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The Pair Approximation method is applied to the antiferromagnetic Heisenberg-Ising spin-1/2 bilayer with a simple cubic crystalline structure. The method allows for self-consistent calculations of thermodynamic quantities, based on the determination of Gibbs free-energy. In the paper the phase diagrams and planar magnetizations are calculated for the system in question. Special attention is paid to the case of magnetically non-equivalent planes, one of which is additionally randomly diluted. The occurrence of a compensation phenomenon is found and the compensation temperature is discussed for such a system. The characteristic concentration of magnetic atoms p , below which the compensation phenomenon vanishes, is examined as a function of the Hamiltonian parameters.

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