Magnetic properties of a bilayer system with anisotropic Heisenberg interaction

A magnetic bilayer system with spin S=1/2, the coordination number z=5 and anisotropic Heisenberg ferromagnetic interactions, is studied by the Cluster Variational Method in the Pair Approximation. Within this approximation the self-consistent thermodynamic description based on Gibbs free-energy is presented. All relevant thermodynamic properties such as the spontaneous magnetization, pair correlation function, entropy, isothermal susceptibility and magnetic specific heat are calculated. In particular, the analytical expression for the phase transition temperature vs. anisotropy is obtained. The influence of anisotropy on all the thermal characteristics is presented in the figures and discussed.