  We present systematic theoretical investigations to explore the microscopic
mechanisms leading to the formation of antiferromagnetism in Ru2MnZ (Z=
Sn,Sb,Ge,Si) full Heusler alloys. Our study is based on first-principles
calculations of inter-atomic Mn-Mn exchange interactions to set up a suitable
Heisenberg spin-model and on subsequent Monte-Carlo simulations of the magnetic
properties at finite temperature. The exchange interactions are derived from
the paramagnetic state, while a realistic account of long-range chemical
disorder is made in the framework of the Coherent Potential Approximation. We
find that in case of the highly ordered alloys (Z=Sn and Sb) the exchange
interactions derived from the perfectly ordered L21 structure lead to N\'eel
temperatures in excellent agreement with the experiments, whereas, in
particular, in case of Si the consideration of chemical disorder is essential
to reproduce the experimental N\'eel temperatures. Our numerical results
suggest that improving a heat treatment of the samples to suppress the
intermixing between the Mn and Si atoms, the N\'eel temperature of the Si-based
alloys can potentially be increased by more than 30%. Furthermore, we show that
in strongly disordered Ru2MnSi alloys a distinct change in the
antiferromagnetic ordering occurs.
