Modified Callen Decoupling in the Green's-Function Theory of the Heisenberg Ferromagnet with Application to the Europium Chalcogenides

Abstract

We present a first-order Green's-function analysis of the Heisenberg ferromagnet based on a decoupling scheme which produces excellent agreement with exact results. We believe this to be the most reliable simple method available for the calculation of Curie temperatures or of other statistical properties. Explicit polynomial expressions for the Curie temperatures of Heisenberg ferromagnets with nearest-neighbor and next-nearest-neighbor exchange are given for the three cubic lattices. The theory predicts a $k$-dependent renormalization of the magnon energies for non-nearest-neighbor models. In the case of nearest-neighbor and next-nearest-neighbor exchange, it suggests an antiferromagnetic-ferromagnetic transition for a certain narrow range of the ratio of the exchange constants. The method is illustrated by application to the europium chalcogenides. It is shown that the empirical paramagnetic and ferromagnetic Curie temperatures are inconsistent with the assumption of first- and second-neighbor exchange only. The inclusion of magnetic dipole interactions removes the contradiction between theory and experiment and allows the determination of the ratio $\frac{J_2}{J_1}$. This ratio is found to be about 0.7 for EuO and -0.1 for EuS.