Constant coupling approximation for antiferromagnetism

Abstract

Synopsis The method developed in a previous paper for the investigation of the statistical properties of a Heisenberg ferromagnetic spin system is extended to an antiferromagnetic spin system with a two-sublattice structure and an isotropic coupling between nearest neighbouring spins. Both the case of a parallel and of a perpendicular external field are discussed. The partition function of the spin system is expressed in terms of the effective Hamiltonian He of a pair of nearest neighbouring spins. In the parallel case, He contains, in addition to the isotropic and anisotropic coupling terms and the effective field term occurring also in the ferromagnetic case, a term representing a staggered effective field which has the same magnitude but opposite direction for the two spins of the spin pair. In the perpendicular case two additional anisotropic coupling terms appear, so that He contains six terms in this case. By introducing specific assumptions about the values of the coupling parameters occurring in He, the molecular field and the constant coupling approximation are obtained. The thermodynamic properties of the spin system, and in particular the critical data, are calculated on the basis of the constant coupling approximation, and numerical results are given for the simple cubic and body-centered cubic lattice. In contradistinction to the ferromagnetic case the constant coupling approximation for an antiferromagnetic spin system leads to the appearance of an anti-Curie point, so that in this case the constant coupling approximation is reliable only above and in the immediate vicinity of the Curie point.