Self-consistent ab initio calculations, based on the density functional theory (DFT) approach and using the full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the MnAu layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn layers. Magnetic moment considered to lie along a axes are computed. The data obtained from the ab initio calculations are then used as input for the high temperature series expansions (HTSEs) calculation to compute other magnetic parameters.The exchange integrals between the magnetic atoms in the same layer and between the magnetic atoms in the bilayers adjacent are given by using mean field theory. The HTSEs of the magnetic susceptibility of MnAu antiferromagnetic spin-S through two model: Ising and XY layers consisting of l=2, 3, 4, 5, 6 and bulk (∞) interacting layers, are studied to sixth order series in β=1/kBT obtained for free-surface boundary conditions. The effects of finite size on critical-point behavior are studied by extrapolation of the high-temperature series. The Néel temperature TN(l) as a function of the number of l spin layers is obtained by HTSEs of the magnetic susceptibility series by using the Padé approximant method and by MFT theory. The critical exponent γ associated with the magnetic susceptibility is deduced. TN(l) for the l-layers are estimated from the divergence of the staggered susceptibility with an exponent for Ising model of γ(1)=2.96, and for XY model of γ(2)=2.82, which is consistent with the basic assumptions of scaling laws. Our estimates for the shift exponent of the Néel temperature for the two models are obtained.