Ferromagnetic Curie Temperature in Cubic Lattices with Next-Nearest-Neighbor Interaction

The Curie temperature for a Heisenberg ferromagnet with nearest-neighbor interaction $J_1$ and next-nearest-neighbor interaction $J_2$ is calculated by a Green's-function technique. The $\frac{J_2}{J_1}$ dependence is found to be significantly different from that given by molecular field theory. The Curie temperature approaches zero when $\frac{J_2}{J_1}\to -1\mathrm{}$ in a face-centered cubic magnetic lattice, and when $\frac{J_2}{J_1}\to 0.6799$ in a body-centered cubic lattice. The face-centered cubic magnetic lattice is relevant to the chalcogenides of europium.