}{J_1}$) on $\alpha$ is examined, and it is found that $\frac{T_c\left(\alpha \right)}{T_c\mathrm{}\left(0\right)\mathrm{}}$ is well represented by $\frac{T_c\left(\alpha \right)}{T_c\mathrm{}\left(0\right)\mathrm{}}=1+m_1\mathrm{}\left(S\right)\mathrm{}\alpha$ for values of $\alpha$ between 0 and 1. The Curie points are also examined for $\alpha <0\mathrm{}$, where $J_2$ is antiferromagnetic in sign.