  We study the exchange interactions in half-metallic Heusler alloys using
first-principles calculations in conjunction with the frozen-magnon
approximation. The Curie temperature is estimated within both mean-field (MF)
and random-phase-approximation (RPA) approaches. For the half-Heusler alloys
NiMnSb and CoMnSb the dominant interaction is between the nearest Mn atoms. In
this case the MF and RPA estimations differ strongly. The RPA approach provides
better agreement with experiment. The exchange interactions are more complex in
the case of full-Heusler alloys Co$_2$MnSi and Co$_2$CrAl where the dominant
effects are the inter-sublattice interactions between the Mn(Cr) and Co atoms
and between Co atoms at different sublattices. For these compounds we find that
both MF and RPA give very close values of the Curie temperature slightly
underestimating experimental quantities. We study the influence of the lattice
compression on the magnetic properties. The temperature dependence of the
magnetization is calculated using the RPA method within both quantum mechanical
and classical approaches.
