Mn$_2$Au is an important antiferromagnetic (AF) material for spintronics applications. Due to its very high Neel temperature of about 1500 K, some of the basic properties are difficult to explore, such as the AF susceptibility and the exchange constants. Experimental determination of these properties is further complicated in thin films by unavoidable presence of uncompensated and quasiloose spins on antisites and at interfaces. Using x-ray magnetic circular dichroism (XMCD), we have measured the spin and orbital contribution to the susceptibility in the direction perpendicular to the in-plane magnetic moments of a Mn$_2$Au(001) film and in fields up to 8 T. By performing these measurements at a low temperature of 7 K and at room temperature, we were able to separate the loose spin contribution from the susceptibility of AF coupled spins. The value of the AF exchange constant obtained with this method for a 10 nm thick Mn$_2$Au(001) film equals to (24 $pm$ 5) meV.
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