Antiferromagnetism in the Face-Centered Cubic Lattice. I. The Random-Phase Green's Function Approximation

Abstract

The random-phase Green's function approximation is used to derive equations for zero-field magnetic susceptibility and two-spin correlation functions which are valid, at temperatures above the Curie or N\'eel point, for all ferromagnets and antiferromagnets which can be described by any isotropic Heisenberg Hamiltonian. At high temperatures, these expressions are also expanded as series in inverse powers of temperature. Detailed numerical calculations are carried out for the face-centered-cubic lattice with antiferromagnetic nearest- and next-nearest-neighbor exchange parameters ${J}_{1}$ and ${J}_{2}$. Susceptibility results are compared with molecular-field estimates at temperatures near the N\'eel point, and with the known terms of the exact power-series expansion at high temperatures. The spin correlations are computed for the first four shells of nearest neighbors. Finally, the sublattice-magnetization curves at temperatures below the N\'eel point are computed, in the random-phase Green's function approximation, for the type-2 antiferromagnetic order of the face-centered-cubic lattice. The curve shapes are found to be very insensitive to $\frac{{J}_{2}}{{J}_{1}}$ and approximate closely the shape of the molecular-field Brillouin-function curves. The significance of this result in connection with the biquadratic-exchange question in MnO is discussed in detail in the following paper by Lines and Jones.