It is well known that for an AF sample, Tn is propotional to (z .Jexc. S) where z, Jexc and S are respectivley the coordination number of the magnetic element, the exchange constant coonecting it to its neighbours and its spin value.
When the size is reduced, one of (or all) these parameters is (are) equally reduced, therefore, the Tn becomes lower!
Antiferromagnetic is a materials including many domains where the spin of domains are orientaed in different directions resulting in a small net magnetization in the absent of external field (like iron oxide). This spin domain orientation is due to competition between the exchange coupling. If one decreases the size such a way it gets close to a few domains, the competition increase resulting in enhacement of thermal fluctuations. These thermal fluctuations reduce the stability of the magnetization, consequently, reduction of the Neel temperature.
iron oxide nanoparticles are the best example for this phenomena, which due to high thermal fluctuations, their net magnetization is almost zero at room temperature, and they called superparamagnet.