Antiferromagnetism in a Layer Structure by Green Function Techniques

A Green function method has been used to investigate antiferromagnetic ordering in a layer structure. Taking a lattice with an in-plane ferromagnetic exchange interaction and a between-plane antiferromagnetic interaction, the method is used to consider a Hamiltonian which there is reason to believe is applicable to the `metamagnetic' salts CoCl₂ and NiCl₂ and which includes a uniaxial anisotropy. It is shown that the Green function techniques are well able to deal with Hamiltonians of this more complex type, and an expression is derived for the sublattice magnetization as a function of temperature. In particular, the antiferromagnetic transition temperature is calculated as a function of the exchange parameters. In the following paper these results are used to assist in the calculation of the actual exchange interactions which are present in CoCl₂ and NiCl₂.